What is logic? Simple explanation
Hi, I've been asked this simple question before. The main reason I make this topic anyway.
Well, what is logic? If you have 1 smartphone and you get 2 more smartphones, you now have 3 smartphones! That's logic. And that's also how people are trying to explain the world/life itself. Religion in the other hand is based on belief. Example: I belive that 1+2=a bolt of lightning.
Right? :chin:
Well, what is logic? If you have 1 smartphone and you get 2 more smartphones, you now have 3 smartphones! That's logic. And that's also how people are trying to explain the world/life itself. Religion in the other hand is based on belief. Example: I belive that 1+2=a bolt of lightning.
Right? :chin:
Comments (95)
Combining and paraphrasing these definitions, logic is the normative science of how one ought to think if one intends to pursue truth; i.e., adopt belief-habits that would never by confounded by subsequent experience.
Logic is an expression of the laws of nature (or the laws of life/existence, however you choose to define the components of reality).
1 + 2 = 3/a bolt of lightning, is not precisely logic. Mathematics is a language that attempts to apply logic to its mode of operation. But, it is only logical in the sense that language is a logical part of communication/expression. For example, an alien unfamiliar with our mathematical language would not know that 1 + 2 = 3 unless the values of the numbers and their association are taught to them. The alien may have their own way of expressing the same relation but it may be a different language than our mathematics. The mode of operation tries to express an already existing relationship (let's call it, 'the process of cumulation') in existence/life. Mathematics didn't invent 1 + 2 = 3, it just realised the validity of it. That validity comes from logic.
Quoting aletheist
I take these two descriptions of logic as somewhat opposed. Andrewk appears to say that logic is innate, something which we do instinctually, while aletheist seems to say that logic is a behaviour which we learn, as in other cases where we learn how we ought to behave. Or am I missing something here, a principle which may establish compatibility between the two perspectives?
No, I agree that the two definitions are incompatible; @andrewk seems to be saying that logic is the science of how humans do think, while I (following Peirce) hold that logic is the science of how any intelligent beings should think, if their purpose is to arrive at true beliefs by learning from experience. This is similar to the distinction that Peirce drew between logica utens, instinctive and uncritical habits of inference, and logica docens, deliberate and rigorous habits of inference. Logic has to be a normative science if there is good reasoning vs. bad reasoning, which I hope no one in this forum would deny.
That's part of why I approach logic as something we do, rather than something we ought to do. Like Hume, I ask, 'whence comes the ought'?
Please elaborate on this assessment.
Quoting andrewk
Which is a myth. As Peirce observed, "The validity of Induction consists in the fact that it proceeds according to a method which, though it may give provisional results that are incorrect, will yet, if steadily pursued, eventually correct any such error."
Quoting andrewk
Like I already said, it comes from having the purpose of arriving at true beliefs by learning from experience.
There appears to be something confused here. Isn't the point of formal logic to go beyond the limits of experience, to learn about things which we cannot experience? Perhaps we need to differentiate between the logical which comes to us naturally through instinct, and this is where I would class inductive reasoning, from formal logic, which is what we are taught.
I think specific forms of logic, like induction come to us naturally, but we are taught not to rely on these types because we have learned of their fallibility. That's why we have developed, and teach forms like mathematics, and deduction, which produce a higher degree of certainty.
Quoting aletheist
I agree with andrewk, inductive reasoning is problematic. The solution you state here is nothing more than trial and error. Sure, trial and error works, but it's not a reliable form of logic. "Learning from experience" is trial and error. Formal logic, I believe is grounded in principles not derived from trial and error.
"The trouble with treating logic as normative is that the claim of normativity requires the use of logic, so it becomes circular. "
— andrewk
Please elaborate on this assessment.[/quote]
Try to mount an argument that we ought to use logic if we wish to arrive at true beliefs, without using logic.
I never claimed that we ought to use logic if we wish to arrive at true beliefs, I defined logic as the science of how we ought to think if we wish to arrive at true beliefs. I also acknowledged that we have instinctive and uncritical habits of inference, but distinguished them from our deliberate and rigorous habits of inference. The latter are the subject matter of (normative) logic, which recognizes that there is good reasoning and there is bad reasoning.
I don't understand whether this is referring to discovery of logic or application of logic. Is this referring to
(1) identifying the best way of arriving at true beliefs, or
(2) taking on faith that FOPL is the best way, and for you 'logic' refers to the application of FOPL?
If it's (1) then how can the identification proceed without logic? How can it be determined which method is the best?
If it's (2) then it is simply a declaration of faith in FOPL. That's fine, but faiths are not normative, as we see by looking at religions.
