How do we justify logic?
I just saw a video on youtube on the why of logic as in how one justifies one's belief in the system of logic as the correct method of thinking.
1. It claims that to question logic is, itself, to be logical and therefore all criticisms of logic already subsume the principles of logic - we are looking for reasons to justify our doubts about logical authority.
2. Others claim that to justify logic is to, again, assume logic's authority. This, they allege, is a circularity and therefore logic has no justification.
So, it appears that we can neither justify nor critique logic. Both are circular.
I feel like Buridan's ass right now.
Please help...Thank you
1. It claims that to question logic is, itself, to be logical and therefore all criticisms of logic already subsume the principles of logic - we are looking for reasons to justify our doubts about logical authority.
2. Others claim that to justify logic is to, again, assume logic's authority. This, they allege, is a circularity and therefore logic has no justification.
So, it appears that we can neither justify nor critique logic. Both are circular.
I feel like Buridan's ass right now.
Please help...Thank you
Comments (95)
That said, logic is not a form of omniscience. There may indeed be many things beyond logic, or for which logical analysis is unsuitable. But insofar as it is real, then the law of the excluded middle, or the law of identity, don’t need further justification - they simply are, they’re what Frege would regard as ‘primitive elements’, like natural numbers. If you ask why one and one equals two, the response can only be: just is so.
Indeed. There must be some stuff out there in this universe or, may be, even inside our minds that transcends logic. Hyper-rationality (not irrationality) is a possibility I'm willing to admit.
Quoting Wayfarer
What about [two]? The problem still continues. May be we can make a choice which argument to accept. Both being circular and equal in all respects, one is left in an impasse. Can you come up with an analogy to better understand the situation?
I see a way out though. Whether it's legit or not you can decide...
The circularity of both attack/support logic prevents us from seeing the beginning. I guess that's where the action started and that's where we'll find the answer.
So, what was/is the beginning of the circularity?
It begins by questioning the authority or, more accurately, the rational basis of logic. In other words, one begins the circularity by questioning the validity of logic. To attempt to justify logic is also to begin from the same point - questioning the validity of logic.
We could say that we begin by throwing doubt on logic in either case whether we try to justify logic or to criticize logic. Am I right?
If I am right then it is clear that we begin not by attempting to justify logic but by attacking it. However, as I've just shown in the OP that isn't possible because it is self-defeating.
Therefore, logic can't be criticized because that's a self-defeating process.
Imagine a method x that is used to find truths. Now how does one know x is a truth? We would have to use, which is our situation, x to judge x. That would be circular yes but the problem began by questioning x using x itself and that is self-defeating.
Is it like, 'how do we determine that logic is logical?' I guess I don't know. Perhaps it depends with perspective. Then again, if that is so, it becomes subjective. Can logic be identified with either objectivity/subjectivity or does it encompass both?
Quite the head-scratcher!
You may consider it a working presumption, if you like, which enables all kinds of things, including our talk.
Its justificiation lies in its use. It enables us to better understand the ramifications of what we say, and spot for instance contradictions in statements we make because of the law of identity.
I guess denying the law of identity would make even the simplest discussion impossible.
What of justifying logic as the authority among truth-finding methods? How does one do that?
Perhaps self-justification isn’t wrong as such. I don’t know.
Quoting BrianW
What then justifies the validity of the path? Why believe in logic? Per logic we should withhold belief unless we have good reason.
If this were true, then deductive arguments would have no application in empirical science.
However, deductive arguments do apply to empirical science.
Therefore this is not true.
That it relates/connects to truth/reality is the justification/validation.
Perhaps. I see logic as well-structured language. So introducing conjunction, disjunction, negation and non-contradiction as formation rules gives us the capacity to reject arguments that do not lead to further disclosure. That is, formation rules express a preference for one sort of language over another; for language that works better.
Given that we choose the grammar that works better over other grammars, its not that remarkable that we have a language that works.
Hence language and logic are inseparable. Pretty much the same thing, really.
And hence induction is not a logic; it's not a set of grammatical rules.
And hence we can find other logics, such as the various modal systems as choosing other grammatical systems that can be accepted or rejected in terms of how well they work.
Quoting Wayfarer
Your argument is valid, but not sound because the first premise is not true :-).
Empirical sciences work with language too, so i don't see how it follows that deductive arguments wouldn't apply to it if logic were only about language.
Buridan's ass was prey to indecisiveness that - hypothetically - caused it to starve.
Do you think that your opinion on the topic in the OP will cause you to starve?
Are you seriously considering abandoning the use of logic? If so, how would you go about doing that?
If not, why do you feel you need help? It seems to me you're getting along just fine.
Thank you.
It’s just that I’ve broached this topic many times (some others too) and no one has given me an answer that would give me closure.
In the beginning I thought it was just the circularity of logic justifying itself. After the video on YouTube I realized even criticism of logic is impossible as it, well, uses logic.
When somebody asks whether logic is justified or not, it is an attempt to find reasons that justify logic or to find reasons that make logic unjustified. As you can see both paths are rational i.e. logical.
Isn’t the situation hopeless? I find it so.
Language is arbitrary and is, if you truly analyze it, a matter of convention. Languages differ from place to place and time to time but logic isn’t like that. Logic is kinda universal unlike language. What do you think is the reason for this? Thanks.
Here’s a kinda-sorta “proof”:
Logic’s justification can be grounded in its ability to find truths. Basically, if logic gets to truths then that’s a justification of its principles and ergo itself.
The problem, of course, is that truth is assessed by the extent to which logical principles were adhered to. We say that a certain proposition is true because of a sound logical argument.
So, we can’t rely on how good a truth-finder logic is to justify logic.
Is there some other way then?
How about this:
Logic can be thought of as a hypothesis about how the world works. Very much like in the sciences.
This hypothesis is that The world is Logical. This should entail some predictions about our world. We then check to what extent do our predictions come true. In fact every instance of the application of logic is a test of this hypothesis.
Now we check if the predictions come true. If the vast majority (the actual truth is ALL logical predictions we’ve made so far except quantum mechanics) of our predictions come true then these serve as justifications for logic. It’s an inductive argument and short of the sound argument I’m looking for BUT it’s better than nothing right?
My inductive argument in explicit form is as below:
Hypothesis: The world is logical
The above hypothesis makes predictions
X% of the predictions are true
As you can see as X approaches 100, as is the factual situation, we get a cogent argument that justifies logic.
Logic does not strictly speaking 'find truth', it's truth-preserving. It's about making good arguments that preserve the truth value of the premises. A good argument is valid. A sound argument is a valid argument which has premises that are true. To determine the truth of the premises you do not use logic itself, you go and verify them with data, or in the case of analytic truth they are true by definition.
So the justification is not that it finds truth, but that it explicates the further implication of truths, and shows you what are good and bad ways to go about that.
Edit: And again, logic is not about the world, it's about language, about the abstractions we make about the world. For instance there no X that equals X in the world, nothing is entirely equal.
Although, if things did not have consistent "logical" relationships, the world might be a much more surprising place to live in.
When it comes to justifying induction, we can use more induction:
In my experience, objects have consistency...
In my experience, I consistently observe that objects have consistency...
In my experience, I consistently observe that I consistently observe that objects have consistency...
To my mind logic is a human construct. It has its own particular subset of language. I don't buy the idea of a closer relationship to 'language' in general than that.
I see other animals, however, making inferences, about food, trails, whether you're an enemy or friend. I don't believe they have logic, or language. But they have inferential systems.
"I never done nothing like that" - a double negative used to emphasis the negation rather than to negate it.
EDIT: One consequence of looking at logic like this is that we have to know something already before we can investigate logic. So it is not a foundation of knowledge, exactly, but something which comes after already knowing -- a generalization of knowledge we know now. Consequently it may be shown, with the more that we know, that some inferential step we once took as valid is shown to be invalid. Logic is something that lives and breathes and changes.
"Man is conscious of a universal soul within or behind his individual life, wherein, as in a firmament, the natures of Justice, Truth, Love, Freedom, arise and shine. This universal soul, he calls Reason: it is not mine or thine or his, but we are its; we are its property and men. And the blue sky in which the private earth is buried, the sky with its eternal calm, and full of everlasting orbs, is the type of Reason. That which, intellectually considered, we call Reason, considered in relation to nature, we call Spirit. Spirit is the Creator. Spirit hath life in itself. And man in all ages and countries, embodies it in his language, as the Father.
It is easily seen that there is nothing lucky or capricious in these analogies, but that they are constant, and pervade nature. These are not the dreams of a few poets, here and there, but man is an analogist, and studies relations in all objects. He is placed in the centre of beings, and a ray of relation passes from every other being to him. And neither can man be understood without these objects, nor these objects without man. All the facts in natural history taken by themselves, have no value, but are barren like a single sex. But marry it to human history, and it is full of life. Whole Floras, all Linnæus’ and Buffon’s volumes, are but dry catalogues of facts; but the most trivial of these facts, the habit of a plant, the organs, or work, or noise of an insect, applied to the illustration of a fact in intellectual philosophy, or, in any way associated to human nature, affects us in the most lively and agreeable manner."
From 'NATURE' by Ralph Waldo Emerson.
This passage makes me think that perhaps within logic belies a universal principle, through which, we use to connect/relate to the many aspects of life. In this way, logic isn't something that is justified, rather, it justifies. It justifies truth as acceptable.
I don't see why not. Actually, I do, for pedantic reasons: we can't criticise logic; it is what it is. But we can criticise the use of logic, which I think is your intention anyway. :wink: Logic should only be used where it is applicable, useful and helpful. Use of logic outside these constraints is wrong, unjustified, and unjustifiable. There, I criticised a particular way of using logic. :smile: :up: ...and I did it using logic! :blush: :smile:
First, what it is not: it is not an object of being, nor is it a property of being. It is a category error to treat it that way (reify it).
What it IS, is a tool for epistemological analysis. I agree with Mollere (above) that it is truth preserving. It is the path of reason through the jungle of possibilities, the path toward contingent truths; and it applies exclusively to propositions.
Quoting Wayfarer
That's a nice view, happens to be not only controversial but probably false. Frege also thought the Comprehension Schema was "self -evident", but Russell proved it led to Russell's Paradox. And if you think Excluded Middle and such "just are", then you are behind on, oh, the last 80 years of technical work in mathematical logic. Intuitionistic logic, paraconsistent logic (esp. dialetheism), da Costa's work on logics without the Principle of Identity (look up "Schrodinger logic", or non-reflexive logic). This is hard technical work, and by no means is any assumption here not controversial. That's just not true, whether you agree with the views or not. Like I'm not an intuitionist, but constructive mathematics is hella useful, even in computer science where I'm more comfortable. It would be borderline stupid for me to tell an intuitionist that they're work is simply incorrect and that's all there is to it.
