What is Logic?
I have my own ideas but I figured I'd open with the simple question: what is logic? (there is more on this than "what is computation," but a lot of it does not seem to address the big questions)
It seems to me like this question often produces three types of responses:
1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted.
The most common answer today is to define logic in terms of formal systems. This is certainly an answer than can be consistent, but it is also a less than satisfactory answer in many respects.
When we say: "you're acting illogically? "or "that doesn't follow logically," we often mean something different from: "you are not acting according to a formal system," or "I am not aware of any formal system where the inference you are making works." Rather, we tend to be criticizing someone for failing to think in a way that is sufficiently rational.. This gets at pre-20th century definitions of logic, where...
Of course, sometimes when we talk about logic we want to refer to the logic of the external world, not just thought. For example, we can talk about an organelle being shaped by "the logic of natural selection." In this case, "the logic of natural selection," might be described by numerous formal systems, but it is not the formal description itself we are talking about, but rather the way the series of causal events that appears to conform to the more general logic. That is, the formal system is itself merely an encoding of the principle we want to refer to.
This is most obvious when we talk about "the laws of physics," and causality. Here we often talk about a sort of logic that guides how physical states evolve over time, i.e., that what comes before implies what comes after. This principle, through which one physical state defines what future states can look like, is obviously distinct from the sorts of formal causal logic systems we develop, "do calculus," etc.
But here is the big question: do we think that these are all different things? That we use the same word out of a sort of confusion? Or is there actually a similarity between these types of "logic?"
The move towards the formalism-based answers was in part born out the failure, and now seeming impossibility, of discovering a "one true logic." But this brings up the question, "does the absence of a 'one true logic' necessitate deflating logic into formalism? Or can we meaningfully speak of things like the logic of cause? And if we can meaningfully speak of things, what is the relationship between the formalism and the referents?
For my part, I don't see how we get to building a definition like 1 without thought having some sort of internal logic (2). But from whence this structure of thought? I feel like we have to look at things like "the logic of natural selection," bringing us to 3.
It seems to me like this question often produces three types of responses:
1. Logic is a set of formal systems; it is defined by the formalism.
2(a). Logic is a description of the ways we make good inferences and determine truth, or at least approximate truth pragmatically.
2.(b). Logic is a general description of the features or laws of thought. (This is more general than 2(a).
3. Logic is a principle at work in the world, its overall order. Stoic Logos, although perhaps disenchanted.
The most common answer today is to define logic in terms of formal systems. This is certainly an answer than can be consistent, but it is also a less than satisfactory answer in many respects.
When we say: "you're acting illogically? "or "that doesn't follow logically," we often mean something different from: "you are not acting according to a formal system," or "I am not aware of any formal system where the inference you are making works." Rather, we tend to be criticizing someone for failing to think in a way that is sufficiently rational.. This gets at pre-20th century definitions of logic, where...
[logic] is the study of the most general features of thoughts or judgments, or the form of thoughts or judgments. Logic thus understood will for example be concerned with the occurrence of subject and predicate structure that many judgments exhibit, and with other such general features of judgments. It will mostly be concerned with thoughts, and not directly with linguistic representations, though, of course, a proponent of this conception can claim that there is a very close connection between them.
Of course, sometimes when we talk about logic we want to refer to the logic of the external world, not just thought. For example, we can talk about an organelle being shaped by "the logic of natural selection." In this case, "the logic of natural selection," might be described by numerous formal systems, but it is not the formal description itself we are talking about, but rather the way the series of causal events that appears to conform to the more general logic. That is, the formal system is itself merely an encoding of the principle we want to refer to.
This is most obvious when we talk about "the laws of physics," and causality. Here we often talk about a sort of logic that guides how physical states evolve over time, i.e., that what comes before implies what comes after. This principle, through which one physical state defines what future states can look like, is obviously distinct from the sorts of formal causal logic systems we develop, "do calculus," etc.
But here is the big question: do we think that these are all different things? That we use the same word out of a sort of confusion? Or is there actually a similarity between these types of "logic?"
The move towards the formalism-based answers was in part born out the failure, and now seeming impossibility, of discovering a "one true logic." But this brings up the question, "does the absence of a 'one true logic' necessitate deflating logic into formalism? Or can we meaningfully speak of things like the logic of cause? And if we can meaningfully speak of things, what is the relationship between the formalism and the referents?
For my part, I don't see how we get to building a definition like 1 without thought having some sort of internal logic (2). But from whence this structure of thought? I feel like we have to look at things like "the logic of natural selection," bringing us to 3.
Comments (89)
Boring answer but I think the possibility you alluded to is correct, the word has separate definitions and the meaning depends on the context.
A consistent definition that works within all the different contexts will poorly represent what the word means in each of those different contexts.
I posted a thread on stackexchange about the relationship of logic and causation. It turns out they’re different topics. Logic is the relationship between propositions whereas physical causation involves many factors. You can find the discussion here. The very first response notes that the ‘because’ of logical necessity is not the same as the ‘because’ of causation. And a lot hangs on this distinction, it turns out.
Another point is, apropos of the other thread on Schopenhauer - his ‘fourfold root of sufficient reason’ also differentiates between the logic of [s]being[/s] knowing (which approximates to what we are calling logic) and the logic of becoming (which approximates to physical causation.)
I personally am very drawn to your (3) - that there is a logic in order of things, as the Greek intuition has it. I think the issue with that is that it seems to contravene the naturalist assumption of there being no telos. But also notice that related to this concern, the whole concept of ‘natural law’ is nowadays called into question. See for example There are no laws of Physics. I *think* this mirrors a confusion, but I’ll leave it there for now.
I think you didn't clarify much what you mean by "formalism". As a starter, I take "formalism" to be broadly speaking the symbolic codification of a set of logic rules. If there are one or many sets of logic rules, this is a distinct issue.
"Formalism" to me is required to standardize a given set of rules and remove ambiguities of ordinary language for certain syntactic terms (e.g. we can attributing different meanings to “to be“, “if…,then…”, “not”, “or” or “all” in logic).
Said that, I find the expression "one true logic" nonsensical. One may be willing to count "logic" by counting the number of "set of ‘logic’ rules" we want to distinguish (for example in geometry different set of postulates can different geometries the same can go for logic see e.g. non-classical logic). But there is no way for me to make sense of “true” as applied to “logic” since the notion of “truth” is built in the “logic” rules themselves, in other words the meaning of “truth” is determined by “logic rules” too. One might be tempted to see “logic rules” as a description of how things are, but that’s a categoric confusion to me: “logic rules“ are rules, not description of facts. To me.
Quoting Count Timothy von Icarus
Broadly speaking yes, if you mean by "logic of cause" the set of semantic rules that govern the notion of “cause”. However, more strictly speaking, "logic" refers to rules governing synthatic terms (like propositional operators, quantifiers, modal operators, etc.)
Quoting Count Timothy von Icarus
Formalism helps us discriminate better different ways allowing us to meaningfully speak of things according to various sets of “logic” rules.
Quoting Count Timothy von Icarus
What does one mean by “being sufficiently rational”? To me, appeal to “rationality” is nothing other than an appeal to the set of rules that must be satisfied in order to make things intelligible to somebody. And this may certainly include logic rules, too.
Quoting Count Timothy von Icarus
Following what I wrote, I disagree with all 3 responses to "what is logic?" partially or totally:
1. Logic is not defined by formalism. Formalism is a way to express a set of logic rules.
2. Logic is not a description of the ways we make good inference or laws of thought, if this is taken to be an empirical enterprise like a scientific theory.
3. Logic refers to rules that make the world intelligible to us.
That's probably fair. But it seems like there is a sort of general principle, perhaps one of necessity or one of "sufficient reason," that undergirds the other. I'd say "Logos" would be a good term, but it has mystical connotations too.
My abbreviated answer to "what is Logic" might be : Mathematics with Words. Note the connection of Greek Logos with the notion of Words as encapsulated ideas about the world and how it works. The values of Math are expressed in abstract numbers (quantity), while the values of Logic are expressed in terms of statistical probabilities (oughts).
Mathematics is the formalism of the physical structure (interconnections) and natural laws (relationships) of the material world. Just as mathematical Physics allows humans to predict the outcome of physical processes, mental Logic allows us to infer (educated guess) a future state of human metaphysical processes, such as Politics. Unfortunately, as with the order-within-chaos of weather patterns, human freewill makes even logical forecasts (e.g. inferences by think tanks) of political outcomes dicey. :smile:
Excellent point. Causation and logic are different areas of philosophy, for sure. That logic and causation are completely different things I think is open to question.
Where do most people turn for their best, most fundamental theories on physical causation? (And does it even make sense to talk of non-physical causation?) They go to physics. And in modern physics, the idea that the universe is computable, and behaves like a computer is extremely popular (Landauer, Lloyd, Deutsch, Davies, Tegmark, etc.).
But then what is computation, how is it defined? Partly in terms of logical operators, stepwise symbolic manipulations that occur according to rules such that prior states of some system entail the system's future states (or entail either a range of states in quantum indeterminacy or, in a multiverse, many existing states). This is how Leibnitz saw computation in his pronouncement that one day all disagreements could be settled through such symbolic manipulations-- "let us calculate!"
You can't separate the definitions of computable functions and computation from logic, and it increasingly seems hard to separate computation, or a process that is computation-like (perhaps involving real numbers?) from physics. But then this makes logic deeply intertwined in how we understand cause, and moreover, what we think cause actually is, sans our experience of it.
We see cause coming together with logic from another angle with categorical quantum mechanics and quantum logic as well.
So, IMO, the separation of the philosophy of causation and logic has more to do with the history of philosophy than the two being fully unrelated concepts. But this is exactly what frustrates me in the literature. There is a move to treat logic as divorced from reality to make it manageable, but then logic is used by other disciplines to justify statements about reality.
Well, at some point you have to make the connection in the other direction. As natural creatures, the products of natural selection, there should be some explanation of where our sense of logic comes from and why we can use it to describe causality so well, and why we can use it to create science and technology. Why does the use of logic and computation allow us to manipulate reality so well if logic is just disembodied systems without relevance to the world? Why would we, and other animals, show evidence of having a "logic sense?" If the connection between logic and cause is merely our construction, there should still be an explanation as to why we construct things in such a way.
There is a similar move in Hegel's Greater Logic with the objective logic, although it's not clear that the logic of being is contained to just the objective logic. The problem with Hegel's insights is that they are hard to formalize and are grounded in speculation, observing bare thought without presupposition (at least as best he could). In this sense, it's not backed up by the type of evidential support or argument that modern philosophy is particularly comfortable with, at least not analytical philosophy.
