Haha it's quite the predicament, right?

The correct thing to do is 1; it's implied by a logical principle. However, practical difficulties arise. So, we have to choose between 2 and 3. Most opt for 2. As you can see, option 3 (circularity) is avoided as much as possible. It's the least preferred choice. — TheMadFool

I've read that there are three main different theories that propose a solution to the trilemma. Each accepts one of the three options and tries to essentially build a theory on top of it. Coherentism= circular, Infinitism= ad infinitum, foundationalism= axioms. There is a bit of a roundabout solution to this problem in the philsophy of pragmatism. The pragmatic maxim states, "Consider the practical effects of the objects of your conception. Then, your conception of those effects is the whole of your conception of the object." So instead of thinking about this problem from the point of view of attempting to develop a kind of certainty, think about it from the angle of 'What would be the consequences of logic being fallacious in itself?'. The trilemma makes it very apparent that non-fallacious proof is impossible. Does that mean that logic should be abandoned? It's impossible to evaluate logic without the use of logic, but are there any other options? Would it be practical not to use logic because it is imperfect at its core?

I personally think that the relative fact that logic is capable of providing reproducible results is all you need to recognize the value of it. Taken to the extreme, when you accept that it is capable of reproducibility, I think it would be irresponsible to reject it outright. With the direction that technology is going in, logic is the only tool we have capable of mitigating impending existential doom brought on by technology. The very logic that built that technology so obviously it has some merit. But when it comes down to it, it really relies on faith in the system of logic itself, because the certainty of its value is impossible, some aspect of faith is necessary. I think that logic is a better tool to place one's faith in than religion, but that is my opinion.

Logic is not innate to the mind. We have to learn it. From where? From the external world. We learn the rules of logic by observing the world. Deductive logic works fine at the macroscopic level. In our everyday lives we never see violations of logical principles and deductive and inductive logic work well. — TheMadFool

I don't know that I agree with this. It is my understanding that to some extent, the circle of abductive>deductive>inductive reasoning is intuitive. I certainly followed that path before I knew what it is, and I think the creation of those terms was less about 'creating a way to think well' and more about understanding how we think. I don't think that logic was created by humanity, I think it is a tool that humanity is capable of intuitively using. So I disagree with the notion that logic is an aspect of the external world. I think it is a mental process that can be applied to external events and can be refined through understanding, not a mysterious product learned through nurture.

I personally think that the relative fact that logic is capable of providing reproducible results is all you need to recognize the value of it. — MonfortS26

I just thought of this but there's a difference between rationality and logic. The latter is a formalization of the former. The need for a good reason as to why logic is the correct way to think arises from rationality. This, as we know, is circular. The moment we look for a reason to be rational, we're already endorsing rationality.

As for ''reproducible results'' they are the work of logic, not rationality. So, if you see consistency and productivity of results in our way of thinking tjen they are due to logic and not rationality. Please note the difference between rationality and logic. The former requires reasons for everything while the latter specifies the rules of thinking. One could say that rationality is an overarching principle (should) while logic is the list of rules (how).

So, the circularity concerns rationality, not logic.

So I disagree with the notion that logic is an aspect of the external world. — MonfortS26

I gave a number of examples of different kinds of logic - paraconsistent logic, fuzzy logic, etc. They're all modified forms of sentential or predicate logic, designed to fit in with observation. The logic I'm familiar with doesn't tolerate contradictions but some say contradictions are part of quantum physics. What should we do? Ignore real observation or change our logic? This is what I mean when I say logic is learned and not innate.

To get back to the problem of circularity of rationality the only thing we can say about being rational is that we learn it from the outside world. This breaks the circularity. We have to be rational because the world is rational.

1. Continue ad infinitum
2. Agree on a starting point (axioms)
3. Enter a circularity

The correct thing to do is 1; it's impled by a logical principle. However, practical difficulties arise. So, we have to choose between 2 and 3. Most opt for 2. As you can see, option 3 (circularity) is avoided as much as possible. It's the least preferred choice. — TheMadFool

I suggest that we don't really have to agree on a starting point. Indeed, the starting point is often invisible (taken for granted). Having to agree sounds like it involves reasoning from these otherwise invisible axioms.