It's not even like this is new. Aristotle, despite defending Excluded Middle, held in his work on metaphysics that there are exceptions to the Excluded Middle, namely contingent statement about the future), or some have (contra-Russell) taken propositions such as "The present king of France is bald" to be an exception to EM.
How so? That some objects may not be self-identical doesn't seem to have anything to do with me talking.
If I were to attempt to answer OP, I'd say in a sense logic doesn't need to be justified. But that assertion is rather difficult to unpack shortly and I'm a bit too lazy to do the whole thing. Because on one hand the truths of logic are necessary, true in all models, whatever. But that's trivial, because the truths of *every* logical system are true relative to the logic in question, e.g. Excluded Middle is a tautology in classical logic but not so in Constructive logics.
Rather, I think logics are justified like any other theory: By the virtues (and deficits) of the system under consideration.
That’s what I meant by ‘not omniscient’.
The circle is closed, to be sure. Perhaps your problem is that you want to know precisely where it is closed. It is closed everywhere. Now do you have closure? :wink:
I was reading a text book on Buddhist logic the other day, which pointed out that while Buddhism is explicit about the fact that Nirv??a is beyond ‘mere logic’, Buddhist logicians are nevertheless quite scrupulous in their use of logic [as indeed was the Buddha]. Indeed N?g?rjuna’s technique was to use logic to show the limits of logic [via a technique called the ‘tetralemma’.] So they don’t hold that logic is all-knowing, but at the same time, they use logical argument.
Quoting MindForged
Perhaps. Yet, that ? is what you meant, right? Not something else (non-identity), or the contrary (contradiction)? Otherwise, this chat will lose traction rather quickly. :confused:
I, therefore, suggest that we familiarise ourselves with non-monotonic logic. In this logic there are no final conclusions. Each conclusion can be revised in the light of new information. Non-monotonic logic is not a closed system – it allows for infinite (open) systems.
The non-monotonic logic has been tested in IT (Information Technology) and offers more realistic scenarios.
Reference: Complex Adaptive Systems.
Enjoy the day,
So for instance, take Schrodinger himself in "Science and Humanism":
Now, that's like seventy years old, but the view has received modern defenses (not dominant views, mind you) by the likes of Newton da Costa by means of distinguishing "identity" from "indistinguishability", and further by Wittgenstein in suggestion we drop identity from our logic as "it is to say nothing". Or on a more practical level, the database language SQL has violations of the Law of Identity:
In the logic of SQL, this expression will never return as true.
Not that I endorse dropping identity (it's pretty obviously useful), just that it's not (as you suggested) literally impossible to do so without falling into incoherence.
Logic is a language-game, and like any language-game it starts with rules. I presume that you're asking what justifies the rules, and the answer is that the rules don't need to be justified, no more than the rules of chess need to be justified. The question is mostly senseless. It's very similar to asking what justifies a definition - nothing justifies a definition, it's just how we play the game, or how we use the word. Why do people think that everything needs a justification? There are some things that are just foundational or basic to the way we do things, or the way we act.
You can think of it this way: Suppose we're looking at the foundational supports of a building, and you ask, "What justifies placing that foundational support there?" - the reply might be that that particular beam is needed to support the extra weight in that corner of the building. However, to ask what supports bedrock, is to not understand that justification ends at some point, i.e., nothing supports bedrock, it's foundational to all that rests on it. You can think of the rules of logic in the same way you think of resting a building on bedrock. It holds up all that follows, it doesn't need a justification.
Also because something is circular doesn't mean that something is necessarily wrong or incorrect. The fallacy of circularity pertains to arguments - not definitions, or rules, or anything outside what the definition pertains to within the framework of arguments.
I think this is mistaken. I mean the chess analogy breaks down too quickly to be a useful comparison. On the outset, chess is just a leisure activity, it doesn't play the broad role that logic does.
But more to the point, we know there's a huge debate within mathematical logic about which rules we ought to adopt, which ones we are justified in taking on and which we ought to dispense with. So intuitionists believe classical logicians are mistaken in their use of the the Excluded Middle rule (and any rules that yield EM) in their proofs when placed within a universal quantifier, because they take logic to be about constructive provability. Isn't that just a case where logicians are arguing about which rules of logic are justified?
But this isn't strictly true, otherwise the bedrock would fall to the center of the Earth. It's true that most of the time one ignores geology when building a house, except when it's relevant to the construction. Like when a fault-line is nearby. Then you need to construct the house to withstand earthquakes.
As for why logic might need a justificaiton, that's because there are sometimes when we ask ourselves whether logic should apply or which logic should apply, as MindForged mentioned above in the debate between Intuitionists and Platonists in what constitutes a proper proof in Math. That's not settled by bringing up the language game of math, since the debate is about which rules of math to use. And that stems from a metaphysical disagreement.
Hello,
Do the Buddhists explain why to show the limits of logic, one needs to use logic?
What would be the fault of trying to show the limits of logic without using logic?
I would be interested in your own perspective on this as well.
Thank you.
It is assumed. If you read the early Buddhist texts, they are mainly dialogues - discussions about the dhamma, the Buddha’s teaching and principles. So reasoning is basic to that - if this, then that; knowing this, then you will know that. The discussions were between people from all walks of life and the Buddha.
Then as the tradition developed there was debate with other spiritual traditions - Hindu and Jain, mainly. And they were all quite fierce debaters. There is actually a discipline in Indian philosophy, corresponding with what in the West is called 'epistemology', called 'pramanyavada' which is 'the grounds for valid knowledge'. For instance Buddhists generally accept only perception and inference, and also sometimes testimony i.e. the remembered sayings of the Buddha or illustrious teachers. Logic is basic to inference and whenever it is appealed to, then it is understood to authoritative in the same sense that valid syllogisms are authoritative in Western philosophy (although the Indian approach to logic was different to the Greek in some respects.)
But over and above that, the ultimate goal of Buddhist practice is Nirv??a which is a spiritual or religious aim and is not something that can be discovered by logic alone. For example in texts on what constitutes the correct understanding according to Buddhism, it is frequently stated that 'There are, bhikkhus [monks], other dhammas, deep, difficult to see, difficult to understand, peaceful and sublime, beyond the sphere of reasoning, subtle, comprehensible only to the wise, which the Tath?gata [i.e. the Buddha], having realized for himself with direct knowledge, propounds to others.' (Emphasis added).
Quoting Shmuel
How would you go about that?
I could use illogical ways. For example, just assert that a specific idea is beyond the scope of logic (and nevertheless true), not providing any cogent reasoning for it.
This does appear to me as somewhat silly.
Howewever, the mere fact that it seems to me to be silly, isn't "proof" that it really is silly, unless I offer some reasoning.
I don't see the issue. If you can demonstrate logic only lets you determine such and such, and not some other things, it seems I've used logic to show its limits.
Depending on the school of Buddhism, reality as it is in itself is taken to be beyond the reach of logic, because reality is what you have once you've stripped away all conceptual structure (it's ineffable). Of course, if this Buddhist also accepts the tetralemma their logic is already beyond the scope of classical western logic (Frege's logic) since the tetralemma does not assume Non-contradiction and Excluded Middle, and sometimes the Buddha can be read as saying even that is too restrictive.
I just realized something. A circularity is a problem in an argument.
Imagine a logical argument X that is used to prove that logic is the method for discovering knowledge. There is a problem if X is circular but not if it isn't.
To give an analogy...
The mind can be used to study the mind just like a logical argument can be used to justify logic. This circularity is benign.
However, if the mind is faulty then whatever comes of applying it will also be faulty. Using an unsound argument (here specifically circularity) would prevent us from seeing the truth. This is a vicious circularity.
So, there's nothing wrong with using a sound argument to justify logic. This isn't a vicious circularity as long as we come up with a sound argument free of fallacies.
Now about that sound argument that justifies logic...
Logic would be justified only if its conclusions are true. Here we face a problem because conclusions are deemed to be true only if logic is justifed. A vicious circularity.
At this point I'd like to bring in a certain class of conclusions - those pertaining to the future - predictions. [I]Predictions[/i] of sound logical arguments can be experimentally/practically verified over and above them being justified just on the basis of correct application of logical argument forms. That means verification of predictions can be used to justify logic.
So, my final argument looks like this:
Argument A:
1. If ALL the predictions of logic are true then logic is justified
2. ALL the predictions of logic are true
So,
3. Logic is justified
Argument A is NOT circular and is a valid application of modus ponens.
As for soundness some may object to the word ''ALL'' because empirical verification is an inductive process and so precludes the use of ''ALL''. However, if we were to consider ALL applications of logic pertaining to predictions coming true up to this point in time then we can use ''ALL''.
Some may disagree and call my argument inductive rather than deductive.
Your valuable comments please...
Erm, (3) is only valid if (1) and (2) are valid. Logic did not predict the election of Trump or the selection of Brexit. There are contexts where logic is not always useful. Human culture is one, very big, one.
You seem to have adopted the standard that objective science places upon its theories, that anything less than ALWAYS correct leads to immediate rejection. Your assertion (2) is not correct for all circumstances. Therefore (as/from above), logic is not justified. QED
That's not the case though. At best we can justify deductive logic in an indirect, non-deductive manner. Further, logical systems have metalogics, but those don't so much justify the object logic as much as they give the semantics of the logic in question.
Quoting TheMadFool
That's perfectly... circular. A fallacy is relative to the assumed rules of a logic in question, it is not some free-floating error that stands outside a logic. What makes an argument valid or fallacious is determined by the inference rules of the logic. In Classical Logic we get from Frege, this argument is invalid (fallacious) because it commits the existential fallacy, but in aristotelian logic is was valid:
All winged horses are horses.
All winged horses have wings.
Therefore some horses have wings.
The problem being that, of course, there are in fact no horses with wings. But prediction can't really be the end all justification because many valid arguments are either impossible to verify predictively or have no physical thing which to reference. The argument from explosion is a valid argument in most logics, but prediction would completely fail as a means of justifying it.
Quoting TheMadFool
And how do we know modus ponens is valid without already assuming it to be so? That argument doesn't justify logic, it's just assuming a rule to be ok and applying it. Not that I object to modus ponens (any reasonable logic ought to respect it) but I wouldn't use it as a means to justify the enterprise of deductive logic by means of a deductive argument. That is circular, viciously so.
We often take a common practice and formalize it, more or less abstractly. Often there are options for how to carry out such a formalization, and it's even possible to screw up, have a formal process that doesn't match up well with the original. It's natural to think of mathematics beginning some such way, and many people have thought just that.