Great point! But do we need a mind for telos? This is a huge problem in the sciences. Terrance Deacon's Incomplete Nature (which I'm still in) looks at just this issue and the diagnostic section of the book, which looks at the ways in which homunculi crawl their way into even eliminitivist theories is pretty spot on.
Obviously, there is something like a "logic" to the way our world progresses because we believe that past states dictate future states. We don't think the universe just popped into existence 10 seconds ago. We don't hop off our beds in the morning and fear we will fall through the floor; there are seeming entailments between before and after. There is not randomness, there is order. All of science relies on this fact. If experimental results gave us no reason to suppose we have learned something about how the world would act in the future than the entire argument against telos from scientific findings crumbles along with the rest of the scientific edifice.
The move against "laws of nature" always seemed more to me about thinking that regularities in the way the world works in due to an intrinsic set of properties (i.e., Kirpke's response to Hume re induction) That is, things do what they do, or the world progresses like it does, because of its traits, not because of any external Platonic laws that guide interactions. That makes perfect sense to me, but the move to intrinsic properties doesn't fix the problem of why the properties are such that they are intelligible and state progression is orderly and can be described with computable laws so well.
Fair point; I worry about making my OPs too long and sometimes gloss over some areas. I agree with your definition. By formalism I mean "the rules" not merely their particular expression, or to borrow a term from information theory, the "encoding." There can be many formalisms that map on to the same rules.
Good points, and we have the problem, per Tarski, of being able to define truth from within a system. But my understanding of the search for the "one true logic" was that the pioneers of post-Aristotelian logic were looking for something that would be both a rigorous system and which would reflect facts perfectly. From the 19th century view, where it looked like all the world would soon be explainable in a rigorous way, this makes sense. They hadn't run into undecidability, the entscheidungsproblem, incompleteness, undefinability, etc. yet.
However, I feel like the response to the aforementioned list might have been to throw the baby out with the bath water, since we've now disembodied logic in a sort of neo-Platonism. This is my problem with "game" theories of language as well. Maybe I'm just too much of a close-minded naturalist, but I tend to think that rules exist out in the world, in minds that are natural themselves, and that the rules must thus have natural causes.
In any event, I've seen more recent appeals to a "logic of being" that work off the idea of systems whose rules change over time, evolving based on meta-principles, essentially being paraconsistent and allowing for dialetheism. The details went over my head though.
Right, but generally in the sciences we think that if a formal system very closely (or ideally, perfectly) describes something in the world, and if it allows us to make good (or ideally, perfect) predictions, this is because the formalism corresponds to something in the world. We don't think our language is magic, that it is sorcery that causes the world to correspond to it (else why all the failed formalisms, right?). But we also don't think our systems can have no connection to the world, because then science isn't about the world at all, its about language and formalisms. Except it also seems to tie to our experiences and have huge pragmatic value, so that doesn't seem right.
Of course, we can justify the sciences on pragmatic grounds, but it feels worthwhile to ask "why is it pragmatically valuable?" Presumably, because our formalisms, e.g. Newton's laws, the Schrodinger equation, etc. correspond to external reality in some way. But then if logical rules correspond to reality, it seems reality has some rules.
Right, but then the question is: why do some formalisms work for meaningfully speaking of things better than others? And why is it that breaking our inference rules, committing logical fallacies, computing incorrectly, etc. all cause our models to fail at predicting what we see in the world? If there is no mapping between the formalism and the world, then using inappropriate inferences, bungling our computations-- these shouldn't necessarily be a problem for predicting nature. They are just violations of a game we invented.
If something needs to satisfy certain rules to be intelligible, and we think the world is intelligible (sort of a prerequisite of the scientific project), then doesn't that mean the world must, in at least many key respects, satisfy such rules too?
I'm most interested in this one. If this is the case, are there rules out in nature that shaped us such that we need said rules to make the world intelligible to us? That is, why would natural selection endow us with such a need if such rules only exist in our minds? This is what I find most puzzling and hard to wrap my mind around; it's hard to know what a satisfactory answer to the puzzle looks like.
I'd like to buy into pancomputationalist physics as much as I used to because that seems to explain things well, but the bloom is off the rose for me.
Two quotes that may be helpful:
Quoting James A. Weiseipl, Preface
And the extended quote from Thomas Aquinas:
Quoting Thomas Aquinas, Foreword to Commentary on the Posterior Analytics
Looking at your categorization:
Quoting Count Timothy von Icarus
It seems to me that (2) is primary, and that (1) is derivative with respect to (2). A formal system is just an attempt to delineate the "laws of thought," and logic pertains more to the "laws of thought" (art of reasoning) than to any formal system.
But what about (3) and the question of computation that you eventually raise? I would say that to describe nature or computers in terms of logic is to use a metaphor. To talk about the "logic of natural selection" is to talk about the determinate and predictable nature of natural selection. It is metaphorical in the sense that it anthropomorphizes the process of natural selection as if it were an agent following rules of logic, and the case of computers is similar.
It may be worth noting that the causative rules we use for computation are not the same as logic. They were made to mimic logic, and this is very helpful, but (for example) philosophers seem convinced that material implication is at best a poor approximation of actual implication, and yet computers "make due" with material implication. Of course there has also been an interesting reciprocal causality between computers and the field of logic, such that it is more difficult to separate the two now than it was in the past.
Does rule following entail intentionality? That's an interesting idea; it would seem to indicate a tie in between the external world and conceptions of subjectivity at a fairly basic level. For instance, ribosomes seem to be "rule following." They "transcribe," and have all sorts of mechanisms for "proof-reading." But while they are part of life, it doesn't seem like they should be conscious.
But the gap between intentional rule following and natural rule-like behavior seems like it would be tough to delineate. How complex does an organism need to be before rule-like behavior is supplanted by intentionality? How might intentional rule following evolve from rule-like mechanism? When does the human fetus or infant transition between these modes?
Interestingly, some behaviors we engage in unconsciously in a rule like way, but at will we can also lend them intentionality. For example, normally we are unaware of our breath, but we can "take control" of it. But the way the heart beats is more an unconscious sort of rule-like behavior. We can do intentional things to slow our heart rate, but we can't "hold our heartbeat" like we hold our breath; consciousness is cut off from stopping the heart, even though the brain could theoretically achieve this through signaling.
Interesting, I'm not familiar with the term "causative rules." I always thought the current definition of computation was defined by mathematical logic, and that this is why infinite alphabets and infinite strings aren't allowed for Church-Turing computation, but I also haven't explored that history all the way to the foundations of the idea.
Exactly! I feel like this is a big reason for the "Scandal of Deduction," the finding that deductive reasoning shouldn't be informative because all the information in any conclusion must be contained in the premises of a deductively valid argument. To my mind, the entire Scandal is simply the result of confusing abstract, timeless entailment and the type of entailments we see in causality. If you think of our understanding things, or a computer's producing an output given some inputs, in causal terms, then it makes total sense that all the implications of some set of premises or messages aren't clear to us immediately. Thinking through implications requires time, information processing, neurons firing. We don't have any thoughts in "no time at all." Any implications we understand, we understand through time, not as eternal relations.
Hintikka and Floridi's responses to this (surface vs depth information, or virtual information) are super technical and complex and I think this obscures the fallacy right in front of our eyes, which is mistaking our (Platonic) abstractions for causal reality. Theories that reach for explanations in computational complexity miss that really simple arithmetic is also such that we don't know the answers until we do the computations. And they can't explain fallacies, why sometimes, even with simple surface-level syllogisms, we can think information is in our premises that isn't really there, e.g. affirming the consequent.
But, if we think nature comes prior to the human, and that it shapes the human, then its the causal rule following that seems more fundamental.
If it does, then I think my point about the usage in (3) being metaphorical would hold. Are you thinking that if it does not entail intentionality, then (3) is therefore not metaphorical? That if something could follow rules without intention or agency, then (3) might not be metaphorical, and could therefore be a more central meaning of logic? I'm trying to be sure I understand how this relates to the OP.
Quoting Count Timothy von Icarus
Oh, I was only thinking of the underlying hardware of computing technology—the physical, causal mechanisms that underlie software. Basically we began with some rules of logic and we instantiated those rules into computer hardware so that software would then be able to appeal to those "rules" in order to manipulate the state of the machine. The basis of a computer is, I think, a (simple) formal system instantiated in hardware. But my point is that because all formal systems of logic have limitations, so too do computers (e.g. material implication).
Quoting Count Timothy von Icarus
I would want to return to Aquinas' claim that logic is the art of human reasoning, and that it involves a movement from what is known to what is unknown. The reason this does not make sense in a computational paradigm is because it is not clear that computers can know, and therefore for a computer there can be no movement from known to unknown. The proper context of a deduction is the human mind (or at least a rational mind), and when it is removed from that context it becomes opaque.
More generally, this is the problem of the Meno that Aristotle takes up at the very beginning of Posterior Analytics.
Quoting Count Timothy von Icarus
That's right, and Aquinas saw this because he was thinking in terms of God, angels, humans, animals, plants, and non-living matter. He would say that human knowledge is distinct because it is conditioned by time and movement, whereas angelic or divine knowledge is not conditioned in that way. This is why logic is a human art (or an art of temporal creatures). It would be of no use to angels or God.
Quoting Count Timothy von Icarus
I should look into the materials that Quixodian provided, but I tend to agree with him that logic and causation are different things. I would want to say that causal rule following, even in the higher animals, is not logic because it is not concerned with truth (or more strictly the truth-preservation that is validity). For example, even if we wish to attempt to make a non-metaphorical claim that natural selection follows rules, I think it would certainly be incorrect to go a step further and claim that natural selection follows the rules of logic. Natural selection is not following a set of rules related to truth, and this is one way to conceive of logic.
I have real trouble accepting this, but then, it is Wittgenstein, so who am I to question it? I myself have often appealed to the ‘illusion that the so-called laws of nature are explanations of natural phenomena’ in arguing against scientific realism but this response taken as a whole seems unreasonably sceptical to me. I mean, there are innumerable ways in which modern existence relies on what we understand as scientific laws (even if the term ‘law’ might be problematic.) It seems to me that Wittgenstein’s argument is similar to Hume’s in denying the necessity of inductive logic. I suppose it’s something to do with the fact that causality - a causing b - is neither deductively true nor directly observable. But isn’t this where ‘Kant’s answer to Hume’ is supposed to apply i.e. causality as being a necessary condition of reason?