Isn't that what the normative principle amounts to (or something similar)? It's precisely because mounting an argument without the use of logic is impossible by definition that such guiding principles cannot be anything other than normative.
I think that the problem is in how one defines "true beliefs". If we define truth along the lines of "what logic provides us with, then we are just begging the question. If we define truth along the lines of that which experience gives us, then logic is not the provider of true beliefs, memory is.
Aletheist, following Peirce, appears to be trying to conflate these two distinct, and somewhat opposing notions, of what provides us with truth:
Quoting aletheist
I would caution against following such a principle because premises which are unclear and confused, as this one is, will produce conclusions which are even more confused and unclear.
What is clear, I believe is that we need to distinguish between the products of experience (sensation, memory, etc.), which we know as extremely limited, and highly fallible in any attempt to extrapolate beyond the range of what was immediately sensed, and the products of logic, which give us a broad range of application, with a high degree of certainty. We can place inductive reasoning as intermediary between these two, sharing in the fallibility caused by the extreme restrictions of the empirical, but also giving us a higher degree of certainty than simple memory and sense experience, in application.
The point being that the basic "experience" can only provide us with knowledge of the particulars to which one has been exposed. But in practise we apply this knowledge of what has been experienced, toward the unknown (in the sense of that which has not been experienced). This requires something, "logic", which we must, through effort (and normative means), separate from experience, in order that it may do what it is intended to do, and that is to bring us beyond the limitations of experience.
I am talking about the study of logic, which is basically your (1), and generally agree with . We employ our instinctive reasoning habits (logica utens) all the time, with varying degrees of success. We develop our deliberate reasoning habits (logica docens) for the purpose of reducing error and ideally (but never actually) arriving at a set of beliefs that would never be confounded by subsequent experience.
Quoting andrewk
I am talking about logic in a much broader sense than FOPL, including not only deductive reasoning, but also retroductive and inductive reasoning. It further encompasses the combination of these that serves as the scientific method - formulating explanatory hypotheses (retroduction), explicating their necessary consequences (deduction), and experimenting to ascertain whether they are falsified by experience (induction). All of this depends on the theory of signs and their relations, which also falls within my (and Peirce's) broad conception of logic.
Would the following be a reasonable representation of your claim?
We ought to use logic if we wish to acquire true beliefs because, reasoning according to my instinctive reasoning habits, which I believe to also be the instinctive reasoning habits of almost all humans, leads me to conclude that it is the only reliable way to develop true beliefs.
Again, normative logic is not something that we use, it is the study of how we ought to think if we wish to acquire true beliefs - i.e., how we can deliberately improve on our instinctive reasoning habits, which is all that we have at our disposal initially. Peirce recognized four specific methods of inquiry - tenacity, authority, a priori, and science. Each can and does lead to true beliefs under the right circumstances, but only the method of science - consisting of retroduction, deduction, and induction, in that order - has self-correction built into it. It is not the only reliable way to develop true beliefs, but it is the most reliable way, given our inescapable fallibility.
Good question. I have never had a clear idea of what people mean by normative, and looking up definitions doesn't seem to help. The definitions don't seem to align with the many, varied ways in which people use the term. The only common feature seems to be that there's always an 'ought' in a normative belief, but the ought could be instrumental (we ought to do X if we want to achieve Y) or absolute (we ought to do X, full stop).
What seems like a likely candidate for a common accepted meaning is that a belief is normative if we belief that almost everybody holds it. This has the troubling consequence that a belief that slavery is wrong - something that seems so important and fundamental to us now - is not normative because in so many cultures slavery has been unquestioningly accepted.
Perhaps something a bit stronger. We could say a belief is normative if we believe that nearly all people, in nearly all practically likely circumstances, would hold that belief. With that definition, I think we could say that a belief that logic is the best way to arrive at true beliefs is normative, but we couldn't say that a belief either in the acceptability or unacceptability of slavery is normative. Further, it doesn't seem to be too much of a stretch from that to say that people 'ought' to hold that belief, if one's prepared to take a pragmatic sidestep of Hume's 'ought vs is' guillotine. Indeed, the 'ought' becomes a simple observation of what we believe to be the case.
What do you think?
As should be clear from my previous comments, when discussing logic as a normative science, I mean it in the instrumental sense - we ought to think in a certain way if we want to adopt true beliefs. Going a step farther, I suggest that we ought to adopt true beliefs if we want to avoid unpleasant surprises in our future experiences.
It was never in question that that was your belief. What I am interested in is what you mean by the 'ought'. My current hypothesis, based on my immediately previous post, is that you:
Quoting andrewk
Does that correctly reflect your position?