That's tricky though, right? Because the sort of abstraction and structure building we associate with mathematics seems to be what we use to formalize existing informal practices. There's some chicken and egg trouble here.
But there are further puzzles. It's also quite natural to think that formalization is possible in the first place because the underlying structure was there and operative all along. Formalization would then be not an invention we superimpose on a practice but the discovery of the true structure, the essence of what we were doing, in our imperfect way, the whole time. That puzzle becomes particularly acute in the cases of mathematics and logic.
I have some sympathy for the idea that logic is a formalization of, say, the pre-logical practice of inference, or of the cognitive virtue of consistency, or of the social requirement of predictability -- I'm not even sure what to fill in there! Maybe all of the above and more. (What I'd really like to put here is linguistic dispute.) But that leaves untouched lots of questions about how that formalization is even possible or why the needs it meets are needs in the first place.
Any thoughts on what we might portentously call "the origins of logic"?
Well, I don't think it's quite a chicken-egg problem, not just yet. Let's take a look at the most well understood historical development in the shift in logic: the creation of Classical Logic. So Aristotle's logic (if we ignore the awesome developments of medieval logicians, which had been lost to time) was the dominant logic for awhile. But it had been known for awhile that the logic wasn't sufficient to formalize the kinds of reasoning that mathematicians were using, and some things that looked similar couldn't be differentiated using the logic (like the difference between the condition for the continuity of a function and the condition for uniform continuity). So these (and other considerations) guided what Frege believed his logic ought to churn out as valid arguments.
Well, that is sort of a chicken and egg problem. It's sort of like we have an informal practice. Professionals doing it assume there is a correct way to do what they're doing, and over time they drill down on that and it eventually gets formalized with the intent to make a "coherent" story that respects what we already thought should come out as true. The development of ZF set theory is much the same. It wasn't the result of a detached attempt to reason to the correct set theory, it was created to avoid Russell's Paradox and just let us get on with math without really worrying if the axioms were capital "T" true and settled for consistency.
Maybe? It's a platonism vs nominalism debate. But I think we can sidestep that and think of it this way. As we see in the Frege example (and the 19th century mathematical enterprise in general), formalization doesn't disregard what we already thought was true. We want certain things to come out true, though we might give up some things if we can get most of what we wanted. But this process might just show that the structures we were using were using the assumptions that matched a possible formalism, which was later developed in part to validate those assumptions. So if historically Intuitionistic Logic and Constructive Mathematics had been what became the dominant formalism, we'd see emphasis placed on the practice which corresponded to (or was compatible with) those assumptions.
My issue is whatever is meant by "true structure" it can't mean "only structure" as we know many kinds are possible. Each has a set of things which can be proven from that structure, whether a particular formalism matches it doesn't seem to indicate much more than which is useful in certain domains (that's my view anyway).
I state again that we "forgot" Gödel's theorem - that there are truths in a closed system that cannot be derived from other truths within the system.
I would also repeat that we need nonmonotonic logic. And in this logic, we can also revise any belief in the light of new information.
Enjoy the day,
Logic is an instrument of justification. The logical systems have or not consistency, completeness, etc. They are some of properties of some logical systems. "Justified" is not a property of logical systems, insofar I understand, so the response is that logic is not "justified". "Knowledge", but not "logic", can be or not "justified", regarding logic and empirical evidence. The apparent paradox emerges when you assume that "logic" have epistemic properties such as "justification".
When referring to logic, it's not a matter of 'if it is true'. Logic is a statement of fact/in relation to fact. If there is any error, it cannot be logic/logical. Thinking may be erroneous and still retain its identity because it refers to a process without the significance of the end result.
A circular argument is just another way of saying paradoxical or 'not-yet-figured-out'.
As to using the mind to study the mind - check your definition of mind. This sounds like 'I use light to observe light'. It may be true when there are separate lights, but, you don't have separate minds, do you? I think the question should be, 'If I study my mind/look into my mind, what is it that actually does the studying/looking? [Perhaps that is the basis for terms like ego, id, self, the 'I',... etc.]
The first thing to be noticed about this definition is that language does not enter into it. Logic is not about expressions or words. it is about how to think.
The second point is that it is about the relation between thinking and reality, so we should not be surprised that to think correctly about reality, we need to think in a way that reflects the nature of reality, of being.
As to justification: Obviously, we cannot "prove" logic because any proof would presume the validity of logical forms. But, we need not prove a proposition to know it is true. We can abstract it from reality. For example, we can reflect on our experiences of being -- abstracting away details that are not common to all existence -- in order to come to an understanding of what it is to be.
When we do this we can see that whatever is, is (the Principle of Identity), that it is impossible to both be and not be at one and the same time in one and the same way (the principle of contradiction) and that a putative reality either is, or is not (the Principle of Excluded Middle). Thus, these principles are not a priori, not forms of reason, but a posteriori understandings that are so fundamental that once we come to grasp them, we understand that they apply to all being.
If we think about what makes a judgement true, we will see that it reflects an underlying identity of source between subject and predicate. If I think
Working through the valid forms of syllogism with this understanding, we can see how the role of identity in propositions, together with the principles of being, justifies them
All logical conclusions are called "true" if they result from reasoning/argument that follows the rules of correct inference. Logic is the rules of correct inference. Calling something "true" doesn't make it so, even when we're calling the conclusion of a valid argument "true". Validity does not equate to truth. Logical truths are a misnomer.
Logic doesn't find truth.
Logic presupposes truth. It's utility is to preserve it. The rules of correct inference are justified - if we must talk like that - solely by virtue of how well they work.
True conclusions do not logically follow from false premisses. False conclusions do not logically follow from true premisses.
Who claims his?
Quoting TheMadFool
We justify Logic by Logic.
Now, that's Logic for you!
:-D
Logic has nothing to do with facts and there relation. Facts refer to ways the world is. Logic specifically deals with (primarily) the logical consequence relationship, nothing to do with the empirical world. (At best one might bring up abstract objects)
Quoting Dfpolis
This seems incorrect. Logic has many uses which either have nothing to do with reality or else is used in a way we might not reason about reality. So just take this website. Now I'm assuming it uses SQL as its database language. If so, then this website operates according to a Non-classical logic. But many propose we ought to reason about reality using classical logic. In which case, we have an example of using at least two logics in different domains, irrespective of reality itself. This is ignoring much of mathematics as well, such as the very useful Constructive Mathematics (based on intuintionistic logic) which rejects the Law of the Excluded Middle.
Quoting Dfpolis
Identity violations: See non-reflexive logics and quasi-set theory.
Excluded Middle violations: see Intuintionistic logic.
Non-contradiction violations: see Dialetheism.
Whether you accept these or not, statements like "so fundamental that once we come to grasp them, we understand that they apply to all being" are just question begging. Sure, if I accept all your definitions for "truth", your preferred inference rules, your semantics/metatheory, then yes they follow. But that simply makes the nature of the disagreements have an obvious location of disagreement (e.g. in the semantics and such).
Quoting Dfpolis
It's weird that you would bring up syllogisms when we know that Syllogistic Logic has the wrong set of valid arguments for a whole slew of things. Like this is invalid in Classical Logic (Frege's logic) but was regarded in Syllogistic as valid:
All winged horses are horses.
All winged horses have wings.
Ergo some horses have wings.
The point being that people can believe you hold the incorrect view about the principles of existence just as much as they can believe (sometimes correctly) that you hold the incorrect logic.
What is logic? A system by which facts are ascertained? What are these facts? But... What is it that logic represents or illustrates? That which eludes a superlative representation? Yes, logic is therefore abstraction.
But this abstraction has its placeholders and aspects of existence can be substituted so to assume a logical intelligibility, but never does logic have anything to do with truth, absolute truth, only a truth that is imaginary.
Knowledge is only as if it were knowledge.
Of course "logic" can be defined in many ways, so it is not one thing, but many related things. That is why I defined what I meant by logic: the science of correct thinking (about reality). That is what I am offering to justify.
Of course, this does not mean that classical logic is unrelated to other forms of "logic." You raise he example of SQL. To apply SQL, we must first realize that, given our actual goals and the reality we are considering, SQL can be applied and doing so will advance our goals. This, of course, is thought about reality, and if our forms of thought did not yield true conclusions, the application of SQL would be irrational.
In the same way, you mention "Constructive Mathematics (based on intuintionistic logic) which rejects the Law of the Excluded Middle." Yet, if, in criticizing the proof of a theorem in Constructive Mathematics I were to say that in addition to an axiom you used applying or not applying there was some other possibility you had not considered, surely you would object. So, while you may construct a system which makes no internal use of the principle of excluded middle, in reasoning about that system, you would use the principle.
Second, whenever we apply any scientific principle to a particular instance, we necessarily use the syllogism in Barbara. Let p be a scientific principle and q describe sufficient conditions for the application of p. Then we think as follows:
All cases such that q are such that p.
A is a case such that q.
Therefore A is a case such that p.
So, when we apply mathematical or cybernetic algorithms, the reasoning justifying their application is quite Aristotelian.
Quoting MindForged
I've said while we can think of impossible states, there can't be impossible states. You have not provided a single example of a real state violating the ontological principles of identity, contradiction or excluded middle.
Quoting MindForged
No, it is not question begging. It is an experiential claim to which you have provided no counter example or rebutting argument.
Quoting MindForged
No. Definitions of terms point to aspects of reality that can be experienced and analyzed. So, the question is not about the self-consistency of semantic relations, but about the adequacy of my account to our experience of reality.
Quoting MindForged
As I said, logic is not about the consistency of language, but about salve veritate thinking. To save truth, you must start with truth. "All winged horses are horses" is not a truth, but an equivocation. "Winged horses" are not "horses" in the sense living equine creatures, which is the sense of "horses" required by the conclusion. In the same way, there is no true statement in which "the present king of England" is taken as having a substantive reference.
It speaks poorly of those who educated you in logic that you are unable to spot so obvious an equivocation. Correct thinking is not about matching letter sequences or manipulating word strings. It is about using conceptual representations rationally.
Logic is about graphing out a particular consequence relation by accepting some set of axioms and inference rules. You can understand this as the relation between particular abstract objects (model theory) or as sequences of proofs (proof theory). There are other conceptions of logic, but most of those (such as the "rules for correct reasoning") make use of these in a normative setting or else they have fallen by the wayside (most professionals don't place primacy on logic regarding thinking anymore).
That's the problem though. Presumably there is only one reality, but we know there are many logics so there seems to be an inherent problem with your definition. Namely, the contradiction with having multiple correct ways of thinking about reality based on different, inconsistent logics.