I think where it seems wrong to me is that it presumes that because causation only pertains to the phenomenal sphere, then it says nothing about ‘the world in itself or its meaning’. I think that’s an unreasonable inference. But I’m interested in what others have to say about it.
It seems to me that mathematics is the study of form in the abstract. Existence must have some form or other, even if it is entirely random, and therefore some mathematics will always apply to it, in the sense of describing its form.
But the notion of change, of succession, of time itself can only arise in the context of stability. A stable self has a cigarette, and then does not have a cigarette. A stable Earth has a change of climate. Without the stable background there would be nothing to make the 'order of succession' — I cannot have coffee in the morning if there is never again a recognisable morning, and a recognisable me. Time and cause depend on that stability. If tomorrow, everything were different, there would be nothing to say it is tomorrow and not a billion years hence, or a billion years ago, or another timeline altogether.
Language, (mathematics is an abstract language) presumes and requires a context of stability and change. Names are given to things that persist, and stand out from the background. And then to processes that recur. To name something is to make a distinction between what is named and 'the rest'.
And that distinction, of 1 from 0, or observer from observed, gives rise to a logical language that can describe all the forms of the world, and all possible worlds.
http://www.siese.org/modulos/biblioteca/b/G-Spencer-Brown-Laws-of-Form.pdf
Very lucid explanation.
I’ve noticed ‘Laws of Form’ but when I tried reading it, found it quite daunting. Maybe we should start a discussion group on it.
I'd love to have a go at it, but I too find it daunting. A logician, a mathematician, and an electrical engineer would be useful contributors. @Anyone?
I read the prefaces and the introduction, and I'm an electrical engineer who would be happy to contribute to such a thread if I saw a way to do so. I'm not sure I'm willing to make the time commitment of reading the whole book, although sufficiently interesting contributions from other posters might compel me to do so. :wink:
With such great encouragement, how could I not start a thread? Here it is:
https://thephilosophyforum.com/discussion/14599/reading-the-laws-of-form-by-george-spencer-brown
Tell all your friends.
From my Information-based perspective, I think your intuition is correct. There is a connection between phenomena (world) and noumena (mind). However, the meaningful "connection" is not a phenomenal object, but a noumenal relationship : a logical link. It's a relationship between "world in itself" and meaning in the observer.
As Hume noted*1, Causation is an inference, not an observation ; a conception, not a perception. What we observe is changes in material objects from T1 to T2. But the causal force we call Energy is invisible & intangible, hence unobservable. We attribute the power of causation to some imperceptible enforming Force at T1 to explain the perceived Effect at T2. A phenomenal event is a physical transformation from state A to state B. As in physical Phase Transitions (e.g. liquid water to solid ice), the before & after states are are observable, but the intermediate cause that connects them is only inferrable. And Logic is the ability to imagine plausible interrelationships between things & events.
For a zombie, Causation may "only pertain to the phenomenal sphere". But for rational beings Causation is significant to the observer, not just for what happened to an object, but for what could happen to the subject*2. That a physical change has occurred in the non-me world is meaningful to me because I am an integral part & participant in that objective world.
Phenomenal Change is what we interpret as Noumenal Causation*3. Change is physical & material, but Causation is metaphysical & mental. Perhaps the notion of causation says as much about the the subject as the object. Without change in the world, to which we accredit causation, there would be no meaning in the mind. :smile:
*1. Causation as conjunction of states :
Causation is a relation between objects that we employ in our reasoning in order to yield less than demonstrative knowledge of the world beyond our immediate impressions.
https://iep.utm.edu/hume-causation/
*2. Objective Data vs Subjective Information :
Data is a collection of facts, while information puts those facts into context. While data is raw and unorganized, information is organized. Data points are individual and sometimes unrelated. Information maps out that data to provide a big-picture view of how it all fits together.
https://bloomfire.com/blog/data-vs-information/
Note --- Context includes observed and observer
*3. EnFormAction :
The novel concept of Enformation is also a synthesis of both Energy and Information. So I invented a new portmanteu word to more precisely encapsulate that two-in-one meaning : “EnFormAction”. In this case though, the neologism contains three parts : “En” for Energy, “Form” for Shape or Structure or Design, and “Action” for Change or Causation. But Energy & Causation are basically the same thing. And the “En-” prefix is typically used to indicate that which causes a thing to be in whatever state or form or condition is referred to.
https://bothandblog2.enformationism.info/page29.html
I don't think Wittgenstein would have thought this was a good reason to accept what he said. In any event plenty of other philosophers with at least as much cachet would say he is simply wrong about this. In the Investigations, Wittgenstein is trying to reframe questions, think outside the box, and so solve issues the generations of great minds ended up banging their heads against. I think it's fair not to expect that he succeeds in all respects.
The idea of the "laws of nature" having causal efficacy does seem open to critique. As Cartwright points out, Newton's "immutable" laws fall apart when we add three or more bodies or imperfect spheres, meaning they are clearly only approximations. Paul Davies among others has offered pretty solid arguments against thinking of "the laws of physics," as Platonic statutes that causally interact with the world.
But this doesn't torpedo scientific realism because we can also think of such "laws" as merely describing the way things interact due to properties that are essential to them. That is, the causal nature of such laws areintrinsic to reality as a whole, or to parts of that whole, rather than laws being something outside nature that guides nature (the extrinsic view popularized by Newton, which Hume was critiquing).
For example, "water is H2O is an a posteriori analytical truth. It is true by definition, but we had to discover it empirically. Water, by this view, will behave like water whenever it interacts with "stuff" like the "stuff" of our world because of what water is due to its intrinsic properties. Just like how 2 is an even number by virtue of what 2 is. So here, the laws are just mathematical descriptions of the standardized properties of being that are internal to being qua being. What might be surprising here is that:
A. Such properties are intelligible to us and so readily describable in mathematics and logical formalisms.
B. That such properties exist at all. After all, we can well imagine a random universe (although we would only exist by chance in one). A random universe is certainly mathematically describable, but we don't see a random universe. We see a universe that always seems to move according to principles. And moreover, the principles exhibit a certain type of fractal recurrence such that disciplines such as chaos theory and complexity studies can identify general principles at work in extremely diverse systems, such as how fireflies decide to blink, hurricane formation, how the heart generates a beat, how earthquakes form, etc.
https://www.oxfordphilsoc.org/Weekend/2003/2_EileenWalker.pdf
Yes, and Leibnitz had the Principle of Sufficient Reason before Kant. Denying PSR gets very dicey vis-a-vis the cosmological argument because it opens opponents up to John Edwards' argument that: "if things can just start existing that didn't exist at any prior state, why don't things start to exist all the time." And moreover, with the intrinsic view: "if things don't initially occur due to any reason, why should they have one set of properties and not another." I don't shake up my water bottle and expect it to become a nice Scotch for instance, or expect that second moon wil pop into existence in the sky some night.
I think Wittgenstein and Hume have a massive pragmatic hurdle. If cause isn't real and induction is invalid, why the hell does it work so damn well? It certainly seems like logical models and mathematics correspond to how the world works.
But really, my views on Wittgenstein are mixed. Genius insights, and a great warning about the problems that come with attempting to theorize, especially theorizing about philosophy like it is the natural sciences. But at the same time, the self-described "purist" reading of Wittgenstein (per Rorty's label) ends up trying to use language to explain everything in the very way Wittgenstein warns against in the same book.
:up: Right, if you believe we are the products of natural selection, then claiming we only see cause because we construct it is a half answer. Ok, then why would we evolve to see cause? Why is it so useful? Why do animals seem to have a basic logical and causal sense? If we are natural, why did nature shape us to hallucinate causation from whole cloth? Why shouldn't we expect vision is the same way, that what we see has no correspondence with the world as it really is? Down this road seems to lie solipsism.
This is my problem with the linguistic turn, it seems to think that because you can't pin language down with a formalism that this entails that it isn't underpinned by nature in a way that is intelligible. This inclination is helped along by some findings in linguistics, namely Chomsky's universal grammar, but I think Chomsky is simply wrong here in terms of the causal origins of such rule-like behaviors.
Maybe this gets us too far afield, but its sort of like how all stem cells from an early fetus can become any type of cell. Tissues only differentiate, organs only develop, because of a complex feedback cycle between cells with the same DNA. It's all epigenetic, not hard coded at all. Kids don't learn language if they don't get exposed to it. We, as fully formed humans, are closer to chimps or even horses then a clump of our fetal cells, given they develop in a different environment, because that clump can be grown into nothing but a giant group of liver cells given the right signals. Hell, scientists can even turn animal stem cells into new synthetic creatures with little in common with the animals they share 100% of their DNA with. Point being that language is probably nothing suis generis, but natural like anything else, and so subject to the same causal principles.
:up: Plus, how do creatures like ourselves develop in a world without stability? It doesn't seem they can, we'd only have various types of "Boltzmann Minds." Our world is stable, and it has a certain type of stability, and that type of stability appears to be what gives rise to us and our languages. So, that's where I see an opening for a base level of "logic" that is posterior to our subjective logic, but perhaps it requires a different name so as to not to confuse the two.
But there appears to be morphisms between the two types of "logic." E.g., Leibnitz comes up with the Principle of Sufficient Reason because of the type of world he experienced and the type of animal that world made him to be. The fact that we understand necessity at all seems to imply something about us and about the world. If you explain necessity to a toddler, you're probably going to use empirical examples. Indeed, I'd argue we understand the abstract from the empirical sort of necessity found in cause, that abstract necessity is posterior to knowledge of causal necessity. E.g. "if you don't eat your dinner, it will necessarily get cold (because of the Second Law of Thermodynamics).
I think philosophy erred in taking Hume too seriously, and this had a big impact on Kant and (apparently) Wittgenstein. A related problem is that such individuals basically started with a critique, and then interpolated their more systematic views on that basis of that critique. This is a particularly poor way to do philosophy. A critique or a problem is not the basis for a systematic approach.
Obviously I will need to brush up on Hume since so many participants on forums such as this one take him for granted, but in general when presented with a Humean premise the response should just be, "Why think that?" The Humean premises are implausible and the conclusions are absurd, and at the end of the day the Humean ends up being schizophrenic because they want to have their cake and eat it, too (i.e. they want both their skeptical philosophy and the scientific enterprise that it undermines). I'd say that we need to be a bit more skeptical of Hume's skepticism, and that newcomers to philosophy need to feel free to question Hume or Wittgenstein when they say silly things.
On a related note, I have Jamal's piece on my reading list, "An Argument for Indirect Realism."
It is fascinating to me that Wittgenstein sees himself, in saying this, as repudiating a modern error. Rather, it seems to me that he has captured the error of modernity in a remarkably pithy formula. But I would want to read more to further understand his context and intentions. He may be arguing against certain deformations.