Not quite; more like: If an infinite community were to engage in infinite inquiry, using any and every method along the way, their ultimate consensus would be that the scientific one - retroduction, deduction, induction - is the most reliable way to arrive at true beliefs.
Quoting aletheist
His distinctions are fine, but incomplete. My take is that there are three especially interesting aspects of logic (I'm ignoring the aspect of how logic is taught and folding that into the norms logic for simplicity):
Normativity of logic: How ought we reason?/What are the correct rules for reasoning. The views of what are the correct logical norms have demonstrably over time (e.g. Classical logic invalidates some of Aristotelian logic and adds what the old logic lacked). This isn't very surprising.
Logical Consequence: Given a set of axioms and inference rules, what theorems can be derived? This is, essentially, what's meant by "logical possibility", it's relative to whatever formal system you're using.
World Logic: Following Pierce, you might call this logica ens, logic itself. It's somewhat hazy but basically it's the logic of the world. It's related to logical consequence, but it's really about the underlying mathematical structure of the world which could be mapped to some specified logic. Sometimes you'll see logicians say something like "In a world governed by Intuintionistic logic, x, y, z would be the case". It's that, what actually follows from what in the actual world.
But logic certainly isn't just normative and to think so is contrary to most of the professional work done in mathematical logic. Sometimes I just want to explore the derivations of some logical consequence relationship. That does not entail I'm asserting we ought to in general reason according to the principles of the logic I'm exploring. That's just mistaking practical reasoning advice with a mathematical calculation.
I agree, but I can see how I might have given a different impression above. Charles Peirce, following his father Benjamin - one of the most accomplished American mathematicians of the 19th century - defined mathematics as the science of reasoning necessarily about hypothetical states of affairs. As such, it includes mathematical logic as distinct from and more fundamental than normative logic. However, deductively ascertaining the consequences of a particular set of postulates does not reveal anything about reality, unless those postulates turn out to be consistent with reality - something that we cannot properly investigate without normative logic.
But I don't think that's right. If I take some arbitrary logical system and work out what follows from what in that system, I am not reasoning about hypothetical states of affairs. I'm simply investigating the properties of the relationship between particular abstract objects. I mean, just take fuzzy logic. I personally don't care for it, but if I were taking a look at the formalism and just did proofs for shits and giggles, that wouldn't be reasoning about hypothetical states of affairs because I don't think the idea of "fuzzy" states of affairs would be coherent in a metaphysics regarding the physical world. I'm just doing math at that point.
If you're defining logic principally as normative, that cannot include mathematical logic as it is easily possible to divorce that entirely from how one thinks one ought to reason. Reasoning can be made more rigorous by adopting a logical formalism, by adhering to a logic, but that doesn't mean the two are the same. Doing logic is not to pick out a type of reasoning as the correct kind.
That is precisely what Peirce and I mean by "hypothetical states of affairs" as the subject matter of pure mathematics - there is no connection (purported or otherwise) with reality as the subject matter of metaphysics.
Quoting MindForged
That depends entirely on what we mean by "doing logic."
OK then I think referring to them as "states of affairs" is inappropriate then because that term is generally used to refer to various aspects of reality, not to the relations of abstract objects. It would sound very... queer to talk about the "state of affairs of the number 2".
Quoting aletheist
Just doing logical derivations, exploring some specified consequence relation. Doesn't commit you to thinking the rules guiding those derivations ought to be the same rules you adhere to when you reason.
I would define a normative belief as one that directly justifies and urges or inhibits action or conduct. It says "You should do this," "This is the right way" or "That is the wrong way." A normative principle is a generalization of such beliefs. When I say "directly" I mean that the normative belief does not acquire its normative status in virtue of something else. It doesn't tell you that you should do this or that for reasons, because if there are other reasons, then they are in turn the source of normativity. Normative beliefs are where reasons bottom out.
The condition that a normative principle applies not just to oneself, but to everyone is a contingent, non-essential property of normative principles, I think. Normative principles are often, but not always universal. Moral relativists typically believe that the force of moral principles is limited to a particular culture or community. Jews believe that their religious strictures apply only to Jews (there are a few Biblical prescriptions applicable to gentiles as well, known as Noahide laws). Personal obligations and vows have force only for one particular person.
I realize that all this is somewhat vague and squishy, and will fray and crumble at the edges when subjected to scrutiny, as analytical philosophers especially like to do. But that just means that the concept of normativity is not simple, clean and sharp-edged, which is to be expected for a concept whose nature is psychosocial.
Yep. It's what is sayable, not what ought be said.