Quoting Dfpolis
This is exactly what I was talking about when I brought up the metatheory/semantics point. You are simply assuming the Principle of Excluded Middle in your metalanguage and then pointing out how it then appears in the object language. No, using Intuintionistic Logic does not mean accepting reasoning about constructive proofs with Excluded Middle. As I said, this and other Non-classical logics have their own metatheories that make do not accept Excluded Middle. Excluded Middle is not false in constructive mathematics, it simply cannot be placed within the scope of the universal quantifier in proofs (so it's application in infinite domains is invalid). You are simply question begging the principle at hand.
I sincerely hope I don't sound rude, but are you kidding me? You do realize that a simple conditional is valid in damn near any logical system, right? I could just as easily say scientific reasoning is Intuintionistic by your lights.
Quoting Dfpolis
Bro, I didn't give everything at once to avoid a massive post. Aside from the fact that logic isn't about reality, take:
Identity violations: Check Newton da Costa's work (based on work by early pioneers in quantum mechanics) about indistinguishable quantum objects. That is, objects that are such that they are *ontologically* indistinguishable (it's not an epistemic limitation), non-individuated objects. Schrodinger himself explicitly endorsed this, hence the old phrase that quantum objects had "lost their identity".
Excluded Middle: nothing here, not my wheelhouse. However, ironically Aristotle disagrees with you. He believes there are metaphysical violations of Excluded Middle: contingent statements about the future (his sea battle argument).
Non-contradiction: The Liar paradox. No, it does not have an obvious or simple solution. Professional logicians have no standard resolution. That aside, the LP (if a sound argument) violates non-contradiction. And if one is, as I am, a Platonist about mathematical and other abstract objects like propositions, one is (as I am) committed the accepting the existence of inconsistent objects from what seems to be an argument from commonly accepting rules for reasoning.
Quoting Dfpolis
It's question begging. You made the argument that in even assessing e.g. Constructive Mathematics one has to use Excluded Middle because you think it results in an situation where you're... violating Excluded Middle.
Quoting Dfpolis
I'm not sure you understood my point. You said this:
"Thus, these principles are not a priori, not forms of reason, but a posteriori understandings that are so fundamental that once we come to grasp them, we understand that they apply to all being."
All this really says is that "once you assume my definitions of the relevant terms and their scope of application is global in all possible domains, you'll see they apply to all of reality" (It's essentially defining your way to victory). The only difference is you're (intentionally or not) cloaking it under language of discovery as opposed to assumption. As it happens, people can and have put forth reasonable objections to your views about these "a posteriori understandings". On a related note, we have definitions for things which do not exist in reality so I don't really know why you're insisting on thinking about definitions in that way.
Quoting Dfpolis
No. The argument I gave there is *valid* in Aristotelian Logic, having the form: All A's are B's, All A's are C, Therefore some B's are C. It's not an issue of language, you have simply run into one of the issues with Aristotelian logic: it has syllogisms it deems valid but which can take one from true premises ('All winged horses are horses') to false conclusions ('Some horses have wings'). Take up existential import with Aristotle, modern logics don't have this issue.
Lame insult aside, its clearly not an obvious equivocation given Aristotle created this issue.
Picture yourself in the woods, where the trees and brush is dense. One can look around and draw logical conclusions based on what it sees. We may even try to extrapolate beyond where the dense forest obscures our view. This may all appear reasonable, but it may be way off base and one may never know if true.
The 3-D side of the brain is like someone up on the hill looking down at the forest below. They see the bigger picture, but not all the details seen by logic. From the hill one can see the larger patterns in the fauna that can't be seen from below, when one is stuck in a small section of trees trying to extrapolate the larger patterns.
The brain goes back and forth from the big picture to the little picture to develop the middle from both ends. Human logic tends to stay in the weeds trying to expand outwards. If the theory meets with exceptions, we add a wildcard called random, instead of revise the theories anchored in the weeds. The reason we do this is, humans have yet to develop a collective way to simulate the 3-D side of the brain. The extra dimension is not processed via human language, but rather via a natural language that is felt with subtle sensations and feelings; intuition.
Development of pseudo 3-D logic could be done via a generalist style education. This is were we learn the basics of many places in the forest; all the specialties, without getting bogged down in the weeds. Then we try to connect all the apparently unrelated specialities, to form a bigger picture. Once the bigger picture is set, this becomes the goal of the specialities. The people on the hill can the patterns below better than those in the weeds. Those in the weeds head toward patterns even if this may not seem logical in the weeds.
You say this like it's accepted wisdom, tested and proven over millennia. But it looks to me like an unjustified assertion, an implication of knowledge that we don't possess. I think there is a great deal more to human brains than you have considered here. And that's before we make the move from brains to minds.... :wink:
There is no problem with my definition. I am not denying that "logic" can have many meanings. I'm specifying the meaning I'm using.
Quoting MindForged
I defined what I am talking about as the "science of correct thinking." The "logics" you are thinking of do not study thinking. Mostly, they study systems of symbolic representation and manipulation. So, while they may be correct ways of thinking about various formal systems, they do not study the structure of correct thought, as does classical logic.
Quoting MindForged
No, I am not.
First, I am not even discussing language. I am discussing thought that may or may not be expressed in language.
Second, I am not "assuming the Principle of Excluded Middle." I am finding that, when I reflect on the understanding of existence I have abstracted from my experience of reality, I see that some conjectured state must either be or not be. This is not an "assumption," but a finding. Futher, it is not a finding about about language, or even about thought. It is a finding about reality.
Quoting MindForged
I am not denying that, because I am not discussing systems of symbolic manipulation and their metatheories. I am confining myself to the study of thought, and specifically, thought that is necessarily salve veritate. This requires us to look at the relationship between thought and reality, not the relationship between systems of symbolic manipulation and their corresponding metatheories.
Quoting MindForged
I note that you did not comment on the syllogism I offered in evidence. Is your claim, then, that to apply a principle to a concrete case we do not need to recognize that the concrete case meets the conditions of application? Or perhaps that we can validly apply principles that are not thought of as universal? Or perhaps you want to claim that if the conditions of application can be stated in words that can describe, in another sense, the case at hand, we can still rationally apply the principle to that case?
Quoting MindForged
You see not to understand the Principle of Identity. it does not make contingent claims about reality, saying, for example that electrons are individually identifiable or even that they are individuals. What is says is: "Whatever is, is." So if it is the case that electrons are not individuated, then that is the case.
Now, do you have an actual example of a violation of the Principle of Identity?
Quoting MindForged
I am sorry, but this does not contradict my position, but a confirms it. The reason the linguistic expression of the Principle of Excluded Middle does not apply to future contingents is that they do not exist. Since they have no being, there is no justification for applying a principle founded in our understanding of existence.
Quoting MindForged
Again, my position offers a simple solution to the Liar paradox, Jourdain's paradox and other conundrums based on the notion of "truth value." It simply shows that "truth value" is an ill-defined construct. Actual truth, however, is not. The liar who says "I am lying" is making no statement about reality. Therefore, what he says cannot be either adequate to or inadequate to the referenced reality. So, the concepts
The same applies to Jourdain's paradox. You may recall that it is a card that says on one side "The statement on the other side of other card is true," and on the other "The statement on the other side of other card is false." Jointly these sentences make no claim about reality, and so, again, the concepts
So, we see that founding logic in a reflection on being provides us with a simple solution to problems for which, as you point out, "Professional logicians have no standard resolution."
Quoting MindForged
I am sorry to see you committed to so many errors.
Quoting MindForged
The assertion of first principles is not question begging. Every line of argument, to avoid circularity, must have first principles. That does not mean that those principles cannot be justified. it only means that they they cannot be deduced. They can, for example, be justified by an appeal to experience. My claim, which you refuse to address, is that the principles of being are abstracted, a posteriori, from our understanding of existence.
You have tried, but failed, to provide counter examples. If you have more to offer, please do so. If you have no more to offer, show how the principles cannot be based on our experienced-based understanding of reality. Claiming that experienced-based knowledge is "question begging" will not do.
Quoting MindForged
Note that while my claim addresses what can be known from our experience of reality, your reply fails to address what we can know from experience. it is, therefore, nonresponsive.
Quoting MindForged
Of course we can't define things into existence. Rather, definitions point to the aspects of reality we're discussing. They suggest that our dialogue partners look in that direction in the hope that they will see what we see. If they do look, and see that we are wrong, they can do us the service of pointing out our error. However, if our partners refuse to look, because they believe there is nothing to see, there is no more we can do.
Quoting MindForged
What you refuse to grasp is that classical logic is not concerned with linguistic forms, but with correct patterns of thought. Aristotle spent a great deal of time pointing out fallacies -- many of which (such as the equivocation in your example) use apparently correct linguistic forms to mask manifestly incorrect thinking.
Quoting MindForged
That is why they cannot resolve paradoxes such as the Liar and Jourdain's.
As for Aristotelian existential import being an "issue," make your case.
Quoting MindForged
I spotted it instantly. Are you claiming that "horse" is univocally predicated in "some horses have wings" and "winged horses have wings"?
Also, you have not applied the little you know about Aristotelian logic. You claim to know about existential import in Aristotelian logic. If so, you know that "All winged horses have wings" is false because it lacks existential import. So, you should have seen that not only does your syllogism have an undistributed middle (because of equivocation) but also that its major premise is false.
And I provided an issue that falls out of using that definition.
Quoting Dfpolis
You are avoiding the issue though. What defines correct thinking? That is determined by articulating some formal set of rules, i.e. a logic, and arguing that such a system ought to be reasoned in accordance with. And really, there's a reason your conception of logic has fallen out of use amongst logicians. That being that there's a difference between logic (a set of symbols and rules regarding their transformation) and the normative roles we give to a certain set of those rules (the correct rules for reasoning, or if you prefer, thinking). The modern development of logic does not treat that latter definition as the base of logic. I mean as a first observation, people do not think in accordance to the rules Aristotle believed were correct. In fact, humans seem to (reasonably) assume that correct thinking is rather domain-dependent. Classical logic says from a contradiction everything follows and yet it would be impossible to actually reason that way in everyday life (just recall how often you come across conflicting information).
A finding which even your own apparent source (Aristotle) disagrees with. And again, reflecting on your own experience does not entail finding a necessity because your experience does not encompass the whole of how reality can be. (this will come up later, so I'm saving it).
Ok, you somehow missed the part of that response where I explicitly responded. I'll summarize: The syllogism you made was followed by you claiming that the justification is Aristotelian. My response was that your argument is valid in basically every logic. Ergo it wasn't resorting to Aristotelian assumptions.