To my point above, imagine saying something like this to a scientist, such as a biologist. It is a truly absurd claim to anyone familiar with reality. There is an important way in which the causal realities known to the biologist are much more real than the logical necessity of the logician. When one has no spectacles besides modal necessity with which to view the world, the majority of the world itself evaporates from before their eyes.
Your way of talking looks confusing to me. If you say in the latter statement that there can be many formalisms mapping on the same rules, then formalism is distinct from rules. And surely, by formalism, you could mean to refer to the logic rules as you also stated. But were this the case the following claim of yours “1. Logic is a set of formal systems; it is defined by the formalism” would equate to “1. Logic is a set of logic rules; it is defined by the logic rules” which sounds, if not tautological yet, very little informative.
To me it’s more clear to simply say that formalism is the symbolic codification of logic rules as opposed to the natural language codification of such rules. My substantial points here are that one thing is the subject of our representations (logic rules) another is our representations (formalised vs natural) and that formalisation would be a fix for natural language ambiguities. Wrt these points the observation that for exactly the same set of logic rules one can have many symbolic or natural language codifications is correct but marginal.
Quoting Count Timothy von Icarus
Independently from the merits of Tarski’s semantic theory of truth for formal systems, if the price for it is to relativize the notion of truth to a given (object) language, my problem with it is: what does “if and only if” in the T-condition mean? If the be-conditional requires the notion of “True” to be understood as a logic operator, but the notion of true can not be applied at the same language level in which the bi-conditional is expressed, then what does that bi-conditional even mean? Besides asserting p (in the most basic object language and since it’s a language it can offer just representations of facts not facts themselves) doesn’t mean that p is true.
Quoting Count Timothy von Icarus
I see your point. But I think it is relatively easy to realign it with what I said. Indeed the “rigorous system” condition can reflect the need to have a system that doesn’t suffer from the ambiguities which e.g. the natural language suffers from. And the “reflect facts perfectly” condition refers to the fact that a certain set of logic rules can serve science better than other conceivable set of logic rules, as much as a set of mathematical analysis rules can serve science better than other conceivable mathematical rules.
Quoting Count Timothy von Icarus
All I can say at this point is that if your naturalist assumptions play a role in your understanding of logic, then they deserve to be addressed as well.
Quoting Count Timothy von Icarus
Without directly joining the debate between idealists and realists, my point is that if we develop tools (formal systems) to better serve a purpose (to describe the world), then we shouldn’t be all that surprised if these tools serve that purpose. What you may be tempted to say instead is that if there are representational tools that can successfully represent the world, then the world must be such that our representational tools can succeed in representing it. But this claim does very much sound like claiming that we can represent the world that we can represent, doesn’t it?
Quoting Count Timothy von Icarus
Logic rules allow us to infer some conclusions from some premises. Such rules ensure that if the premises are true, then the conclusion is true. And that’s possible because from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises. The mapping to the world can be done by the premises. But logic would work even without any such mapping. E.g. Premise 1: squares are triangles; Premise 2: triangles are circles; Conclusion: squares are circles.
Quoting Count Timothy von Icarus
It’s not the world that satisfies such rules, but our representations of the world. While we can represent and logically process representations of state of affairs that do not map into reality and do not correspond to facts, are there real states of affairs that we can not represent ? But how can we answer such question without possibly representing such state of affairs? What are we picking with the notion “state of affairs“ for whatever goes beyond our means of representation (so including the notion of "state of affairs" itself)?
Quoting Count Timothy von Icarus
I guess that these questions are all the more pressing because of your naturalist assumptions which I’m afraid I do not share. My assumptions have been more shaped by a certain reading of Wittgenstein’s views, especially in his later phases, and according to such reading there are reasons to be skeptical about both platonism and naturalism.
Concerning your claims, let me list just the points I’m having problems with: 1. if by “rules out in nature” you are literally referring to the “laws of nature” then I find your usage conceptually confused, because the former concept is conceptually distinct and irreducible to the latter. And rules are not “in our minds” if this means a private phenomenon, something only a given subject can possibly have access to. I won’t elaborate further such claims now 2. If by “laws of nature” you are referring to some theory of natural selection then I’m not sure we have such a theory for logic rules. Notice that logic rules can be used to justify anti-natalism, human killing and suicide depending on the premises so both for human beings’ survival as much as for their extinction. Besides natural selection can be used to explain also failures to follow logic rules, think of our cognitive biases (and more radically, if you remember, even Nietzsche claimed that the notions causality, will, subject, substance are false representations of the world which we have to survive).
Anyways, as far as I’m concerned, a more Humean understanding of “laws of nature” plus some form of “emergentism” may help us make the coexistence of “laws of nature” and “rule following” less untreatable.
Sure, it's tautological. That was the position of Russell and the Vienna Circle. Moreover, by this view, all of mathematics is itself tautological. This is logic as defined as: "the study of certain mathematical properties of artificial, formal languages. It is concerned with such languages as the first or second order predicate calculus, modal logics, the lambda calculus, categorial grammars, and so forth. The mathematical properties of these languages are studied in such subdisciplines of logic as proof theory or model theory."
(quote from https://plato.stanford.edu/entries/logic-ontology/#DiffConcLogi)
The rules define what the system is. And per deflationary theories of truth, that tend to go along with this sort of view, truth is itself simply something defined in terms of such systems. That is, truth is "neither metaphysically substantive nor explanatory. For example, according to deflationary accounts, to say that ‘snow is white’ is true, or that it is true that snow is white, is in some sense strongly equivalent to saying simply that snow is white, and this, according to the deflationary approach, is all that can be said significantly about the truth of ‘snow is white."
E.g., many axiomatic theories of truth: https://plato.stanford.edu/entries/truth-axiomatic/
The most austere versions of "logic as formalism" seem to deny any direct relation to thought or metaphysics. Many versions aren't quite so austere, but the general idea is that logic is about abstract systems, not thought and certainly not the world or metaphysics.Logic might inform our metaphysics, but our metaphysics (or philosophy of mind) should not inform our consideration of logic.
(After being very impressed by the North Holland Handbook of the Philosophy of Complex Systems I was excited to grab their book on the Philosophy of Logic, but it seemed to hew fairly close to these sorts of views throughout the submissions, which was the impetus for this thread.)
This seems right to me. What I wanted to get at with description 1 is the conception above.
Right. Or what does it mean to "describe things" at all in a language we are pretending is completely divorced from anything else in reality? At a certain point, when you get into very deflationary views, you're no longer describing "things." All you can say is that "a system can produce descriptions."
Sure, and I can totally see how my concerns might be irrelevant for people who are less concerned with naturalism. But most philosophers are naturalists, so it doesn't seem too outlandish.
It sounds similar; I don't think it's identical. First, if we posit that any intelligibility we find in the world is hallucinatory, something we project onto a world that lacks it, I don't see how this doesn't slide into the territory of radical skepticism. The steps to get us to "how do you know cause and effect exist? Maybe your mind creates all such relationships," seem like they should also get us to "why do you think other minds exist?" Or "why should we think an external world exists outside of our perceptions?" Afterall, don't we suppose that others have minds because of how those minds seem to effect their behaviors?
The fact that animism is pretty much universal in early human cultures (e.g., "the river floods because it wants to"), and that children tend to provide intentional explanations for natural phenomena ("the clouds came because the sky is sad") seems to show we can "hallucinate" other minds to some degree. But if we think all of the intelligibility we find in the world is simply projected, then I'm not sure how solipsism isn't a problem.
Most philosophers are naturalists though, and most think the natural sciences are one of the best sources of information we have about how the world is though. And if we accept we are formed by natural selection, then it is prima facie unreasonable to think how we "make the world intelligible" has nothing to do with how the world is.
Second, what is the point of positing aspects of reality that we cannot ever, even in principle, experience? To be sure, people have experiences all the time that they say they cannot put into words. That makes perfect sense; we do more than just use language. But aspects of reality we can never know? They are like Penrose's invisible fire breathing dragon who is flying around our heads and not interacting with anything. We can imagine an infinity of such entities. But as long as they are, in principle, forever unobservable, their being or not being seems identical. When we move to the existence of that which cannot even be thought it seems even weirder. It's the inverse of radical skepticism, instead of seeing a way to doubt everything, now we can posit anything (so long as we can never know of it).
This gets to the "Scandal of Deduction." If in all valid deductive arguments all information in the conclusion is contained in the premises, what exactly is the point of deduction? It tells us nothing. So why does deduction seem so useful? Why can't we memorize Euclid's axioms and then immediately solve every relevant geometry problem we come across?
This is probably the best example I know of where thinking of logic as completely abstract runs into problems. A lot of ink has been spilled trying to figure out some sort of formal solution to the Scandal, because the idea is that any solution has to lie within the scope of the abstract systems themselves.
I don't think this works. Floridi and D'Agostino put a lot of work into their conception of virtual information, trying to figure out how it is that at least some inference rules introduce new information in an analysis. But it seems like such a project is doomed. As both they and Hintikka agree, Aristotelian syllogisms only deal with surface information, information explicit in the premises. The problem is that we can still find this type of analysis informative, just as we can not know the answers to very simple arithmetic problems until we pull out a pencil and start computing.
Naturalist approaches have no problem here. We don't see things and immediately know what they entail because thought is a complex process involving a ton of physical interactions, all of which occur over time-- simple as that.
Not everything can be put into words. I'm not sure if it makes sense to posit things that can be known in any way though.
Anyhow, would you agree that the world has an influence on how we represent it? This is the logic behind using mathematical patterns to contact extra terrestrials. If the representations of intelligent life forms aren't the result of bidirectional influence, then of course this won't work of course. But then if nature doesn't shape our representations than I don't get why even members of the same species should understand each other.
One way to get logic without compromising your naturalism is to push it away from basic brain function and toward social interaction.
I don't think you have to look for logic in the world at all. You can instead say that there are regularities in the world -- I just don't know any way around this -- and our minds are built pretty much entirely around making predictive inferences based on these regularities.
But neither are the domain of logic. We can approximate the sort of things our minds get up to, but it's not logic; it's probability, Bayesian inference, that sort of thing. (And the most we can say about the world is something statistical.)
If that mathematical formalism is in some ways a simplification of what our minds do (and also of how the world is), logic is a further simplification, even exaggeration, of that, and its use is not primarily in our prediction-generating and updating machinery, but in discussion.