I think that logic is a better tool to place one's faith in than religion, but that is my opinion. — MonfortS26

To me this is like saying that apples make better banana than oranges do. I'm coming from the perspective that logic is the structure of our reasoning. We have no choice but to be logical. Of course we can take a conscious notion of virtuous rationality as our ideal. This seems like a belief that we should be able to make our reasoning explicit when asked sincerely and meet sincere objections to this reasoning. In short, we prioritize the quality of our reasoning over its tentative results. How and why we believe is (theoretically) more important than what we believe.

To be fair, some religion really does reject this ideal of explicit rationality (logicalness as virtue). In this case we do have being logical as primary virtue versus other goals that put being logical (explicitly, virtuously) in an inferior position.

That said, when we investigate logic itself, we find we're immediately involved in a circular argument. Simply put, we need proof that logic is the best mode of thinking but thinking this way presupposes that logic is the best mode of thinking. Note that we're looking for a deductive proof that logic is the best mode of thinking. — TheMadFool

Interesting. I think it supports the idea that we rely on know-how that cannot be justified. It's like the hand trying to grab itself in this case. It's like the eye trying to see itself to make sure it is really there --even though the essence of this eye is its seeing.

This is an example for me of us trying to get behind our own use of language. That which makes explicit cannot be made explicit itself. It functions as the action of insight and not its object, I'm tempted to say.

So, the circularity concerns rationality, not logic. — TheMadFool

I'd say that lines up with the reasoning that led me to my OP. That is if we're using rationality and reasoning as synonyms.

The logic I'm familiar with doesn't tolerate contradictions but some say contradictions are part of quantum physics. What should we do? Ignore real observation or change our logic? — TheMadFool

I don't know enough about quantum mechanics to make a statement on that lol.

To get back to the problem of circularity of rationality the only thing we can say about being rational is that we learn it from the outside world. This breaks the circularity. We have to be rational because the world is rational. — TheMadFool

I can get behind this.

We have to be rational because the world is rational. — TheMadFool

All you are doing is stating a belief which is what logic is all about. Stating a belief and then stating some observation as ever evidence of the belief followed by a conclusion that follows the belief. Logic is self-fulfilling in all cases and proving logic with logic is just a subset. It is the belief that creates disagreement, always.

I suggest that we don't really have to agree on a starting point. Indeed, the starting point is often invisible (taken for granted). Having to agree sounds like it involves reasoning from these otherwise invisible axioms. — dog

Well, the axiomatic approach is a foundation of logic and mathematics I think. It works.

Can you rephrase this. I didn't understand.

Think of it. In a world that has no rules/laws, logic, which is the rules of thinking, wouldn't work. In a chaotic universe without order logic would be pointless. Right?

So, we are logical because the world is logical.

Interesting thing is at different levels of our world the rules seem to be different. Sentential and predicate logic work well in the world humans can experience through the senses (imperfectly I believe). But the laws of nature are different at subatomic levels, requiring us to develop a new type of logic to make sense of it.

the axiomatic approach is a foundation of logic — TheMadFool

Maybe not. Natural deduction uses assumptions that can be introduced ad hoc, rather than axioms.

Maybe not. Natural deduction uses assumptions that can be introduced ad hoc, rather than axioms. — Banno

Axioms are, by definition, without logical support BUT they have to be obviously true. ''Ad hoc'' sounds too much like a game and logic, as enjoyable as it is, isn't just a game. Is it?

Of course it is.

Of course it is. — Banno

Well, everything can be taken to be a game. Doesn't that make ''logic is a game'' a pointless expression?

Games are rules-based.

1. Continue ad infinitum
2. Agree on a starting point (axioms)
3. Enter a circularity — TheMadFool

A varient on (2) would be to choose any arbitrary truths as starting points.

A varient on (2) would be to choose any arbitrary truth as a starting point. — Banno

Google definition of Axiom (emphasis mine): a statement or proposition which is regarded as being established, accepted, or self-evidently true.

So, axioms have to be self-evident. It must be so obvious that it would be illogical to deny it. A loop of sorts but it's definitely more reasonable than "ad hoc". Perhaps you meant the same thing and I misunderstood.