Ok, this is not an argument on your part. I gave you an example of a (potential) empirical violation of the Law of Identity. Your response was simply to claim that Identity is necessarily true (in the world) therefore my example is off the table because it posits the Law of Identity is only contingently true (only holding for some objects). Again, you are either question begging about Identity being true or else your assuming identity can only be conceived of one way with no debate (which is probably just question begging since, again, people can disagree on the correct account of something). So for instance, we could define Identity such that it applies to some class "M", indirectly limiting what it applies to and yet retaining the principle where it seems to apply.
If objects are not ontologically individuated, they are not self-identical. To be self-identical is to be (though not the best phrasing) the same as oneself and different than every other thing (to be individuated, essentially). That's what is referred to when Schrodinger was talking about in "Science and Humanism", such objects may if fact lack any ontological individuation and thus have no identity:
Now I don't care if you accept this as actually being the case (I doubt I would even accept it), but we know that it is at least possible for this to be the case.
This might contradict Relativity so I don't see how you aren't just picking and choosing what to accept based on principles that only hold in limited experiences and generalizing them to everything needlessly. It's not obvious that the future doesn't exist, or at least, you've no experience on which to say anything about it.
At this point you cannot even use modern logical systems, nor even modern mathematics based on those systems. Most of pure maths don't even have referents in the world by which they could be made "really true" or whatever.
Says the guy who cannot even accept truth values (and therefore none of modern maths and logic). Cute.
That's not what you did. When I brought up a possible empirical violation of Identity,you simply claimed that because Identity is not contingent, but rather necessary, the example must be incorrect. Just saying "Such and such are my first principles because they're abstracted from my experience" does not entail they are necessary truths, or indubitable, or whatever. As it happens, your experiences (even ones you may think must be true) can be incorrect or else not justified to the extent that you treat them as applying to everything.
Your claim makes an assumption that from your experience you have found some necessary portion of reality, but note you've given no argument that it is actually necessary or how you know it to be so other than by saying "Upon reflection".
That's not what I said. Pegasi do not exist. That does not mean I cannot define a meaning for "Pegasi". In fact, given you understand what "pegasi" means you can't really dispute that. Definitions do not always point to actual things, sometimes they just point to ideas or concepts.
Classical logic is the logic Frege created in the 1870s, Aristotle used Aristotelian logic. And what you refuse to accept is that the argument I gave is valid in Aristotelian logic.
Oddly enough, despite no standard solution existing there are many potential solutions to such paradoxes (reworking the T-scheme, using a different truth-bearer besides sentences, etc.). And the Liar-type paradoxes have nothing to do with existential import, because the arguments don't have any quantifiers in them so your response here makes no sense.
You seem to have mixed up the point. That being that "All winged horses are horses" is obviously true unless you make the (now discarded) Aristotelian assumption about existential import. Otherwise we have this infinite class of perfectly analyzable statements (in ordinary language) and yet we cannot reason about them meaningfully. And a logic like that is so weak as to be inadequate in modern mathematics. That's why Frege had to invent the theory of quantifiers in the first place, traditional logic wasn't up to the job of parsing out how mathematicians were reasoning.
I disposed of.
WhichQuoting MindForged
I have already said. Let me be more precise: forms of thought that are salve veritate, not accidentally, but essentially.
Quoting MindForged
Not quite. It is observing that if you're reasoning, and want the truth of your premises to guarantee the truth of your conclusion, your reasoning needs to reflect the principles of being. Adhering to certain forms is one way of doing this.
Quoting MindForged
Since you admit there is a difference, between what you call "logic" ("a set of symbols and rules regarding their transformation") and the science of correct thinking, let us agree that what I am discussing is not what you call "logic"
Let us also agree that mere fact that two areas (correct thought vs the transformation of symbolic forms) differ is not a reason for the study of one to be more in vogue than that of another.
Quoting MindForged
From a contradiction, anything does, in fact, follow. And yes, we are told conflicting things. ( I would not call both conflicting statements "information" because they cannot both reduce what is logically possible.) Does the mere existence of conflicting claims warrant treating contradictory statements as equally true? Hardly.
Do you think that the existence of conflicting claims is new -- that the people of Aristotle's time were not beset with half truths, misunderstandings, rumors, myths and outright lies? If they were, then there is no more reason now to ignore the study of correct thinking than there was when Aristotle taught invented logic.
Of course if you are not interested in truth, Aristotelian logic can be of little use. I want to be able to deconflict incompatible claims. I see the goal of philosophy as providing us with a consistent, experienced-based framework for understanding reality -- resolving the conflicts you find so overwhelming as to justify giving up on correct thought.
Quoting MindForged
Please! I've already dealt with this absurd claim.
Quoting MindForged
Of course my "experience does not encompass the whole of ... reality. It does not need to. As with many lacking a adequate background in perennial philosophy, you are confusing induction on the Hume-Mill model with abstraction. Hume-Mill inductions are not reliable because, to reach a universal conclusion, they must add an assumption (that all other cases are like those already encountered), to the data. Abstraction is quite different, It does not add to the data, it removes some notes of intelligibility, fixing on others to form actual knowledge. So, to form our concepts of
So, it is completely immaterial that we have not encountered all possible beings, or even all actual beings. All that is required to apply our understanding of being is that anything to which we wish to apply it be able to evoke the concept
Quoting MindForged
Let's be clear. The syllogism only reflects a valid thought process in words. Aristotelian logic is not about verbal forms. It is about the ways of thinking expressed in those forms. (See Henry Veatch, Intentional Logic.) So, no, the form of thought is not addressed in non-intentional systems of "logic." They only deal with rules of symbolic manipulation.
Quoting MindForged
That is precisely the point. Your example has nothing to do with the Principle of Identity we are discussing. To continue to pretend that it does, after I have shown you its utter irrelevance is arguing in bad faith.
Quoting MindForged
My response was that granting the facts you put into evidence does nothing to show that "Whatever is, is" is false. Please do not distort my position. If it is the case that electrons are not indiviualizable, then it is the case that electrons are not indiviualizable. (BTW, I have no reason to doubt this.)
Nor is it useful to pretend that the Principle of Identity is something else. I am not following you down a Trumpian rabbit hole, so I am skipping the rest of your comments on identity.
Quoting MindForged
No, it does not. The Sea Battle (on earth) tomorrow is in the future in all frames of reference.
Since you brought it up again, her is what Aristotle actually says:
The reason Aristotle give is exactly that I gave, i.e. that because the case is not actual (does not exist) neither proposition can "be either actually true or actually false."
Quoting MindForged
You can redefine "exists" if you wish, but doing so will not change what I mean by the term.
Quoting MindForged
I do not base the math I use on symbolic logic, as no mathematical system reducible to arithmetic can be shown to be self-consistent. I justify my mathematics by abstracting its foundations from reality -- thus guarantying its self-consistency.
Still, I wonder why you are not commenting on my simple resolution of the "insoluble" paradoxes, or jumping in with an actual defense against my charge that "truth value" is an incoherent concept. "Cute" is not a counterargument.
Quoting MindForged
So, you want me to seriously consider that I may never have encountered existence? I'm not following you down that rabbit hole either.
Quoting MindForged
I invite you, and all readers, to make a similar reflection and determine whether or not your understanding of
Quoting MindForged
I was not talking about your example, but responding to your claim that I had made my case true by definition.
Quoting MindForged
Quite right, they do not always indicate some reality. I was imprecise. I should have said they specify concepts that may or may not be instantiated.
Still, unless we are discussing ideas or concepts, they do not just point to ideas or concepts. The definition of "Pegasus" is not the definition of an idea, but of a mythical beast.
Quoting MindForged
Yes, symbolic logicians have appropriated "classical logic" for a class of propositional "logics." In some sources, Aristotle's logic is the first example of a "classical" logic," and you have used the term to include the kind of logic I am discussing. ("Classical logic says from a contradiction everything follows.") Still, I don't want to confuse you, so I'll say "Traditional Logic" -- which has a long history of development after Aristotle.
That said, you have once again pettifogged instead of addressing my point, viz. that traditional logic is not primarily about linguistic forms, but about correct thinking, and the alternatives you raised look no deeper than the surface of formal expression.
Quoting MindForged
I did not say the sentence of the Liar paradox had existential import. I said that that the concepts of
Stepping back, you're so dogmatic in your commitments that you will not even discuss the merits of my solution. instead, you employed the Trumpian tactic of raising other issues (T-schemes, existential import, etc) to distract from my proposal.
Quoting MindForged
1. No, it is not true. Truth is the adequacy of what is inthe mind to reality, and your claim adequates to no reality.
2. You were trying to show the outright stupidity of Aristotelian logic, but you could only do so by violating its canons, specifically by ignoring the requirement that Universal affirmative propositions have existential import. That is shabby at best. It is like a high schooler trying to reject algebra by "proving" that 1=2 -- forgetting that there isw a prohibition against divideing by zero.
Quoting MindForged
Again, you are closed to my fundamental point. Traditional logic is not about sentential or any other form of symbolic manipulation, It is about correct thinking. There is no explicit or implicit contradiction in requiring existential import of universal affirmative judgements about reality. If you think there -- have at it.
Quoting MindForged
Thank you for your faith claim.
1. I've already shown you that you cannot rationally apply axioms without the line of thought reflected by the syllogism in Barbara.
2. Nothing in traditional logic prevents you from postulating axioms of whatever sort and working out their consequences. The axioms can specify any of the systems of symbolic manipulation that so amuse you. So, understanding how to think correctly can do noting but help you think correctly about the several systems you choose to call "logics."
You're not being precise at all. You're simply saying that a certain set of rules are necessarily correct but have no reason for believing so that isn't contentious. Anyone can say that, actually showing it has been my repeated argument against you.
This is incorrect. Logic is the enterprise of creating a system which preserves truth by not resorting to "principles of being" (which, again, you do not have some inherent claim to the correct principles of being without argument) but to principles of inference.
This doesn't make any sense. The reason the symbolic side is more in vogue is precisely because the normative role of logic requires first having your inference rules and axioms laid out first. It's exactly akin to having your moral principles laid out before declaring to know the moral status of every act.
If you accept the Principle of Explosion then you do not accept syllogistic logic. In Syllogistic, one cannot derive any arbitrary conclusion from inconsistent premises, e.g.
Some As are Bs
No Bs are As
Therefore, All As are As
What warrants accepting contradictory claims is that you might well have good reason to believe both and possess no (current) means of picking one over the other. This happens in everyday life (conflicting statements from trustworthy friends) to even science and mathematics (the early calculus was known to be inconsistent, but people just rolled with it for a couple centuries until limits were hammered down). Explosion didn't become standard in logic until Frege created classical logic. That's why Syllogistic is often regarded as a paraconsistent logic.