We present our views to others in a drastically simplified form -- even more simplified than the form in which we ourselves become aware of our own beliefs. Some of that may be down to the nature of language, built as it is on conceptual generality, but some of it is strategic: we need only bring to the discussion a view, with the expectation that others will bring other views, and the cooperative process of comparison and critique will lead to a more-heads-are-better-than-one conclusion.
We're each biased toward our own ideas, and notoriously bad at judging how well supported those ideas are. Others make better judges of the soundness of our thoughts.
Around here is where it makes some sense to talk about logic, in the critique of the reasons others offer in support of their views, and in the contest between positions that are presented as more perfectly opposed than they really are. It's efficient and productive to present and critique ideas this way, and the process should lead not only to a better view than any individual would produce on their own, but through the exchange and critique of supporting reasons and evidence, to a view that gets buy-in from participants. Reasons need to be persuasive because it's not just the least wrong belief we want; it's cooperative behavior reliant on a shared point-of-view.
Some of this can be supported by research, and probably some of it can't yet, but it's the overall story I lean toward these days. The inferences that we think of as 'belief formation' aren't really much like any sort of formal logic, so there's no such process that would be isomorphic to some logical structure of nature. Even single-cell organisms can display behavior we might as well call 'rational' in avoiding danger and seeking nutrients. But they don't deal in reasons and persuasion and counter-arguments and counter-examples and all that stuff that logic is useful for.
What do you think of computational theory of mind? I'm not totally sold on it, but it remains the most popular theory of how consciousness emerges (Integrated Information Theory is fairly similar too).
If these theses are mostly true, then logic absolutely can be used to describe all our beliefs and how we come to them, since these theories take mind to be a product of computation. It's simply that forming such a complete description of how said computation works is very difficult because parallel processing is harder to follow and because we're talking about quadrillions of operations per second (at lower end estimates).
If computation is symbolic manipulation based on logical rules then it seems like simple organisms use computation all time time. But I get your point. It squares with views that computation only occurs in virtue of a human observers recognizing a process as such. E.g., "Chat GPT doesn't "compute," computing is just a label we project on to what the machines running the program are doing."
This particular example I find puzzling because the same thing can be said about all our concepts. For example, "burning" is a human concept and label we attach to a class of phenomena. All incidences of combustion are actually different events, but we don't tend to say "wood doesn't [I]really[/I] burn." I suppose the difference here is supposed to be that computation necessarily requires intentionality, but I've never been convinced about why this should be the case. My phone seems to compute.
I find the "computation requires intentionality," view less convincing because I haven't seen one that can define how sentient an observer needs to be before they can "view computation," nor one that explains why mental constructs should be causally disconnected from the rest of the world. Presumably, under intentional versions of computation, when my cat is looking at my computer, it doesn't see something that is computing. Likewise, when my son plays with my phone, he doesn't understand that it is computing, so for him it isn't computing. But how well does he have to understand the process before he is projecting computation onto the phenomena? This is not a way we tend to think about other processes such as combustion or acceleration. "Reading" might be analogous though: does a ribosome "read" DNA? Does a license plate scanner "read" license plates?
In biology, the idea that simple organisms compute is fairly mainstream. If a bacteria computes, then there is a sense in which logic, or a very similar sort of thing, plays a role in organisms that we tend to think lack intentionality and social organization, at least in any way that is qualitatively like our own.
But in biology and biosemiotics there is often a move to cut off the definition of "computation," at the domain of life. Cells compute, self-replicating silicone crystals do not. Digital computers might compute, but only in virtue of their having been designed by living things.
The problem here is that the definition of life is squishy, and this doesn't seem that much less arbitrary than saying computation and logical manipulation only occur in organisms that are "sentient and social enough."
Plus, paired with findings that give rise to the popularity of computational theory of mind, the view of computation as something that only occurs in sentient consciousness starts to get a little wonky. Presumably, I am computing if I am not a math wiz and have to consciously think about the steps involved in summing some list of figures. But then am I not computing if the entire process happens unconsciously and I just know the outcome by glancing at the symbols? Do I compute when I consciously try to read French, but acomputationally experience when the meanings of English words fly into my awareness with no conscious effort? If unconconcious computation is possible within a human, it seems harder to justify it not existing outside the mind. But then knowing the answer to 3+7, 2+2, etc. [I]doesn't[/I] seem to require anything conscious or intentional on our part.
Socrates is a man
All men are mortal
Socrates is mortal
Can be explained as:
Socrates is contained in "men"
"Men" are contained in "mortals"
If Socrates is inside "men" then Socrates is necessarily inside "mortals" because "men" is inside "mortals."
But containment seems like a concept that is harder to bracket off as existing only in the subjective sphere than "reading," or "computation." A box doesn't need to be conscious to contain anything. And if boxes only contain things in virtue of our observing them then it seems like all factual statements must not truly be [I]about[/I] the world sans our experiences of it. "If a box is alone in a forest, can it contain a rock?"
Unless we want to say that the containment relations we discuss in mathematics are in fact a different sort of "containment," than physical containment.
:up:
These all seem to be, as you say, common definitons of 'logic'. The question that arises for me is whether these definitions have a common element or thread running through them.
Is logic as a set of formal systems not a set of formulations built based on what we do naturally when we think deductively, "the ways we make good inferences and determine truth, or at least approximate truth pragmatically", a making explicit of what is implicit in our practice of consistent thinking?
Are these formulationsnot all built on a few basic principles. consistency, non-contradiction and excluded middle, which may be thought of as 'laws of thought"?
And do these principles not reflect our experience of the world? It doesn't seem that we see things in the world being inconsistent, such as appearing as a tree then morphing into an animal, or contradictory, being an apple and the same time not being an apple (unless maybe we have partaken of some psychedelic).
If we think of the laws of nature as formulations of the perceived regularities which abound in the natural world, just as the laws of thought are formulations of the natural ways we think, then why can we not say there is a logic, a logos, at work in the world?
I take it by "disenchanted" you mean that we have come to see this natural order as an immanent nature and not as imposed from on high, by a transcendent or divine order?
Certain logic formulas are tautologies e.g. "( P ? Q ) ? ( ¬ P ? Q )" in the sense of being always true whatever is the truth value of the variables P and Q. However not all logic formulas are tautologies (e.g. P ? Q). The idea that logic (and mathematics to the extent it is reducible to logic) is tautological basically comes from the idea that logic theorems can prove only tautological formulas. And this is in line with what I also said about deductive reasoning “from premises to conclusions we are manipulating our own representations so that, semantically speaking, there is no more truth in the conclusion than there is in the premises, there is no more information in the conclusion than there is in the premises.“
But your statement “Logic is a set of formal systems; it is defined by the formalism” (which is neither a logic formula nor a logic tautology) seemed to offer a definition for “Logic”. And valid definitions should not be tautological in the sense that what is to be defined should not occur in what is defining. Yet your other claims made your definition of “logic” look tautological (even claiming “Logic is all about tautologies” would sound tautological if it equates to “Logic is all about logic”).
Quoting Count Timothy von Icarus
I’m not persuaded by the deflationary theories of truth so I can’t share your assumption. The most intuitive objection I can make against it is that, asserting p doesn’t mean nor implies that p is true.
Quoting Count Timothy von Icarus
Notice that “abstract” in “abstract systems” may also have a metaphysical connotation: namely, being out of space and time. And this understanding would lead us to a form of platonism about logic (which is also a metaphysical view). However “abstract” can simply refer to the result of a cognitive task by which we are focusing on certain set of characteristics or type of information while ignoring others. So “abstract systems“ refers to the possibile result of such cognitive task. I guess that’s the understanding suggested by your claim, right?
Quoting Count Timothy von Icarus
Indeed, I’m not even sure that such views would even justify anybody saying “a system can produce descriptions”, since the notion of “description” to me conceptually implies the idea that representations of states of affairs are distinct from the states of affairs in the world as the former refers to the latter (not the other way around), and the idea that the former can correctly or incorrectly apply to the latter (hence the distinction between “true” and “false”).
Quoting Count Timothy von Icarus
If you mean that this thread is specifically about naturalist views of logic, then I didn’t get it but I will take it into account from now on. On the other side, if you mean that this thread is about views on logic and your views on logic are grounded on popular naturalist assumptions, then I’ll confirm what I said that I do not share such popular views and I’m open to discussing them.
Quoting Count Timothy von Icarus
I’m not positing “that any intelligibility we find in the world is hallucinatory”, I’m not a radical skeptic, I’m not a solipsist. My point is more that we have a network of concepts (like representation, world, truth, fact, possible fact, logic/semantic inference) that enable us to talk meaningfully and reflectively about our own cognition. Since they are mostly primitive concepts they can not be questioned or explained away without ending up into some nonsense or implicitly reintroducing them. To me “realism” about the existence of the external world (that can be experienced or referred to by other minds beside mine) is matter of conditions to talk meaningfully about the external world, so any attempt to question the existence of the external world sounds nonsensical to me as much as any attempt to demonstrate it, because one needs demonstration were things can be questioned meaningfully.
On the other side, our representations of the world may not correspond to what is the case, and may refer to mind dependent facts (as human linguistic conventions or social institutions). Unfortunately we may hold more false beliefs than we are able to detect or wish to admit. And human representations and logic/semantic inferences may serve human biological extinction as much as they can serve human biological survival.
Quoting Count Timothy von Icarus
Concerning the "Scandal of Deduction", even though I do not share your naturalist assumptions, my way out is somehow similar to yours. We do not have the full list of valid representations of the world in our mind simultanously. We process them progressively according to some logic/semantic rules. And we may also fail in doing it.
Quoting Count Timothy von Icarus
Sure we may be unable to describe many of our experiences to any arbitrary degree of detail. For example there are many varieties of “red” and yet we can refer to all of them simply as “red”. That’s not the point, the point is that in order to talk meaningfully about experiences we can’t put into words, we still need to apply correctly a sufficiently rich set of notions and make inferences accordingly: e.g. that the varieties of red are not varieties of grey, they are colors and not sounds, that they are phenomenal experiences and not subatomic particles, that one normally needs functioning eyes and not functioning ears to experience them, etc.
Quoting Count Timothy von Icarus
The term “influence” may express an ontological notion of causality, but I find this notion problematic for certain reasons. On the other side, if we talk in terms of nomological regularities, surely I do believe that certain external facts (e.g. the light reaching our retina) correlate with visual experiences which then we have learned to classify in certain ways. That would be enough for me to talk about “influence” but at the place of ontological causal links, there are just nomological correlations plus a rule-based cognitive performance.
Best answer might be that it is rules of grammar; rules for stringing symbols together.
But I would draw your attention to logical pluralism: the view that there are no "Laws" of logic.