But on the other hand, if you have 1 raindrop and you add 1 more raindrop, you still have only 1 raindrop.
There's a bit of selection in what you talk about.
An example of what can't be said.
He just said it. Just because moving your queen in a square isn't allowed doesn't mean you can't do it.
Quoting frank
Just as in performing an illegal move, on ceases to play chess, one fails to make a move - so @Limitless Science failed to say anything.
Trivially, it is possible to adopt the Humpty Dumpty Argument so that any given statement can mean whatever you want it to. Is that the way you want to go, @frank?
Limitless can make the noise; but what has he done, apart from that? What use is "I believe that 1+2=a bolt of lightning"?
Quoting aletheist
This is the view I am rejecting, Frank.
Suppose I argued that your view on, say, abortion is wrong because your mother wears army boots.
@aletheist seems to think (and doubtless I am wrong here, but it will serve) that the appropriate reply is something like "one ought not make such conclusions", as if an ad hom argument were a bit rude, subject to the same sort of rejection as "one ought not pick one's nose in public".
I don't think that is enough. It's not enough to say an ad hom argument is a bit rude; it is also plain wrong; the conclusion does not follow from the premise.
Logic does not just set out how we ought speak, but how we can speak. It shows us what sorts of speaking are wrong.
You think you are saying something different, but you are not. You just understand "normative" in a narrow ethical sense.
So is it propositional speech that's bounded by logic? If so, that leads to my concern: that logic has something to do with the way the world is.
Is speech a subset of the ways the world works?
Propositional and predicate logic are certainly about propositions...
Quoting frank
Language is about the world; logic is about language; so yes, logic has something to do with the world.
I don't see the distinction you are trying to set up. If something is wrong, you ought not do it, and if you ought not do something, it is because it is wrong. If murder is wrong, you ought not do it. If picking your nose in public is wrong, you ought not do it. There is no division here, between things which are wrong, and things which we ought not do. To imply such a division is to speak nonsense.
Quoting Banno
If and only if it is wrong, one ought not say it. By your principles, you have said here what you cannot say. There is no such thing, by way of contradiction, as what one cannot say, because to identify it as 'the thing which cannot be said' requires that it be said. The sorts of speaking which are wrong are those which we ought not engage in, but this says nothing about our capacity to speak them.
I don't want to be awkward, dismissive or negative, but that's arithmetic, my friend, not logic. :chin:
I find that oddly reassuring...
Here's the problem with the assumption that there is such a thing as what cannot be said. You can assume such a thing, just like I can assume a square circle, but these assumptions don't make these things real.
Logic is developed from the intention of allowing us to know everything. That is the will of the philosopher, the desire to know, and this means everything, without exception; all is to be placed in the realm of knowable. We cannot designate anything as unknowable because then we'd lose the will to know it, being already designated as unknowable. To say that there is something which cannot be said is to say that there is something which cannot be known, and this is contrary to the first principle of philosophy, which is to render everything as knowable.
Therefore nonsense statements, as in the example, are sayable, and also knowable, but they are known as nonsense. And your claim that some things can't be said is also knowable as nonsense.
Logic has something to do with propositional language, not all language.
Propositional language is unusual in that it can be spoken by the great third person. In a sense, it is the world's voice.
I don't think FOPL really captures the intuitive reasoning we're drawn to either, I don't any logic does. That's why people get tripped up by things like the material implication paradoxes or find "ex falso quodlibet" strange, because they don't map onto how we actually reason. FOPL is really, I think, about capturing a certain type of mathematical reasoning, as that was explicitly why Frege created it.
And...?
So when we come across something illogical, we have said it wrong, and look for a way to say it right.
Logic is not telling us how the world is, but how we can talk about the world.
The results of the double slit experiment appear to defy logic. Who misspoke and what did they say?
They are described using the appropriate equations. The language was adjusted to the world, not the world to the language.
I don't seriously think you disagree with me on this.
Quoting frank
https://arxiv.org/pdf/1508.00001.pdf
The article was cited by @StreetlightX in a recent thread.
Have a look at the section on Linear Algebra. Note:
The language that describes the odd quantum world was created for that purpose.
‘What we observe is not nature itself, but nature exposed to our method of questioning’ ~ Werner Heisenberg.
Or do you think his comment was targeting something less mundane?
That's cool, but it doesn't diminish the fact that the double slit experiment appears to show a contradiction. A mathematical expression of the situation doesn't change that. Quantum theory is made of multiple attempts to explain what's happening, none of them entirely satisfying.
You had said that if we encounter something illogical it's because someone said something wrong. I was trying to identify that wrong statement in the context of quantum experiment.