Nope. Agree on an arbitrary starting point. If a contradiction arrises, go back and have another go.

Nope. Agree on an arbitrary starting point. If a contradiction arrises, go back and have another go. — Banno

That's it. An axiom that mustn't lead to contradictions can't be "ad hoc".

Why not?

Also, where did "mustn't" come from?

Both Quine, Wittgenstein and Lewis Carroll have each denied that any statement is necessarily implied by any other. To paraphrase, any explicit representation of a rule divorced from the practices of a custom can be variously interpreted. For example, to interpret an arrow as pointing in a particular direction relies implicitly on a notion of "point" "base", and so on.

Hence what we mean by a "rule" cannot be represented independently of our case-by-case demonstration of it and our intentions. Rather, our behavioural demonstrations in concert with us presenting a signification of our actions to others and expressing normative reasons why they should follow our example, testing their understanding of our intentions and so on, IS the rule.

A strip of concrete isn't a path outside of an established custom for walking, and it is the intentions of the walking community that define what it means to say that it is necessary for pedestrians to stick to the path and that the path determines where they can walk.

The concrete path is also analogous to physical laws established by the scientific community. Their scientific observations in relation to their laws are like foot-prints that are discovered by the walking community to frequently wander off the concrete path.

Imagine if the elders of the walking community relaid, extended and widened the concrete path whenever foot-prints veered off the path in the hope that future walking would automatically abide by the path. This is analogous to the epistemology of science. But if the path is relaid whenever it is trespassed, would it now make sense to say that the movement of walkers is determined by the path (or vice versa)?

I'd rather put it this way. One modern view of logic boils down to: logic is really just using symbols consistently in some symbol-shuffling game (or algorithm: recipe for symbol-shuffling). In this sense, logic is thought of as pure syntax, intrinsically detached from semantics (or the "interpretation" of those symbols, which makes the symbols stand for things in the world).

In that case, it's just happenstance that some dreamed-up algorithm happens to fit reality.

But then a lot of people go an illegitimate further step, and think that means logic isn't inherent in nature, isn't bundled into semantics.

But if a dreamed-up algorithm fits reality,it really fits. i.e. nature really, objectively hasthat particular pattern. So in fact, the syntax of logical statements that do happen to actually describe the world is derived from semantics (which is another way of saying what the later Wittgenstein was banging on about, the sort of thing Sime talks about above). Even though we can extend logic and play with patterns that are divorced from anything real, the starting point is the logic of the middle-sized furniture of the world that we commonly interact with from birth - just the standard logic. What logically follows from what depends on the nature of the things being symbolized.

The upshot is that you can't demonstrate the validity of logic in general (because logic is just dreamed-up consistent play patterns that may or may not fit some reality). But for any given logic that does fit the world as we find it, the world as we find it necessarily has that logic, that nature, that flow, that grain.

However, of course while that's obvious in principle, in practice, since the scope of our knowledge is limited, there may be any number of unknown factors that could make our deduction wrong, unbeknownst to us.

And this is really what makes the difference between induction and deduction. Induction isn't actually any different from deduction - rather, it's deduction that's aware of knowledge limitations, hence it's expressed in terms of probabilities. Induction is the punting of a specific nature or identity for experience, then the deducing of necessary conclusions (for experience) from that nature or identity. This is the process of science, in essence - we think up a possible character for things, and see if experience bears out the logical implications of the character we've posited for the things. But because of knowledge limitations, we have to hedge our bets ("all things being equal", "presuming no confounding factors", "it is probable/possible/likely that ..." etc.).

Just one final thought: it's unproblematic to think of logic as innate to some degree. It's pretty obvious that we bootstrap ourselves all the way from childhood into adult knowledge not from a pure blank slate position, but from an innate understanding of some basic logical primitives. However, that understanding has to be drawn out from us (in the Platonic sense of anamnesis), it's not in front of us reflectively from infancy, rather it's just innate in the way we act from infancy (e.g. reaching out expecting to touch something), and comes to conscious reflection as a result of interaction with the world. (Rather analogous to the way genes are expressed in the phenotype, in fact.)

