Logically in the classical sense (categorical, sentential, predicate logic), the key premise being the law of noncontradiction (LNC) can't be violated!

I'm concerned because there seems to be no deductive proof for The Fundamental Principle of Epistemology. — Agent Smith

This "law of noncontradiction" has essentially been disproven by the principle of quantum superposition.

This "law of noncontradiction" has essentially been disproven by the principle of quantum superposition. — Hermeticus

1. I'm not really sure about that because the violation doesn't seem to carry over into the math i.e. the equations or whatever mathematical propositions are part of superposition, they don't amount to a contradiction! This has been bothering me!

2. Suppose the LNC is violated through and through. That would mean, as evidenced by the statements from many (quantum) physicists, the universe, parts of it at least, don't make sense or, more optimistically, they do make sense, just not in classical logic.

I'm concerned because there seems to be no deductive proof for The Fundamental Principle of Epistemology. — Agent Smith

Why is the lack of a deductive proof a concern? Suppose (a) it's a sound principle (b) we know it (c) we have good reason to rely on it and (d) we don't have a deductive proof of it. Suppose further that we have some reason to think that no matter how hard we look we will not find a deductive proof - and that this does not in the least diminish its soundness or our knowledge of it. I'm supposing all those things. Where (if at all) have I gone wrong?

I think there must be lots of propositions we don't have deductive proof for. The sun rose earlier today, for example.

I think there must be lots of propositions we don't have deductive proof for. The sun rose earlier today, for example. — Cuthbert

Well, I was hoping to cause the same amount of dismay in epistemologists as the problem of induction (vide Hume) caused scientists.

Why should the universe (1) make sense (2) to us? — Agent Smith

We are natural outcomes of the universe and its properties that we find ourselves. It's like asking how does anything exist in the way it does? Because that is how this universe works. Natural selection has selected organisms with opposable thumbs and large brains because this form of ours is more compatible with survival in this universe, or at least on this planet. What species has been able spread out like we have all over the globe and into space?

This "law of noncontradiction" has essentially been disproven by the principle of quantum superposition. — Hermeticus

Then the LNC has both been proven and not proven. Remember that by dismissing the LNC you accept ALL contradictory ideas as both being true, not just one.

Remember that by dismissing the LNC you accept ALL contradictory ideas as both being true, not just one. — Harry Hindu

How? The law of noncontradiction states that contradictory propositions cannot both be true in the same sense at the same time.

Disproving such a law does not mean that the opposite applies - merely that the law doesn't always apply.

By dismissing the LNC I accept that:
Some contradictory ideas can be both true.
Some contradictory ideas can be both false.
Some contradictory ideas cannot be true in the same sense at the same time.

Disproving such a law does not mean that the opposite applies - merely that the law doesn't always apply.

By dismissing the LNC I accept that:
Some contradictory ideas can be both true.
Some contradictory ideas can be both false.
Some contradictory ideas cannot be true in the same sense at the same time. — Hermeticus

Now you're going to have to explain in what instances it doesn't apply and why. Examples would be nice.

https://thephilosophyforum.com/discussion/11575/logical-nihilism

Don't blame me. It was Banno.

Why should the universe (1) make sense (2) to us? — Agent Smith

There is no reason why the universe should, or should not make sense. The point of knowledge is to attempt to make sense of the universe for our survival and proper use of it. The struggle of epistemology is to come up with a tool that can enable us to do this in the most rational manner possible.

Logic is the tool we use for rational thought. Rational thought eliminates as much uncertainty as possible, but also recognizes its limits. Calculus for example is a form of logic that evaluates limits to never ending equations. When we apply that tool, we are able to get consistent enough results about reality to use it to our ends.

Logically in the classical sense (categorical, sentential, predicate logic), the key premise being the law of noncontradiction (LNC) can't be violated! — Agent Smith

As for this, try to disprove the law of non-contradiction yourself. Can 1 equal, and not equal 1 at the same time? And by equality, I mean down to the smallest scale of measurement you can imagine, that 1 is both equal, and not equal to 1 at the same time.