This is exactly the same problem you make in multiple different ways. People
Do not form always the same concepts of being and existence.
Aristotelian logic does not map to the "ways of thinking". In fact, probably no logic does to any degree of usefulness (otherwise developing AI would be much easier).
Yes it does. The particles in question are, quite possibly, not identical to themselves (it's a question of science and not one solved by recourse to abstraction from everyday experiences). To pretend that's not the argument I was making is a lie. Or you just refuse to read the Schrodinger quote again. That's a neat move.
It does show that. If "Whatever is, is" holds for quantum objects as well (take Schrodinger's case of electrons) then they necessarily must be ontologically individuated. If they cannot be individuated, they are not self-identical. This does not mean you cannot say true things about such objects, simply that you cannot say they are identical to themselves.
This is silly and borderline ridiculous. Can people defensibly have different accounts of an idea which goes by the same name? Obviously so, just look at *any* disagreement in terminology. Intuitionists believe classical logicians incorrectly define Excluded Middle for instance.
I'm honestly trying not to laugh because your point doesn't make any sense. I said Aristotle gave this argument as a metaphysical example of where the Law of the Excluded Middle does not apply. Your response is to say that the rules are different there. Well, yea, that's what I was saying. Aristotle does not believe that particular rule applies to potential events in the future. But Aristotle does not assert time negates the application other principles (e.g. Non-contradiction) but that one specifically. So it's not posited as a domain where logic does not apply.
Ah the good ol' "My definition is inherently the default one". As a matter of fact, I don't believe I redefined "exists" at all, as the ontological status of the future isn't obvious (whatever you may insist, philosophy doesn't tend to settle such matters).
I didn't suggest you were a Logicist. My point was simply stated and obvious: if you cannot accept truth-values then you cannot even use modern mathematics. Mathematicians do resort to such formalisms when necessary, and they use these concepts.
I believe I said "cute" in reply to you saying "I'm sorry you are committed to so many errors", which was equally as much a non-argument. Rudeness begets rudeness my friend, and you have a habit of using it and pretending it didn't happen.
That aside, the notion of truth-value isn't what causes the Liar paradox, it's having a semantically closed language and a language which uses Tarski's T-scheme. You can construct contingent Liar paradoxes by pure reference to real world things (Kripke gives examples in "An Outline of a Theory of Truth", which you can find online (it's on the first few pages)). So even by the criterion you gave it doesn't do anything about the paradoxes.
No, I'm saying that "reflecting" upon it does not by virtue of magic entail you have developed an adequate understanding of it. It's not a rabbit hole, it's just not how you do philosophy unless it's with sycophants.
Yea, one which we can say true things about. If your definition of truth is just what we can point at and think about correctly then a lot of normal things people says is either nonsense (because we think we're speaking truthfully of non-existent things) or your definition fails so fundamental adequacies (e.g. "All winged horses are horses" should come out as true). I mean, imagine if zebras vanished tomorrow and we then said "Sorry mate, it's no longer true that zebras are black and white because, obviously, there are no zebras anymore!"
I've already addressed this point when I brought up contingent, empirical examples of the Liar paradox forming in natural language exchanges (just read the Kripke paper I referenced otherwise this is pointless).
No, I ignored the "merits" because the "cost" includes rejecting modern logic and mathematics which make crucial use of the concepts you're dispensing with, not to mention rendering innumerable natural language expressions as mistaken.
Not the stupidity, the lack of usability. If it cannot even work for expressions such as that then its use of existential import (and the ill-defined notion of "correct thinking") just aren't worthwhile to keep.
Yes I've addressed this. In doing so it leaves itself unable to do basic reasoning and so as a theory of "correct thinking" it leaves much to be desired. Classical logic, whatever issues I may take with it in certain domains, does not have this issue (and, at the first-order level) is not susceptible to the self-reference paradoxes.
Oh stuff it. Without a theory of quantifiers (which we get in classical logic) one cannot, for instance, distinguish between the condition for the continuity of a function and the condition for uniform continuity. The difference is the placement of just two nested quantifiers and Syllogistic has no way to even formalize this. Once Frege had done his work we found out theat hitherto mysterious difference. And that's just one example, doubtlessly historians of logic know others.
i am ceaselessly amazed how I can explain my position repeatedly, and spark no glimmer of understanding. You asked "What defines correct thinking?" I defined the term, saying "forms of thought that are salve veritate, not accidentally, but essentially. "Rules." were not mentionde.
Your reply doesn’t address a word of my response. Instead, you put in my mouth something I did not say. Further:
1. You didn’t ask for a justification, but criticize me for not giving one here.
2. I have previously given a justifying argument, but you claim I’ve given no reason for my position. Whether you agree with my reasons or not, saying I have given none is a lie.
3. In a good faith dialog, the partners do their best to understand one another, asking for clarifications when needed. They then respond, to the best of their ability, to what is actually said. You are not doing me that courtesy.
Moving on:
Quoting MindForged
First, if you "create" a system without foundational reflection, there is no reason to think its principles of inference will besalve veritate. Since truth is the adequacy of our thought to reality, any foundational reflection must include an understanding of reality, of being.
Second, the principles of being are not my personal discovery, nor are they limited by finite domain of human experience and cognition. Rather, just as our understanding of unity applies to anything that can properly elicit the concept
Third, as first principles, they cannot be the conclusion of a more fundamental deduction. Still, we can examine the processes by which we come to them, and I’ve offered such an account. You have chosen not to criticize my account, nor have you offered viable counterexamples to the resulting principles.
You’ve made hand-waving remarks about the unreliability of human cognition. I could make similar, but substantiated, objections to the beliefs of symbolic logicians – say to Hilbert’s program and its demise at the hand of Goedel. Of course humans make errors. I've made plenty, but the strength of communal research lies in its power to identify errors and correct the processes leading to them. So, if you have a specific criticism of my abstractive justification of the principles of being, please spell it out.
Quoting MindForged
That is a good reason to begin with an examination of correct thought, as Aristotle did. It is no reason to "create" rules of inference that lack an adequate foundation in human thought or in the reality it seeks to reflect.
Quoting MindForged
Your syllogism has an undistributed middle, and the conclusion, while true, is invalid.
Consider:
Some Americans are Hispanic.
No Hispanics are pure Irish.
We can draw no conclusion linking "Americans" and "pure Irish" from this data, so your "syllogism" is formally invalid. Substituting "American" for "pure Irish" does not make it a valid form.
Quoting MindForged
With reasoning like this, no wonder we disagree! Knowing the truth of neither, warrants neither.
I have no good reason for believing p if I have a good reason for believing ~p. Why? Because reasons for belief do not work in isolation, but in the aggregate.
The "shaky" foundations of the calculus before the theory of limits was developed is not an example of your claim. No one using calculus in that era doubted that it was a reliable tool. No physicist used it despite thinking it was "false." Mathematicians recognized that its foundations needed work, but did not simultaneously believe it was well-founded.
Rational people do not accept contradictions. If they can't decide, they suspend judgement.
Quoting MindForged
You mean there was no Principle of Pseudo-Scotus before Frege? In which of Frege's Latin works did he write "ex falso sequitur quodlibet"? Or "ex contradictione sequitur quodlibet? Was it in Die Grundlagen der Arithmetik: eine logisch mathematische Untersuchung über den Begriff der Zahl? Oh, wait, that was in German, like the rest of hie works, wasn't it? Have you read anything about logic before Frege?
Quoting MindForged
Yes? Are you going to explain?
Quoting MindForged
I suggest you read John Poisot's Ars Logica (translated in part as The Material Logic of John of St. Thomas) or Henry Veatch's Intentional Logic.
Confusing AI, implemented in with instrumental signs infinite state machines, with human thought, which employs formal signs, betrays an inadequate grasp of material logic.
Quoting MindForged
Really? If that’s what you think, you have completely misunderstood the text. Let's look at it:
Note that the "identity" being discussed here is not that expressed by the Principle of Identity (“Whatever is, is”) -- which is unitary -- but a binary identity linking two cases. Using one as a counterexample to the other is equivocation.
Quoting MindForged
It does no such thing. "Whatever is" assumes no specific structure to reality. It applies to whatever is actually the case.
Quoting MindForged
If you mean by “accounts” explanations of the genesis of the idea, then, of course, the same idea can have a different genesis in different people. If you mean essentially different [i]definitions[\i] of the same [i]idea[\i], then no, because essentially different definitions specify essentially different ideas.
If what you meant to ask was: Can one apply the same name, say “Principle of Identity,” to different ideas, then of course they can. The Principle of Identity in abstract algebra is not the Principle of Identity in ontology. Equating them can only lead to the fallacy of equivocation.
Quoting MindForged
No, I did not say the "rule" is different. The "rule" is exactly the same. What is different is that future contingents do not exist, and so fail to meet the conditions of application for the rule -- which applies to all existential situations. This goes to the heart of what I am saying, and what you fail to see -- namely, unless you understand the foundational role of the principles of being, you cannot understand when the conditions of application for logic are met, and when they are not.
I gave another example earlier, when I showed how simple it was to resolve the Liar and Jourdain's paradox if one understands the dependence of logic on being.
Quoting MindForged
I have pointed out that unary and binary identity are different, If you cannot or will not grasp this, there is no point in my pressing the matter further.
Quoting MindForged
Not at all. I am only saying that you cannot claim to rebut my position when you do not use my definitions. If I am talking about the associative property of fields and you argue that there is no such property in a corn field, what you're saying may be true, but it's entirely irrelevant to my position.
Quoting MindForged
I do not reject all use of truth values. I simply see that they are not well founded for every well-formed formula. In other words that truth is a prelational, not na intrinsic property.
Quoting MindForged
I admit to being rude to you. When I encounter an uncivil jibe, I sometimes post rude rejoinders. I will try to be more charitable,
Quoting MindForged
I suppose you are talking about this, from pp. 691f:
Note that "Everything Jones says about Watergate is true." is not a statement about the reality of Watergate, but one about Jones' statements. Similarly, "Most of Nixon's assertions about Watergate are false," is not a statement about Watergate, but about Nixon's locutions. Thus, it cannot be counted among "Nixon's assertions about Watergate."
Since truth is the adequacy of our thought to reality, it is not intrinsic, but relational. Thus, not all statements have to be true or false. Some can be non-referential, having no relation to reality. and so neither true not false. Accordingly, if some of the subject statements are non-referential, it is a category error to assert that they are true or false.