I see. Well, in this case, I suppose it is you - if you claim that the double slit shows a contradiction. But you included "appears" to avoid that.
As a rule of thumb, if a philosophical question becomes tied down in QM, it's gone up the garden path.
So you support some proposition X that logically explains things. Reaching out for that unexpressed proposition is like trying to hear the world's truth: that third person information that resolves the trouble.
You believe that logic tells us how the world should be. Admit it! :death: its almost Halloween! Do you guys do Halloween?
The mysteries surrounding quantum experiment haven't been resolved. There is no consensus among scientists about how we should think about it. If someone gave you the impression it's otherwise, you were misled.
In fact, Lawrence Krause has suggested that at some point in the distant future, all of our present theories may be found to be primitive and laughable.
If you insist that the relevant truth must be logical, you demonstrate faith that logic tells us how the world should be, not simply how we should speak.
The capacity of consciousness to relate two or more of its contents and perceive their relationship.
It's a bit more general than andrewk's and makes no reference to brains. We're a bit obsessed with brains. I'll make a topic about that when I get a mo I think.
Now you're catching on. It is not a case of "we cannot say it", but a case of "we can say it wrongly". Forget about that claim that logic dictates what can and cannot be said. It's completely unreasonable.
This is a good example. Wave/particle duality is contradictory. Energy can move from one place to another in the form of a wave, or it can move as a massive object. The same energy cannot move as both, that is contradictory, therefore illogical. Since logic dictates the correct and incorrect way of speaking, we can conclude that this is an incorrect way of speaking. This description of that phenomenon is incorrect.
SO you are suggesting we adopt a theory that is inconsistent? You sure about that?
No. I'm noting that you deny that illogical statements can be true. Therefore you think logic tells us something about the way the world is.
...anymore than they can be false.
You can see that there is a bit missing from your argument.
Whether an illogical statement can be truth apt is an interesting question. Probably depends on how we want to handle truth. Ordinary language-wise, I dont see a problem with saying that "The fox is both red and not-red" is false.
Other cases of illogic might be treated as non-truth-apt.
Well that about captures what I might've said, only better, so I don't need to bother. :smile: :up:
Making sense presumably means being the subject of some sort of discussion...
So saying that the world makes sense is just saying that we produce sentences about it that cohere.
That's about the sentences, not the world. If the world were other than it is, we would presumably use different sentences...
The simultaneity polydynamics of the movement (Reproduction/Feed/Reasoning) generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
The simultaneity polydynamics of the movement (Reproduction/Feed/Reasoning) generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
Didn't you say that illogical statements make no sense? Then is it not per you that "making sense" means adhering to logic?
Does that, for you, imply that the world is in some way restricted in how it can and cannot be, by logic?
Because that's not my claim. If the world were different to how it is, then we would have adopted a different logic, one suitable for that world.
Our grammar can change to match the world.
As if logic is a puppet master? No, I wasn't suggesting that. I thought you were saying that non-logical language is nonsense and non-truth-apt. I was asking if we could therefore conclude that the world can't manifest a lack of logic.
Quoting Banno
What's the basis for these assertions?
A non-logical language - a language without a grammar? How could you recognise a non-logical language, as a language?
The world doesn't manifest logic. We make logic to manifest the world.
They are part of a description of what language is.
I don't know. Did you not say that non-logical statements are nonsense?
Quoting Banno
I don't think I have the experience of either making logic or manifesting the world. What am I missing?
Quoting Banno
That if the world changed, our logic would change? How is that a description of language?
If it's possible to witness illogical language use, then it has to be prescriptive. Since "X and not-X" is clearly illogical, it would appear that you must be talking about prescriptive, governing rules.
True?
If it's a duck, then it's not a rabbit. If it is a rabbit, then it is not a duck.
So is it both a duck and not a duck?
What could (p & ~p) say?
Only that something has gone wrong. It's the conclusion of a reductio.
As such, it might lead to the conclusion that one of our assumptions is wrong; or, it might lead to the conclusion that our way of setting out what is going on is muddled.
Do we change our spelling to fit the word, or the word to fit our spelling? Is the direction of fit spelling-to-word or word-to spelling?
Neither your question, nor mine, are sensible.
Spelling rules are prescriptive. :brow:
I'm struggling to get some concepts straight. I need more percolation.
If you're associating a lack of logic with malfunction, then you could be saying that rules of logic are descriptive rules of language use.
Or could you be saying they're prescriptive and the enforcement is a communication breakdown?
Fit doesn't have to be restricted to word and world. We can look at rule-to-world, world-to-rule, world-to-telling and so forth.