Quoting Banno
Pick the logic that works for the sort of discussion which you are involved - a grammar for your argument.
It's like formalism in mathematics; there are rules for manipulating symbols and nothing else. The most austere definitions of logic I've seen tend to take the line that logical systems are like Chess, they are a set of rules that have been developed. Their relation to what they are used for in the world (e.g. the sciences) is pushed off to the side (which you see a lot in definitions of mathematics as well). I don't particularly like these definitions, but I don't think/hope I'm not misrepresenting them. The rub seems to be, "the system is what it is because that is how it is defined," and then we go from there in talking about the properties the systems have in virtue of their rules.
This isn't the only type of austere definition. There is also "logic as the study of logical truths," that is the identification of the most general truths that must be true under all conditions. This seems even more tautological, but you can make it at least more descriptive by saying it's about the truths that follow from an empty set of premises.
Me either. I'm just trying to explain the bucket of answers to "what is logic," that I was trying to group together with point 1.
Yeah, in general. Again, I was just trying to explain what seems to be a popular collection of definitions of logic, so it's hard to generalize. In general, from my limited poking around, this does seem to be the type of "abstract" that people have in mind. That said, I have come across the argument that the "landscape of mathematical systems," are the real Platonic objects that mathematicians study, and so I imagine someone has probably made the same argument about logical systems at some point.
Good point.
No, by no means. Your replies have been interesting. I just find it interesting that naturalism is so dominant in culturally and in philosophy writ large, but that the subfield of logic seems fairly well insulated from this.
Gotcha. But then why do we only progress through these rules so quickly and why are some people much faster than others at doing so? Or why are digital computers so much quicker than any person? I'm curious how that can be answered without reference to the physical differences between people or people and machines.
That makes sense to me. I thought you were drawing some distinction between "the world as it actually is, which might lack anything corresponding to the order we see in phenomena" and our view of things. I think I may have misread that.
Yeah, I think that works for what I'm thinking of. I don't really like eliminative views on causation, e.g. Russell's "a complete description of the solar system includes no room for cause," but even accepting his view it seems like there are still relations of a sort between the world and beliefs. But this to me suggests that our perceived order corresponds to an order that exists outside of our perceiving it.
But is it logic by which physical states seem to orderly evolve into only other certain configurations of future physical states? I feel like a different word should be used because "logic" is more associated with definitions 1 and 2 I laid out. It is certainly very common in the natural sciences to read phrases like "because of the logic of thermodynamics...." etc., but it's obviously not a reference to thought in those cases.
I'm reading Terrance Deacon's "Incomplete Nature," right now and it makes the same sort of argument. I'm really enjoying it, and I think he has a point here.
But Deacon is also coming from a naturalist frame, so he has different ideas about where to go from there. He has what I thought at first glance was a good argument against nominalism and the idea that all our categories are products of mind "in here," as opposed to reflections "out there." Perhaps not directly relevant to what we're talking about, since he is focused on how universals can have causal efficacy, but somewhat related:
All right, I think I got it now. In my own words, your summary amounts to pointing at 3 ways of approaching the question “what is logic?”:
1. The formalist, which understands logic as a system of rules independently from any reference to mental processes or the world.
2. The psychologist (comprising behaviourist, cognitivist, neurologist views), which understands logic as an empirical description of “laws of thought”.
3. The realist, which understands logic as metaphysical description of meta-empirical principles.
Quoting Count Timothy von Icarus
Your questions about cognitive performance in processing logic inferences are empirical questions not conceptual ones. So they deserve an empirical answer as offered e.g. by cognitive sciences.
What is crucial to me here is the distinction between empirical and conceptual questions. Naturalist views tend to conflate them. The co-existence between two distinct domains (the empirical and the conceptual) is undigestible for naturalists. Naturalists are mostly reductionists or eliminativists (there are also the mysterianists though) about the mental.
Quoting Count Timothy von Icarus
The empirical method obliges scientists to check their theories against the facts, therefore the confidence one can scientifically grant to scientific theories remains conditional for any empirical theory no matter how successfully it looks in competition to other theories.
Anyways I too find the expression “because of the logic of thermodynamics” a bit confusing (e.g. “logic of thermodynamics” is not yet another a logic system distinct from “propositional logic”), however I find it harmless if it simply equates to claiming: “Given the premises of the theory we call ‘thermodynamics’, we can logically infer this and that”.
Quoting Count Timothy von Icarus
Unfortunately I didn’t read "Incomplete Nature". And I find that passage rather obscure, even in relation to what I said. From what I gathered around he seems to support a peculiar notion of causality that would allow to bridge the gap between mental phenomena and physical explanation, so I guess it might be an interesting reading.
Logic seems best defined as a set of rules forming the axiomatic basis of correct reasoning.
Tarski Undefinability, Gödel Incompleteness and the Principle of Explosion seem to indicate
issues with current systems of logic.
[b]My unique contribution to this is that the above issues can be easily abolished by simply
requiring all conclusions to be a semantically necessary consequence of all of their premises.[/b]
Copyright 2023 PL Olcott
The key change that this requires is to fully integrate model theory into the notion of formal systems.
While there are industry-wide standards for how programs (and any related logic) should be structured, Developers are able to build anything they want, anything they can imagine. And as long as their work meets requirements, such a thing/process is an example of software.
Based on these observations and similar experiences, I have come to conclude that "logic" is primarily "applied values".
That's an interesting question. In programming an unapplied value is generally considered wasteful and ultimately ignored.
I think this is exactly right. "Logic is a set of formal systems," does not approach a coherent definition of logic. The question that immediately comes to mind is, "Which set of formal systems?" It's much like saying, "Hyenas are a set of animals." It gives the genus without a specific difference. The specific difference of logic is related to (2), namely that logic aims to provide us with a means of reasoning well and arriving at previously unknown truths.
Those who study formal systems as some sort of end in themselves are doing meta-logic, not logic. It would be like if a traffic engineer became so interested in traffic lights that he comes to focus on the lights themselves, independently of traffic. At that point he is no longer a traffic engineer—he is just a guy who studies a specific sort of light. I think this sort of detachment from reality is a big problem in contemporary philosophy.
If the thread is about cataloguing the different ways that the word 'logic' is used, then (1) has a place. If it is about logic, then I think it doesn't.
Quoting neomac
On the other hand, I don't agree with this. Logic can be said to be true insofar as it does what it is supposed to do: aid us in reasoning well. Currently our central criterion is validity, where the truth of the premises ensures the truth of the conclusions. So if I take a logical system and I scrupulously follow the rules, beginning with true premises, but then arrive at false conclusions, the logical system is bad or false. It is false in the sense that it is not doing what it was meant to do (i.e. preserve truth). Truth is not built in logic; it transcends it.
Quoting Leontiskos
Notice that quote of mine was questioning the notion of “true logic” if applied to different logic systems or different sets of logic rules which are all supposed to “preserve truth“. On the other side if your claim is supposed to question my claim that “the notion of ‘truth’ is built in the ‘logic’ rules themselves”, then you are failing since your own notion of logical system as a set of truth preserving rules is also grounded on the notion of “truth”. That doesn’t compromise the distinction between valid and sound deduction, by any means.
If something is meant to preserve another thing, then it is not building or creating that thing.
That is, there are logical systems that do not involve truth.
It follows that logic cannot be defined only in terms of preserving truth.
Well, I never said that logic can only be defined in terms of preserving truth. But that someone makes up a formal system that has nothing to do with truth and calls it 'logic' is not much of a counterargument. Logicians can temporarily and usefully prescind from truth, but entire detachment is something different.
Quoting Banno
But logic is not merely rules for stringing symbols together. If I make rules for stringing symbols together I have not necessarily done anything related to logic.
Formalists need to take a step back and consider why the formal systems were constructed in the first place.
Well, that would mean that, say, an uninterpreted explication of propositional calculus does not count as part of logic.
The point here is just that logic is bigger than the preservation of truth in an argument.
Quoting Leontiskos
I wouldn't be so quick to draw that conclusion. We do say strings such as:
"have a certain logic to them...".
Logic has advanced somewhat since the middle ages.
I added to my last post, "Logicians can temporarily and usefully prescind from truth, but entire detachment is something different." There are more proximate and more remote relations of logic to truth, but something with a perfect non-relation to truth is not logic.
Quoting Banno
This is an ignoratio elenchus, as I already noted.
Quoting Banno
This is a metaphorical use of the term, similar to what I pointed out <here>. Logic depends on order, and thus ordered things are sometimes called "logical." But logic is more properly an art of ordering, not mere order. You are appealing to usage, but the etymology and the historical usage point very clearly to logic as an art of reasoning.
They say that one of the best ways to learn something is to teach it. A few weeks ago I looked at your thread which is intended to teach propositional calculus (link). It's no coincidence that in your third substantial post you were already into truth tables. But even in your first substantial post you said, "What we want to do is to examine the relations between these propositions, rather than their contents." It seems to me that it would have been more apt to say that we want to examine the relations that obtain between these propositions based on their content. Relations hold or fail to hold in light of the content of the relata, and this has everything to do with truth.
Now a pedagogue might choose to introduce the rules of logic before introducing the purpose of logic, much like you could teach a child to kick a ball before introducing them to the game of soccer. Of course I am not convinced that this is sound pedagogy.
Quoting Banno
Do you have any actual acquaintance with the logic of the middle ages?
Take a look at Gillian Russell's work. Let me know what you think.
If logic is "rules for stringing symbols together," then these rules can either be arbitrary or non-arbitrary. If they are non-arbitrary, then logic must itself be connected to the non-arbitrary determination of these rules.
I see that Russell defines logic in terms of the preservation of truth, so that's an interesting start. "Logics are theories of validity: they tell us, for different arguments, whether or not that argument is of a valid form" (SEP). (She appeals to the Generalised Tarski Thesis to define validity.)
I'm guessing I might agree with much of what she thinks. But 'logical pluralism' feels a bit like 'situation ethics', in that it gets at something true but mixes up epistemological and metaphysical spheres. I clearly think formalized systems have significant limitations, so if "logical monism" is the view that there is some formalized system without limitations then I am not a logical monist. It's not hard to think that two different 'logics' "can be getting things right."
The next sentence is "Different logics disagree about which argument forms are valid". There is some considerable subtlety here.
Russell is playing with Logical Nihilism, rather than pluralism. https://gilliankrussell.files.wordpress.com/2018/05/logicalnihilism-philissues-v3.pdf
The picture is of an organic logic, which grows by lemma incorporation.