Yes, except

...and our intentions... — sime

happens too fast.

It's not clear that bringing intent into the discussion helps; why not stop at behaviour?

If I accelerate towards a red light, but my car stalls so that I stop at the light, haven't I obeyed the traffic rule despite my intent?

n that case, it's just happenstance that some dreamed-up algorithm happens to fit reality. — gurugeorge

Speaking for myself, I think logic is derived from the world outside. I've read a few books on logic and all of them make a similar point - that logic is essentially about finding truths about the world. Isn't it obvious then that our logic (its structure) must mirror the structure of reality itself? I don't think this is "just happenstance".

Just one final thought: it's unproblematic to think of logic as innate to some degree. — gurugeorge

I agree but here too I believe evolution has played a part. From all the different possible brain structures only those that conform to the rules of the world have been selected. All the other types of brain structures, with logical components that didn't reflect the world's structure, were culled.

Why not?

Also, where did "mustn't" come from? — Banno

It's my understanding that any logical system developed must be useful in the sense that it can find truths about the world. I agree that we can arbitrarily choose the axioms of a logical system BUT the systems with axioms that lead to nothing must be discarded. Right?

Isn't it obvious then that our logic (its structure) must mirror the structure of reality itself? I don't think this is "just happenstance". — TheMadFool

What I'm saying is that even if the fit between our dreamed up logical puzzle games and reality is happenstance, if we find one that fits, then the fact that the puzzle structure came from our side doesn't in and of itself mean that nature doesn't actually have that structure. Indeed, if the structure fits reality, that's prima facie evidence that reality has that structure, that it objectively has it, that the structure is "out there" in the world.

I don't see why. Logic is just bunches of symbols matched up according to rules. It's a game.

If every now and then a logical system is useful, so much the better.

I don't see why. Logic is just bunches of symbols matched up according to rules. It's a game.

If every now and then a logical system is useful, so much the better. — Banno

But a game can't be played before we've learned the rules.

Unless the game is inventing the rules.

Unless the game is inventing the rules. — Banno

Yes.

That said, when we investigate logic itself, we find we're immediately involved in a circular argument. Simply put, we need proof that logic is the best mode of thinking but thinking this way presupposes that logic is the best mode of thinking. Note that we're looking for a deductive proof that logic is the best mode of thinking. — TheMadFool

Why would we need to presuppose that? For one, logic is *not* a mode of thinking, that's silly. Logic refers to a theory of logical consequence, that is, a theory of what follows from what. In other words, when some things are true, it appears other truths can be derived from it. E.g. If it's raining, then there are clouds in the sky. It's raining. Therefore there are clouds in the sky. No thinking is needed here, as computers (which are not sentient) operate according to the rules of (essentially) classical propositional logic. And really, if logic were simply a mode of thinking, what logic do we think in accordance with? If anything, it's an extremely weak logic that can hardly derive very much unless we force ourselves to adhere to and specific set of inference rules (because we often have inconsistencies in what we think, meaning we cannot reason via classical logic because of the law of explosion).

So, how does one get out of this predicament, The Fallacy of Logic?

Logic is not innate to the mind. We have to learn it. From where? From the external world. We learn the rules of logic by observing the world. Deductive logic works fine at the macroscopic level. In our everyday lives we never see violations of logical principles and deductive and inductive logic work well.

I've heard that this isn't the case at the quantum level. I believe there are many situations where contradictions (a no-no in logic) arise. For such experiences we need a different kind of logic - something that accomodates the ''strange'' behavior of quantum objects.

This is just wrong and I wish people would stop saying it. Quantum mechanics is a consistent theory, it doesn't portray an inconsistent quantum realm (unless you're Newton da Costa). Quantum physicists use the standard mathematical formalism (ZFC + classical logic) so it's necessarily consistent since otherwise trivialism would follow. Quantum logic is a separate logical system, but that logic only discharges the Distribution Axiom, not the Law of Non-contradiction.


This isn't a logic specific problem at all, it's just a broad epistemological issue. One simply picks their logic in accordance with a model of theory choice (logical systems are competing theories about logical consequence after all) and proceeds to do their work from there. Not everything needs to be justified so this is not an interesting problem to me.