So, Kripke's paradox just like Jourdain's. While either statement here, or in Jourdain's paradox, could be ultimately referential, in the scenario given, they are not. We can confirm this by a thought experiment. If we change anything about Watergate not covered by Jones' excepted statements, the change will not alter the supposed truth or falsity of either Jones' or Nixon's claims. Thus, just as in the Jourdain case, the sentences, considered jointly, are unrelated to reality.
The fundamental error here is assuming that truth and falsity can be assigned t statements which can't be cashed out existentially. The same principle shows the rationality of requiring universal propositions to have existential import.
Quoting MindForged
I am not claiming to have an exhaustive knowledge of being. My understanding only needs to be adequate to justify the principles of being that underpin traditional logic.
If you have a supperior way of justifying fist principles, please be good enough to share iit. If you believe my grasp of being to be inadequate, you need only show that one or more of the principles of being implicit in it (as stated -- not as extended by you) is false. So far, you have not.
Quoting MindForged
No, one we can say conditionally true things about. The condition is what Aristotle called "the willing suspension of disbelief." If you impose this condition on a premise, then it remains imposed on any dependent conclusion. So, if you want to say "In an imagined world with Pegasi, some horses have wings," I would have no objection. But, that conclusion does not make your case.
Quoting MindForged
Only in the dissociated world of symbolic logic where "truth" does not mean adequate to reality.
Quoting MindForged
Future contingents never had actual existence. Extinct animals had actual existence. We express this with past tenses. So, "Pterodactyls have wings (today)" is not true, while "Pterodactyls had wings (when they lived)" is true. Of course, common language isn't precise, so we have to consider the intention expressed, not just the words used. So, if someone says "Pterodactyls have wings," meaning "One characteristic of being a peterodactyl is having wings," she is speaking the truth, but imprecisely.
Quoting MindForged
I already pointed out that this is baloney. There is nothing in traditional logic that prevents anyone from stating a set of axioms and working out their implications. Knowing traditional logic only means that they will be able to bring greater insight to the task.
So, now that I've taken your fig leaf, and shown that there is no "cost," what is wrong with my solution?
Quoting MindForged
So, you you think its "useful" to be able to prove that some living horses have wings? And believe that "salve veritate" thinking is not "worthwhile"? I am trying to be charitable here, but it's not easy.
Perhaps you have in mind some theorem or empirical finding that cannot be arrived at using traditonal logic? I surely know none.
Quoting MindForged
Universal quantification:
"For all n (a natural number), n has a successor." How is this more or less informative than "All natural numbers have a successor"?
Existential quantification:
"There exists an n such that n is q." How is this more or less informative than "some natural number is q"?
Or lets take a "problem" from the quantification article for Wikipedia:
1 · 2 = 1 + 1, and 2 · 2 = 2 + 2, and 3 · 2 = 3 + 3, ...
This sis supposedly problematic because it is infinite. But, it can be stated as a universal affirmative: "All natural numbers are such that 2 times the number is the sum of the number with itself."
Admittedly, modern notation is far less cumbersome. Still, that is not a problem of principle, but of notation.
You are unbelievable. I, again, repeat: What makes them (let's speak plain english) "correct thinking"? You haven't answered that, you simply said they are not accidentally so, but essentially so. No argument is given, you're just saying they are. Great argument.
"Foundational reflection" will necessarily presuppose other principles. In the case of logic, all you'll end up doing is presupposing what constitutes "correct thinking", if it's even defined at all or explained what makes it so. And what do you know, you've done exactly that. There's no reason to think the rules you presuppose in entering such reflection are inherently correct.
The problem is such an examination will require reasoning. And correct reasoning (or form of thought, correct thinking, whatever) already presupposes a set of correct logical rules you are abiding by. You don't get around this by recourse to "reality" (an already contentious concept; people consider many different things part of reality).
That. Was. Literally. My. Point. You claimed the principle of explosion is valid. My response was that it's not valid *in Aristotelian logic*, and I gave an explosive argument in Aristotelian terms but which is not valid because contradictions do not imply anything in traditional logic.
Interesting how you missed the words "standard logic". I didn't say Frege created the principle of explosion, I said it was not what you might call logical orthodoxy until Frege made it part of Classical Logic. The works of medieval logicians cannot in any way be said to have been the standard logic, ever. By Kant's time they had been lost to history and not even remembered.
"Two case" as in two cases of observation, not two cases of different objects. Schrodinger goes to pains to make clear that the object is not self-identical despite the reasonable assumption of there being a causal connection between what one observes.
Identity entails that objects are individuated. If some object (or set of objects) lacks individuation conditions, then they are not self-identical.
I did not say the rule was different, I said the rules were different. I went on to say that, according to Aristotle (as per your quote), Excluded Middle does not apply to future contingents. Note that which you did not address: In the case of future contingents, we can still reason about them. Aristotle does not say Non-contradiction no longer applies, nor does he say that Identity fails to apply. But that Excluded Middle no longer does. That's why the received view is that Aristotle is suggesting a different logic for such instances, one where Excluded Middle is not a tautology. The primacy of ontology just makes this clear: Future contingents require dropping Excluded Middle to reason about them, but we keep the other rules to think correctly about them. So correct thinking, even on your view, is not captured by one set of rules or a single set of ways of thinking.
You earlier referred to them as an "incoherent concept". Anyway, I don't really get this. It's a common view that liar-type sentences are not well-formed, not that truth-values are not well-formed.
Statements that people make are real. Statements made about other statements are common, e.g. "You're lying" or "Your words are untrue". But in this case, I've no idea how you came to that conclusion. If Jones only says Nixon is mostly lying about Watergate, and Nixon says everything Jones says about Watergate is true, then the issue is these cannot be jointly true and yet they *entail* each other. If your issue is just that it's about a locution (which in turn is about Watergate) then that's easily remedied:
1) Jones: Most of what Nixon says about Watergate is false.
2) Nixon: Everything Jones says about Watergate-related issues is true.
The paradox is the same (what Jones says about Nixon watergate claims counts as "Watergate-related", surely).
You went beyond that, you said your understanding was sufficient to claim (as you did) that the principles are true essentially, rather than accidentally. My point is your experience doesn't generate anywhere near the justification for that. Experience is fine for generation provisional assumptions that go into your logic, but that's not what you've argued for. You think there is one correct way of thinking and that traditional logic corresponds to that thinking (correct me if I'm mistaken).
With the lack of conditionals in traditional logic I'm not even sure this is consistent with the logic being proposed. I mean, there's even a bit in Prior Analytics where Aristotle considers a conditional but deems it not a syllogism despite the conclusion following necessarily. But I'm not even sure how your example works. An imagined world is by definition non-existent so how are you reasoning correctly about it? After all, the principles which apply to existing things is not supposed to apply to that which has no being.
What I was saying was that if we take your view that truth-values are an "incoherent concept" (as you said), then modern maths/logic are not usable because they make crucial use of this and other concepts (conditionals), and dispenses with aspects of traditional logic (existential import is not assumed in quantifiers). And I don't see how traditional logic has done anything to further knowledge in these areas, it's mostly a curiosity post-Russell (Frege was mostly obscure, sadly).
No. It was an example of a type of reasoning which ought to be invalid as logic rightly concerned with forms of argument which always preserve the truth. In the traditional case, it only meets this criterion if we only talk about what we know to be true about reality, so it's application to hypothetical and mathematical cases becomes less useful.
I already pointed out examples of what I was talking about (e.g. uniform continuity vs continuity of a function).
The problem the Wiki article mentions doesn't seem to have anything to do with the logic, but that syntactic rules are expected to be finite. Traditional logic had no theory for the quantifiers it used, the quantifiers weren't detachable, and that's in part why its application to mathematics was so limited and thus Frege had to develop a new logic. Prior, until the medieval logicians there was no real understanding of them, and even the medieval logicians treated quantifiers sort of like names. Frege made them clearer by making them a new kind of linguistic object.
Put it this way. Mathematicians did not commit themselves to instantiating every object they reason about in mathematics, even before classical logic was created. Making sense of this is a bit part in why Frege created classical logic, because the mathematicians were clearly not assuming existential import in quantifiers the way traditional logic requires.
Speak of unbelievable! You asked about about correct thinking, which is singular. I replied in the singular. You, in the plural, speaking of "them." As I mentioned no "them" you must be confusing me with someone else.
Somehow, for the 3rd or 4th time, you have skipped over the core of the answer: Thinking about reality is correct when it preserves the truth of what we know of reality (is salve veritate) -- and preserves that truth, not accidentally, but in virtue of the processed followed (i.e. essentially). This is an operational, goal-oriented definition.
It is amazing that, while noting that I said, "essentially, not accidentally," you seem unable to grasp what essential note is required. Just so you do not miss it again the essential note is truth preserving (salve veritate),
I am not discussing any "them" such as rules, but the definition of correct thinking.
Quoting MindForged
This claim fails to see that being aware of reality as given in Quoting Dfpolis
experience is not a deductive process based on the application of prior principles. It is simply the actualization of present intelligibility.
Quoting MindForged
As no "rules" are presupposed, the question of their correctness cannot arise.
Quoting MindForged
Awareness of present intelligibility is an immediate, not a mediated, process.
Quoting MindForged
No, it does not. It presupposes a scientific examination of the kinds of reasoning that work and do not work, and then discovering why some methods of reasoning preserve truth, while others do not.
Let me give you an example. Any sensory representation that can properly evoke the concept
This line of thought can be expressed by a syllogism in Barbara:
"All apples are fruit."
"All fruit is a plant product."
"Therefore, all apples are a plant product."
We see that the reasoning in the process is not dependent on the specific concepts we are thinking about. So, we can abstract the form of reasoning from specifics of the example. Thus, the validity of Barbara is not an assumption, but a consequence of the role of identity in the corresponding thought process.
Quoting MindForged
We can discuss this another day. i think we can eliminate much of the contentiousness.
Quoting MindForged
You are confused. Just because you could not formulate a valid example does not mean that there are none. An argument with contradictory premises cannot be sound, but it can be valid.
The following example is from https://rationalwiki.org/wiki/Principle_of_explosion:
Please do not tell me there are no disjunctions in Aristotelian logic, because the Principle of Excluded Middle involves one.
Quoting MindForged
OK. I admit that the history of the principle is complex. Pseudo-Scotus stated it in the late medieval period, but the Scholastics were more concerned with consistency and truth, than inconsistency. So, the point of arguments such as that above, was to show that forms cannot be applied blindly, Thus ex contradictione was not a major principle.
