Logic is a poorly developed ability of a single half insane semi-suicidal species on one little planet in one of billions of galaxies. A useful tool in a limited context, but not a god.

So, it appears that we can neither justify nor critique logic. — TheMadFool

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:

Its important tho consider what sort of thing logic is.

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.

There's a lot of... weird statements made in this thread.

Of course [one] is correct. Logic has to rest on something. It’s not controversial, although it never ceases to surprise how many people seem to think it’s fishy or suspect.

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. — 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.

You may consider it a working presumption, if you like, which enables all kinds of things, including our talk.

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.

Frege also thought the Comprehension Schema was "self -evident", but Russell proved it led to Russell's Paradox. — MindForged

That’s what I meant by ‘not omniscient’.

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. — TheMadFool

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'm just saying even the deepest intuitions about logic don't have a sort of indubitability (what I thought you were saying).

I’m saying that they are indubitable within limits. What I said to the aptly-named OP is that there’s no more point trying to explain the fundamentals of logic, than there is in trying to explain why elementary arithmetical proofs are valid. To explain anything about logic you have to appeal to logic. I can’t see an alternative, short of Dada-ism.

I was reading a text book on Buddhist logic the other day, which pointed out that while Buddhism is explicit about the fact that Nirvāṇa is beyond ‘mere logic’, Buddhist logicians are nevertheless quite scrupulous in their use of logic [as indeed was the Buddha]. Indeed Nāgārjuna’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.

You may consider it a working presumption, if you like, which enables all kinds of things, including our talk. — jorndoe

How so? That some objects may not be self-identical doesn't seem to have anything to do with me talking. — 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:

A suggestion – you obviously imply the static, monotonic logics. Once you derive a conclusion – there is no way to correct it based upon new information. In addition, all monotonic logics imply rules of a finite system. Note, Gödel’s proof that there are truths in finite (closed) systems that cannot be derived from other truths within the finite (closed) system.

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,

You don't seem to have understood me. Some things may well be self identical. My statement is in fact identical with itself. But that has no bearing on *everything else* also being identical with themselves.

So for instance, take Schrodinger himself in "Science and Humanism":

"When you observe a particle of a certain type, say an electron, now and here, this is to be regarded in principle as an isolated event. Even if you observe a similar particle a very short time at a spot very near to the first, and even if you have every reason to assume a causal connection between the first and the second ob servation, there is no true, unambiguous meaning in the assertion that it is the same particle you have observed in the two cases. The circumstances may be such that they render it highly conve nient and desirable to express oneself so, but it is only an abbre viation of speech; for there are other cases where the 'sameness' becomes entirely meaningless; and there is no sharp boundary, no clear-cut distinction between them, there is a gradual transi tion over intermediate cases. And I beg to emphasize this and I beg you to believe it: It is not a question of being able to ascer tain the identity in some instances and not being able to do so in others. It is beyond doubt that the question of 'sameness', of identity, really and truly has no meaning."

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:

SELECT * FROM tbl WHERE NULL=NULL

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.

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 — TheMadFool

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 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 — Sam26

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?

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. — Sam26

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.

I was reading a text book on Buddhist logic the other day, which pointed out that while Buddhism is explicit about the fact that Nirvāṇa is beyond ‘mere logic’, Buddhist logicians are nevertheless quite scrupulous in their use of logic [as indeed was the Buddha]. Indeed Nāgārjuna’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.

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.

Do the Buddhists explain why to show the limits of logic, one needs to use logic? — Shmuel

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 Nirvāṇa 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 Tathāgata [i.e. the Buddha], having realized for himself with direct knowledge, propounds to others.' (Emphasis added).

What would be the fault of trying to show the limits of logic without using logic? — Shmuel

How would you go about that?

What would be the fault of trying to show the limits of logic without using logic?
— Shmuel

How would you go about that? — Wayfarer

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.

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 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. Predictions 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...

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 — TheMadFool

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

The mind can be used to study the mind just like a logical argument can be used to justify logic. This circularity is benign. — TheMadFool

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.

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. — 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.

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. — 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"?

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.

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.

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.

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).

So, it appears that we can neither justify nor critique logic. Both are circular. — TheMadFool

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".

"If ALL the predictions of logic are true then logic is justified" but if we dont know the end result, how can we know the logic is true?

You realise that those words belong to TheMadFool, not me, yes? I was arguing against what TheMadFool was saying.

oh, shit, I didnt know. im just new to this :)

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 old definition of logic, as "the science of correct thinking" still works for me. We might be a little more explicit and say it is the science of correct thinking about reality -- because we want it to be salve veritate -- if our premises reflect reality, then we want "correct thinking" to be such that our conclusions will necessarily reflect reality.

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 <this ball is rubber>, is it not because the object that evokes the concept <ball> is identically the object that evokes the concept <rubber>? In other words the copula of categorical propositions expresses identity, not of concepts, but of the source of concepts.

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