"Built-in" is a figure of speech, we are talking semantics. So the point is that the notion of truth is semantically built in the idea of correct inference. This holds even if we occasionally fail to process the inference or if the inference is simply valid but not sound.
Quoting Banno
Notice that the opening post takes "formalisation" to be but one approach to answer the question of "what is logic?" so we are not just talking about logic in formal systems or just formal systems.
I can get that "formal systems" do not all make explicit use of the notion of truth and false (e.g. algebra). But my claim is more radical than it appears. Indeed, I take the notion of "truth" to be so primitive and pervasive along with the notion of "logic" that I take the concept of "truth" to be built-in that of "logic" ALSO independently from ANY interpretation. Indeed, any rule-based manipulation of symbols would still have a correct or incorrect application and this necessarily equates (even if it may not be identical) to answering the question: "This application conforms to the rules, true or false?". Besides if the meaning of "logic" (classic and non-classic) is not stretched to the point of not being about propositions/sentences (in other words representations), then it is still linked to possible interpretations.
The social role of logic does bring up an interesting issue re the concept of group minds. If we take as a given that organizations can exhibit their own emergent form of intelligence, problem solving techniques, and goal directed behavior, such that organizations' goals are not merely the sum of the goals of their individual members' goals (and even cut against the goals of the individuals who compose the organizations), then doesn't the social rules of one level of organization become the "rules of thought," for the higher level entity?
No doubt many will find the idea of organizations behaving like group minds to be metaphysicaly dubious. We would need a whole thread to get into that issue in particular. I will just note that it is an idea with significant support in the realm of theories of embodied cognition and some areas of the life sciences. Ant and bee "hive minds" would be a potent example, and there is decent evidence to support the contention that the human mind itself is emergent from a number of surprisingly distinct systems. There also doesn't appear to be clear cut "levels" to group mind organization, so this would be more a sort of fractal process through which different levels of community give rise to different levels of mind.
Yes, this is the view I was getting at with approach #1, which is the most common in the study of logic itself. But I think there are obvious isomorphisms between all three definitions that are worth exploring. More on this later when I have a bit more time!
This just isn't right. It is not true that, "[T]he notion of 'truth' is built in the 'logic' rules themselves, in other words the meaning of 'truth' is determined by 'logic rules' too" ().
The notion of truth is not semantically built in the idea of correct inference. Truth is something beyond inference and beyond validity. Validity can be formally defined, but truth cannot be formally defined. Of course we can talk about "truth" qua some logical system, but this is technically an equivocation. This sort of "truth" is different from actual truth, and we do not hesitate to call it false in certain instances.
---
Quoting Banno
But they do not disagree that logic is about validity, and that validity is about the preservation of truth. So what you say here is not to the point.
Apparently you disagree with yourself. Indeed you yourself wrote “Currently our central criterion is validity, where the truth of the premises ensures the truth of the conclusions” so you determined the meaning of “valid inference” by explicitly referring to the notion of truth. If a valid inference must be truth-preserving then the notion of truth is built in that of valid inference. Q.E.D.
Again, "If something is meant to preserve another thing, then it is not building or creating that thing" ().
Let's apply your reasoning to mortuary. "A mortician is concerned with preserving bodies. Therefore a mortician builds/creates bodies. Q.E.D."
"Built-in" is a figure of speech. We are talking semantics. Let's apply MY reasoning to mortuary "A mortician is concerned with preserving bodies so the notion of 'body' is semantically built in the notion of 'mortician'".
The contention I criticises was that logic consists in the preservation of truth.
I pointed out that parts of logic do not involve truth. For example the sequent calculus consists in a bunch of rules setting out what you can write down next - or previously. Truth doesn't enter until the tack, and even then it's the false that is introduced...
A valid argument is one that follows the rules. Yes, that usually also means that if the argument is given an interpretation, truth will be preserved, but that is incidental.
I am not claiming that preservation of truth does not enter in to logic.
I'm saying that there is a difference between a valid argument and a sound argument.
For a third time now, that "contention" is a figment of your imagination. Do you think that when I spoke about the "central criterion" as validity in our current day, I was saying that logic "consists" in validity? Or that logic is "defined only in terms of preserving truth"?
Russell, on the other hand, asserts that "Logics are theories of validity..." (my emphasis). If there is anyone who thinks logic consists in validity, it is Russell, at least if we can take this general statement from her SEP article to reflect her views.
Quoting Banno
But your argument here is no good. There are rules in logic which must be attended to, but from this it does not follow that this part of logic is unrelated to truth or validity (I happen to think that logic is more consistently related to truth than validity, but your argument fails on both scores). The rules are themselves related to truth and validity.
To take an analogy, language is about meaning. Someone might say, "Ah! But when we utilize rote memorization to teach children to spell words we are not teaching them about meaning." True enough, but the whole reason we teach children to spell words is so that they can use the words in sentences and paragraphs to convey meaning. The spelling of a word is not unrelated to meaning, and the rules of a formal system are not unrelated to validity. To think otherwise would be to fundamentally misunderstand language and logic.
Quoting Banno
According to what definition of validity? Russell prefers the Generalized Tarski Thesis to define validity, and this is altogether at odds with the definition you now offer.
Quoting Banno
I think most anyone would agree with such an innocuous claim. Yet according to Russell logic is about validity, not soundness. Such is the received view, and I have not challenged it here.
Well...
Quoting Count Timothy von Icarus
Quoting Count Timothy von Icarus
Quoting James A. Weiseipl, Preface
Quoting Leontiskos
The post at https://thephilosophyforum.com/discussion/comment/834084 wasn't directed specifically at you. I was simply making a general observation; seems it hit a nerve.
Quoting Leontiskos
And again, (third time?) yes, I agree. There are bits of logic that involve truth, and bits that don't. Truth alone will not suffice to define logic.
You were making a general observation? About truth-preservation? When I was the only one who had brought up or defended the idea of truth-preservation in the entire thread? :brow:
Quoting Banno
Realizing that the analogy might not suffice, I amended that sentence to make the idea clearer, but I think we are agreed that we should be done in this thread, no? We're not going anywhere.
You weren't the only one to bring this up:
Quoting neomac
It seems like a fairly popular position in contemporary metaphysics to allow that these sorts of abstract entities, particularly propositions, do indeed exist. That is, there is a real set of all possible propositions that can be true or false, and likewise a real set of all possible states of affairs that can obtain or not obtain. Only some of these states of affairs are actualized; only some propositions are made true by the actual facts in the world. However, they all exist as abstract entities.
I am curious about this because objections against such abstract entities that I am familiar with tend to be made on naturalist grounds. Something like: how can a human being, a natural system, "grasp" an abstract entity like a proposition or state of affairs that exists outside space-time? How can language, which develops in space-time, come to accurately reflect these abstract entities?
But it seems to me that if these abstract entities are accepted, a second path opens up to seeing logic "out there," in the world, outside of minds or formal systems. Realist metaphysicians tend to assert that there are relationships between propositions and states of affairs, such that they map to one another. There is a relation between "I throw the rock at the window," being true and "the window breaks," being true, for example.
My point would be that, just as metaphysicians accept that there are isomorphisms between the set of all propositions, all facts, and all states of affairs, there seems to be other isomorphisms between how members of these sets relate to one another. And this set of relations would seem to be what people are talking about when they refer to "the logic of the world," or things like "the logic of natural selection, the logic of thermodynamics, etc.," i.e. a sort of "logos," external to mind and systems, but inherit to the way the world evolves.
These relations could be put in the form of broad propositions about how broad sets of these abstract entities relate to one another, i.e., propositions about "rules" that obtain for describing how one state of the universe will evolve into future states.
So, on the one hand I see a bridge between all three "types" of logic laid out in the initial definitions that comes from naturalism. Humans are natural systems and our minds formed by nature and our systems are formed by our minds. Thus there seems to be a way in which our minds and representational systems should map to things present in the world and be shaped by any patterns therein.
But on the other hand, if we are less inclined to naturalism and embrace abstract entities, then an abstract sort of logos seems to go hand in hand with the existence of entities like propositions, states of affairs, etc.
I suppose a thoroughgoing nominalism that takes logic to be solely a property of mind doesn't have this problem. But to my mind such ontological commitments seem to threaten a fall into radical skepticism and solipsism. On the other hand, from the standpoint of the "formalist," it seems possible to embrace a sort of epistemic nihilism and deflationary theory of truth that avoids having to assume that logic is ever anything more than a set of "games" we play, but this seems to have follow on consequences for epistemology as a whole and also lend itself to a sort of extreme skepticism.
It seems to me that a general difficulty here is that the third account of 'logic' that you give has not yet been shown to be coherent. It seems to piggyback on the Stoic or Christian idea, but "disenchanted," as you say. It is not the anima mundi of the Stoics nor the divine Word of the Christians, but it attempts to inherit and "naturalize" that concept. But again, is this really coherent? Do naturalists really speak this way when they are being rigorous and are not engaging in loose and poetic metaphor?
The crux is that there is an age-old connection between Logos and mind or spirit, and its not clear that one can take one and leave the other. What is in fact occurring, I aver, is that an entirely new concept is being introduced under an already-established word. This results in a sort of equivocation, where a new concept gets disguised in the garb of an old word, and an attempt is made to pass it off under the old concept. Those promoting such a thing perhaps do not understand how radical is their break with the traditional and established meaning.
Yes? We speak of the "law like behavior," of the universe and it is considered perfectly legitimate to rule out a scientific explanation if it suggests that nature is somehow preforming a contradiction. Work in quantum foundations for instance is largely about how to explain puzzling phenomena in a manner that is consistent and doesn't admit contradictions.
When there are references to the "logic of natural selection," vis-á-vis evolutionary game theory we mean to say that logic of our simplified models "maps onto" nature, that there are isomorphisms there, not that the logic is something "we create in order in our mind to make an orderless process out in the world comprehendible." In the physicalist, naturalist view, our ability to "make sense," is after all, the product of nature, in no way suis generis. This is why biology admits both "functional," and "adaptive," explanations as distinct types of causal explanations in its field.
I've read enough biology and philosophy of biology to feel fairly confident in saying that talk about the logic of selection is about morphism between our model and how nature is in-and-of-itself. Physics is less clear on this. QBism for example punts on such an assertion, but many theories in quantum foundations are saying that our mathematical formalism is mapping to nature, that nature embodies this formalism.