Quoting MindForged
Only in Protestant countries -- due to prejudice against the Scholastic tradition. For example, John Poissot's Cursus philosophicus Thomisticus, which includes his famous Ars Logica, was reprinted in 1883 -- the year before Frege published his Die Grundlagen der Arithmetik.
Quoting MindForged
As you have just pointed out, in addition to identity, your example requires additional assumptions that you consider reasonable, but those of us who've studied the matter don't. Once you grasp this, you see that your example is not a valid argument. ~(~(p && q) => ~p)
In addition to assuming a causal connection between the observations, you need to assume that the causality involved ensures object persistence. It does not.
Just so you know, one of many possible ways (Feynman diagrams) to get two successive electron observations is for a second electron to leave the Dirac sea of negative energy electrons and the first electron to fill the resulting hole. (This process can be described in other ways, involving virtual positron creation and annihilation.) Thus, when you understand quantum field theory, your assumption ceases to be "reasonable."
Still, you do not need to know QFT to see your error. All you really need to know is that 2 != 1.
Quoting MindForged
Yes, if a putative "object" is not individual, then it is not individual. That has nothing to do with the ontological principle of identity which only requires that whatever is the case, be the case.
Consider an ocean wave field. It is the superposition of many waves of a range of wavelengths, so that there are no "individual" waves, except as abstractions. Still, if the wave field, or a portion thereof, existents, it exists.
Quoting MindForged
You seem not to understand scientific principles. They are not bare propositions, they also have conditions of application (the "such that" phrase of universal quantification). The condition for applying traditional logic is that we are dealing with an existential situation. The fact that future contingents are not such that they are existential situations does not change the principle. It simply makes it inapplicable.
Quoting MindForged
First, the existential condition can be granted conditionally. That is to say that we can reason on the assumption of actual existence, even when there is no actual existence, but in doing so, we must remember that our conclusions are not categorical, but conditional.
Second, in the context of assuming that the see battle will occur, we can apply all of the principles of being, including excluded middle. (Contrary to your claim, "Future contingents require dropping Excluded Middle to reason about them") For example, it is rational to say "Either the enemy commander will be killed, or the enemy commander will not be killed." Similarly, we can apply all the principles on the condition that the battle will not occur.
What we cannot do is combine conclusions conditioned by the occurrence of the battle with conclusions conditioned by the nonoccurence of the battle. This is what the paradox attempts to do.
One way to see this, that chosen by Aristotle, is to say that propositions conditioned by the assumption of an existential state can be neither true nor false (for they are not adequate to reality, but to assumed conditions). Thus, the logical principle of excluded middle, dependent as it is on the impossibility of a a state both existing and not existing, does not apply. This is not changing the rule, just abiding by its conditions of application.
Note the explicit reference to reality in the following:
Later in the chapter, Aristotle makes it clear that the reason we cannot apply Excluded Middle is not because the principle is false, but because truth and falsity are not well-defined:
To make clear that the Principle of Excluded Middle is not false, but merely inapplicable when truth is ill-defined, Aristotle gives us its correct usage near the end of the chapter:
And to make clear that his logic is ontologically based he concludes:
Quoting MindForged
Yes, I know how the analytically inclined try to bend language to their preconceptions. Still, as shown by Jourdain's and Kripke's Paradoxes, this is at best a patch. My solution works for all three paradoxes.
Quoting MindForged
Quite true, but that does not make statements about sentences statements about Watergate.
Quoting MindForged
I came to the conclusion by reading the text (as you suggested). The text refers to certain statements, not to events at the Watergate apartments.
To be true, a statement must be adequate to reality. If a statement, or a system of statements, cannot be cashed out in terms of one or more claims about reality, then it is neither true nor false, but simply non-referential. Here the system of statements makes no empirical claim.
Your suggested revision does nothing to make the system referential.
Quoting MindForged
You continue to ignore and distort what I actually said. For the 6th or 7th time, I define correct thinking as thinking that is salve veritate, not accidentally, but essentially. So, I gave "essential, not accidental" as an attribute of correct thinking abstractly considered, not as an attribute of principles or rules. Once you have the goal of understanding correct thinking, the scientific approach is to study thinking that is actually truth preserving or fallacious, and see what rules can be extracted and how they may be justified by our understanding of being. So, the rules are not the starting point, but the result of a scientific process.
Quoting MindForged
The reason you think "experience doesn't generate anywhere near the justification for" infallible principles of being is that you are stuck with the Hume-Mill model of induction. In it, I experience a certain, hopefully large, number of cases, and frame the hypothesis, that all cases are like those I've experienced. Treating this as a true universal requires adding the assumption that all other cases are like those I have observed. As the extending assumption has no intrinsic justification, the resulting universal judgement is inadequately justified.
There is another type of induction that avoids problem inherent in the Hume-Mill model. Suppose I count apples for my job, and notice that after I've counted 2 apples, if I count two more apples I always have four apples. On the Hume-Mill model, I can only hypothesize that 2+2=4, and assume that other cases will give the same result.
However, that is not what actually happens. After children count apples, pennies and pebbles, they notice that the counting process does not depend on what is counted. (I call this the "arithmetic insight.") Once you have the arithmetic insight, you understand that the relation, 2+2=4, does not depend on what is counted, and so is universally true.
How does this differ from the Hume-Mill case? In the H-M case, we have to add an assumption to arrive at a universal judgement. In the second case, we abstract, which is to say that we subtract information actually present to arrive at the universal judgement. (Specifically, we abstract away from the kind of thing being counted.) As this is a subtractive process, no assumptions are added.
The same thing happens with the principles of being. We understand that an apple is an apple, a penny is a penny, etc. Then we have an ontological insight, and see that the identity in these cases does not depend on what is being considered, so, for all reality, whatever is, is -- and similarly, whatever is not, is not. That is how we come to know (and justify) the Principle of Identity.
If you're interested in pursuing this further, you might want to look at Aquinas's Commentary of the De Trinitate of Boethius.
Quoting MindForged
You persist! Yes, you are wrong again -- and on this very point. For the 8th or 9th time, to think correctly is to think in a way that preserves truth, not by accident, but because the way we are thinking will always preserve truth. This makes no a priori assumptions about what ways of thinking preserve truth, and what ways don't. To discover that, we have to examine actual ways of thinking, find those that seem to work invariantly, and then find justifications for the claim of invariant correctness.
Quoting MindForged
The lack of a formal theory of conditionals is not a lack of conditionals. For example, in the discussion of the sea battle (above) Aristotle is quite clear about the conditions under which the Principle of Excluded Middle applies.
Quoting MindForged
As I said, we grant "existence" by a willing suspension of disbelief. This means that we treat the imagined world as if it existed and instantiated the principles of being.
Quoting MindForged
Once you realize that truth is a binary relation (the adequacy of thought to reality) and truth-value is a unary property of propositions, it is clear that they are very different concepts. The fact that truth-value is problematic is shown by the paradoxes we have been discussing.
So you can define whatever you like (including truth-values) and work out rules to try to make your set of posits self-consistent (creating meta-linguistic structures, Russellian type theories, etc, etc.). If you take that course (and traditional logic is open to it), then in view of Goedel's work, you may never know that the system you have defined is actually inconsistent and you have wasted your life's work.
Alternately, you can abstract systems from reality, or from systems traceable toQuoting MindForged
reality -- and you will be guarantied that you are dealing with a self-consistent structure (because reality is self-consistent) and know that you will not have wasted your life's work on a possibly self-contradictory system.
Strange, I just showed you how a single insight can dispose of a whole series of paradoxes you admit vex modern logicians.
Quoting MindForged
As with the sea battle, we can apply logic to any premises we assume true for methodological purposes.
Science woks quite well applying the hypothetico-deductive method with the deductions using traditional logic. Just because we are treating a hypothesis as conditionally true does not mean that we cannot work out its consequences with a view to confirming or falsifying them.
Quoting MindForged
And I showed you how to restate quantified sentences in traditional proposition form.
Quoting MindForged
Without going into the innards of modern logic, either it deals with correct forms of thought, or it deals with other subject matter, such as linguistic forms or rules of symbolic manipulation that can be isomorphic to features of systems we are interested in.
If it deals with correct forms of thought, it is part of what I've been talking about, and if it presents new, correct ways of thinking, these are to be greeted with jubilation. If it deals with other subject matter, as scientists we need to think about that subject matter in truth-preserving ways -- and so employ traditional logic (as founded by Aristotle and advanced subsequently).
It is my view that modern logic is not concerned with correct thinking (as its object), but has for its object of study the manipulation of symbolic forms that may be isomorphic to various systems of scientific interest.
So, I see comparing them as involving a category error.
I am sorry, I haven't been closely following this entire exchange, but this just sounds like a wordy way of saying that the correct way of thinking is the way of thinking that is correct ("preserves the truth of what we know of reality," etc.) Not terribly illuminating.
Yes, that is why it is annoying to have to repeat it multiple times. Once, in my first post, should have been enough.
Once you get the point, the next obvious thing is to examine cases of truth preserving and fallacious thinking to discover rules that preserve truth, and then seek to justify them by showing how they reflect the nature of existence.
The next step cannot rationally be to posit axioms without examining how they relate to thought about reality.
It's not clear in this story what sort of question is being asked, and what sort of justification is being provided.
What does it mean to "question logic"? Is the question whether logic is useful for some purpose, or perhaps for every purpose?
Is logical consistency essential for good cinema, for amusing rhymes, for effective persuasion of millions of voters? Clearly not. Must we say that trees or stones are in themselves "logical", or that they somehow "employ logic"? No. Are these logically valid claims? So it seems. Does this amount to "questioning [the role of, or the limits of] logic? I guess so.
As a sort of skeptic I have wondered whether all my experience, including my memory and current use of a set of practices I associate with the terms "logic" and "language", are just so many incoherent figments of a confused dream. This sort of thought lands arguably at the boundaries of coherence, but I suppose it involves a logically consistent "questioning" of, say, the ultimate validity of logic. I suppose so... but if in fact the answer to the question were affirmative, and this logic were just an illusion, then my supposition may be false, and the question may not have been logical to begin with....
Need every "questioning" be a questioning in explicit language? Imagine I protest my friend's or my employer's overestimation of the power, utility, or purview of logic by farting, or by making some other extralinguistic gesture. I suppose I could translate the protest into any of a range of utterances with the grammatical form of a question. Some of these questions might involve vague poetic allusions or logical contradictions or grammatical nonsense. I'll allow that such illogical questions may be employed to satisfy a logically coherent intention by "questioning [the power, utility, purview of] logic".
What does it mean to "justify logic"? Justify it in what regard, for what purpose, against what charge...