The concept of Logos is problematic not only for its spiritual connotations and connotations of intentionality (the idea that nature is not teleological is a bit of a dogma in naturalism today) but even moreso because it implies that any order in nature is enforced externally, say by eternal "laws of nature," that exist outside nature. This isn't popular due to Hume's "problem of induction" and Kripke's essentialist response. We generally now think that nature has the properties of order that it does because of what nature is, or because of what natural entities are. That is, the "logic" of state progression in nature is intrinsic, not extrinsic. But this in no way means that the order doesn't exist outside the mind, it simply means that such an order is inherit to nature because of what nature is.
Any ability we have to recognize such patterns and develop logical systems is itself the result of natural causal interactions. Further, while logical systems have "contrived, mental sources," writ large natural language, and the logical explanations it allows, is an evolved capability in hominids that appears to have likely predated homo sapiens. Further, language itself, and maybe even the sciences arguably appear to advance due to the same sorts of dynamical processes that lead to biological evolution. This isn't particularly surprising given how the same mathematics can describe such a wide range of phenomena in complexity studies; the world seems to display a sort of multiscale fractal recurrence in causal patterns.
Okay, I think that's accurate.
I think the Logos idea has to do with the whole, whereas the idea that you've been focusing on has to do with subsets of the whole, "isomorphisms between how members of these sets relate to one another" (). Then there is the other question of the
So let's look at how Merriam-Webster defines logic:
[/list]
[/list]
[/list]
[/list]
[*]1b
[/list]
[/list]
[*]1c: Interrelation or sequence of facts or events when seen as inevitable or predictable
[*]1d: the arrangement of circuit elements (as in a computer) needed for computation
[*]2: something that forces a decision apart from or in opposition to reason
[/list]
Now let's subdivide your third definition:
Quoting Count Timothy von Icarus
Interestingly, there is no correlate in Merriam-Webster (MW) for 3(a). I think this is right. Logos and logike are two different things. 3(b) maps to MW-1c. I think the idea about isomorphisms between mind and reality is implicitly related to MW-1a(1), MW-1a(4), and MW-1b(1). This idea is implicit in science and phusis, especially Aristotle's "form or source of motion" vis-a-vis phusis. To speak about the "logic" of natural selection is to speak about the nature (phusis) of natural selection.
The other central question is the question of what exactly you are asking or aiming to do in the OP. Apparently you are trying to understand how the various different usages relate to one another, no? We must inevitably ask what methodology is being presupposed in responding to this inquiry. But I will leave this for another post.
It seems you are suggesting 3 alternatives: naturalism, platonism, or nominalism. But I don't think these alternatives are the only ones available. I think that Wittgenstein offered a distinctive philosophical approach which is reducible to none of such alternatives.
Quoting Count Timothy von Icarus
Then the link between nominalism and radical skepticism or solipsism should worry naturalists too. Quine was both naturalist and nominalist. Wilfrid Sellars too.
Quoting Count Timothy von Icarus
Take a deduction like Premise1: "If Trump won the 59th presidential elections, the earth is flat", Premise2: "Trump won the 59th presidential elections", Conclusion: "the earth is flat", how do you figure such mapping?
Logic are necessary conclusions, when we say that something is "logical" we say that it follows from the information we have available, while non the less expressing that information in a way that were different from the way that information occurred to us initially by application of dualistic concepts (non of which are abstracted from experience) in our major premise such as "all/some".
It is impossible to know that something follows (as a conclusion) from the information available without also knowing at the same time that something else would not or that it did not have to before we concluded so.
In other words, logic are the reversed order of subject -> predicate, constituting the ongoing falsification of the predicate by the plurality of subjects experienceable or thinkable in existence. One posits a predicate, a fireman, it may be preceded by an experience or from imagination, and it is then either affirmed or denied by the pattern that is recognised in the subject a moment later.
Everything is possible until it is necessary, and both these concepts are contingent on the concept of negation, and negation contingent on the disjunction of plurality of experience, as in derived a posteriori. Logic precedes that of which there is formal systems, or of which there are the field of "Logic" the same way physics precedes everything ever thought in the field of physics.
Inductive systems are no different, they are wholly downstream of deductive ones, the only change is that predication takes an extra step or that the subject becomes our own ideas (the realists imagines that the precise opposite happens), which is to say that whether someone is a fireman or not is not known by him merely wearing the uniform, but whether we have reason to believe it is known, which in turn is another way of saying that all we have is knowledge, the propositions we have imagined for ourself by means of that knowledge are exactly that: fictions of our imagination, we create the non-knowledge by allowing (though really perpetuating) propositions to refer to something that does not correspond to experience, this is the invention of "truth" and though it seems to be irrelevant to the precise topic discussed I ended up here because it follows directly from analysis of logic.
Quoting Julian August
This take on logic sounds more compatible with Analytic than with recent Continental approaches. Re your analogy of logic to physics, for many continental philosophers there is the field of formal logic, and there are the more general presuppositions grounding this formal field, which limit it to subject-object propositions generating necessary relations of truth or falsity, negation or affirmation. But there are more fundamental logics which are not propositional in nature.
(Can’t believe it took three pages for someone to say that.)
It is hard for me to imagine away the behaviour of my own which characterises my whole life and appears to characterise everyone I have ever come in contact with, yet this is that I am asked to do by people who says that my thoughts can be empty of truth value.
Thoughts could hardly do anything besides appear a) in a way they did in my past or b) appear in a way they never before did to me, and in either of these cases, say a bus in the former case and a bus with unicorn-wheels in the latter case, I would as a thinking subject know that I am distinguished from these thoughts and that they thereby fail to predicate me.
In other terms: nothing human appear to ever happen in absence of instantiations of the concept of negation, regardless of whether external objects of phenomena were present, what would it even mean to say that a logic could be composed of modalities and quantifiers to the exclusion of truth-values if all examples of either are involved in the process of negating the self with which they come conjoined?
https://www.marxists.org/reference/archive/hegel/txt/system2.htm
Hilbert said, "Mathematics is the art of giving the same name to different things." This applies to all of logic, as does its opposite. For logic is also the art of giving different names to the same things, and in a sense, these two actions are the same.
For my definition of logic, you'll have to wait for my magnum opus, if it ever comes.
Is this a riddle?
Above point tells us Logic is not just simple symbolic formula manipulation.
Some people (not the OP) seem to think Logic is just a bit of formulas which has no content, and it cannot describe the reality. I feel it is too narrow and restrictive view of Logic. Logic is the way how the world and universe works, and how our reasoning and intuition works to discern right from wrong, the valid from invalid etc.
For instance it is a logical phenomena that it is likely to rain under the low pressure and high humidity in the sky. It is a logical statement describing a phenomena in nature.
I am conscious of myself, therefore I exist. Being conscious means, by necessity, having the conscious being. This is a simple psychological logic based on the deductive reasoning describing how the self existence is deduced and proved.
If Age >= 20, then the client is an adult.
Writeln "OK, you are allowed to buy the ticket"
Do Issue Ticket
Print Ticket.
End.
This is a simple computational logic in computer programming algorithm snippet showing how the applied logic can work describing adult (set age >=20), and then picking out adult members in the business clientele.
They are at the very heart of the development of digital computers, such as the one you're reading right now.
Seems you're conflating Hilbert with Poincare.
Quoting TonesInDeepFreeze
What Corvus should have said is that they are not very good at cognizing in the way living systems do, as Hubert Dreyfus famously showed 60 years ago with his ‘What Computers Can’t Do’ and his more recent update ‘What Computers still can’t do’. Of course they are a part of the real world. Specifically, as technological
implementations they function as appendages to human ecological systems , the way a nest belongs to the bird’s ecology and the web belongs to the spider’s built niche. While an animal species are stick within a single ecological niche, humans continually construct new ones. As we evolve culturally, so will our built niche, which may involve the replacement of symbolic logic with different technological languages.
Without comment on the specifics, I think that's a pretty good perspective.
I'm a bit more cautious about that. It seems like the die is already cast on logic generally referring to formal systems in philosophy. I was searching around for a good term to refer to the idea of "what we use logic to describe in nature," but I haven't thought of a catchy one.
"Logos" has a nice ring, but it's quite pregnant with mystical and theological connotations, and I don't necessarily want to imply all of those.
Sure, logic must be the working engines of all the computers and even AI agents suppose. But there would also some custom logics they set up, and embed into the programs in the devices depending on what they are used for. It wouldn't be just the plain classic symbolic logics only in use.
Yeah, that was written sometime ago, when I knew little about logic. Since then I have read a few different logic textbooks, which totally changed my ideas and views on logic.
The traditional classic logic wouldn't be able to deal with the dynamic and unpredictable nature of the real world. From quite some time ago, various types of non classic logics seem to have been implemented, and used such as Temporal Logic, Description Logic, Fuzzy Logic, Epistemic Logic, Many-Valued Logic, Probability Logic, Topological Logic, Assertion Logic, Deontic Logic ... etc to deal with the dynamics of the real world.
The world does not depend on logic. Our understanding of the world (which is semantical) is improved through valid logic. If we were omniscient, logic would be pointless.
Right.
Quoting Corvus
Ordinarily, 'classical logic' refers to any of the equivalent formulations of predicate logic, in first or higher orders, with the ordinary features such as excluded middle, non-contradiction and explosion.
Advancements have been added to classical and non-classical logic, such as modal logic, temporal logic, etc. And some advancements may be incompatible with classical logic, such as multi-valued logic, relevance logic, paraconsistent logic, etc.
It is of course granted that predicate logic is not adequate for all forms of inference. However, that does not vitiate that predicate logic (and even just sentential logic) is useful.
Note also that I replied to a claim about formal, symbolic logics. And such things as temporal logic, deontic logic, fuzzy logic, etc. are given as formal, symbolic logics, even if they may also be studies informally. So their uses does not vitiate the point that formal, symbolic logic is useful, since they are themselves formal, symbolic logics. And usually an intellectual prerequisite for study of those advanced logics is an understanding of plain vanilla predicate logic. Moreover, as far as I've seen, set theory may be a meta-theory in which those advanced logic are studied, which is to say that in set theory we may formulate those other logics and prove theorems about them.
Classical logic is useful, even just in its sentential component, which is the Boolean logic used in ordinary computing, and further as classical logic is the logic for the ordinary mathematics for the sciences and for the study of recursive functions and the theory or computability that are at the very heart of the invention and development of the digital computer. And, while predicate logic cannot account for all forms of inference, predicate logic is usually prerequisite for study of the more advanced logics.
Whether or not mathematics is a subset of logic, it is decidedly not the case that mathematics is only about quantity.
Good point. Yes, I agree with that. Classic logic is very useful in checking out logical validity and soundness in the spoken languages and written documents. It is also the foundation of all the other non-classic logic too. One must learn classic logic first in order to understand all the non-classical logics.