Equality is a term we've invented, so of course its impossible for something to be a contradiction. Something cannot be both equal, and not equal to itself. At that point, we need a refinement of words or measurements. And that is partly what logic is. An invention of terms and words that consistently work with each other, and apply to reality without contradiction.

Can 1 equal, and not equal 1 at the same time? — Philosophim

According to one view in this thread, no, 1 cannot both equal and not equal 1. But one particle can both be and not be in the same place at the same time. That's because LNC applies to arithmetic but (as it happens) not to superposition. So the theory goes.

You hit a contradiction. If you can find no other way out, jettison LNC. Ta-da!

It's like some politicians' approach to their country's Constitution. As soon as it's inconvenient, you just ignore it.

A more modest approach would be - "We haven't found a way to describe superposition without apparent contradiction. Therefore we haven't yet found a good way to describe superposition. But we're working on it."

According to one view in this thread, no, 1 cannot both equal and not equal 1. But one particle can both be and not be in the same place at the same time. That's because LNC applies to arithmetic but (as it happens) not to superposition. So the theory goes. — Cuthbert

I think this is misunderstood. Superposition can only occur when the particle is not observed. This doesn't mean observation from humans fyi, but observed by anything, like what we use for measurements. For math purposes, we state they are in simultaneous positions when we have no way of measuring which specific position its in.

Setting limits on our knowledge, and consequences of them, is a common practice in math, like in calculus. If I wanted to tell a layman how calculus works in a mysterious fashion, I could state, "Calculus brings limits where they do not exist. The math itself creates limits out of infinity. This is only due to the existence of human brains however. Without them, the reality is there is no limit, but the conclusions of the equation extend into infinity".

Quantum mechanics is really understood at a mathematical level, and people make mistakes in applying that math to reality beyond what is intended. Just like calculus does not magically create a finite solution out of the infinite, quantum mechanics does not prove that a particle can exist in two places simultaneously, beyond the mathematical limitations it works with. In practice, testing, and application, a particle cannot exist in two places at once.

quantum mechanics does not prove that a particle can exist in two places simultaneously, beyond the mathematical limitations it works with. In practice, testing, and application, a particle cannot exist in two places at once — Philosophim

Yes, I'm sure you are right. I was questioning the idea mentioned in a post above that superposition disproves LNC. Even if superposition seems (to somebody) to disprove LNC, it probably doesn't. And as you say, even the idea that it seems to disprove LNC is based on a misunderstanding. Still, it will keep coming back. It always does. The parallel with calculus vs Zeno's paradoxes is useful.

I'm concerned because there seems to be no deductive proof for The Fundamental Principle of Epistemology. — Agent Smith

Because there isn't one. The universe doesn't make sense; it just is. You apply the sense - as best you can, and while your sense appears more sophisticated than the medicine man's, that's just for now. As for the LNC, it's just a rule of logic, the kind called an axiom, a fancy way of saying not provable. But I did find one proof: it works because it had better work!

It's like a hammer. If you don't understand what a hammer is or is for, or how it works, then you don't understand carpentry and a lot of other things. That is, the understanding and "proof" of a hammer is in terms of those other things. In a way its grounds and warrants are all in itself, bootstrapped, in a sense. And if not, then nothing at all.

Because there isn't one. — tim wood

I see.

So, would I be right in saying that our, especially a philosopher's, attempt to make sense of it all is, in a sense, misguided as it is not at all certain that this can be done.

This reminds me of what the great Albert Einstein said (vide infra).

The most incomprehensible thing about the universe is that it is comprehensible — Good ol' Albert

The way Einstein phrased it, he was quite taken by surprise that the universe makes sense (is comprehensible) which is proof enough (for me) that The Fundamental Principle of Epistemology (see OP) is, if challenged, untenable.

Merci!

There is no reason why the universe should, or should not make sense. — Philosophim

:up: Good point. It appears that, given what we know till date, taking into account all that we know, the jury's still out. However, if I'm to let the pessimist in me take over, sense in the universe seems to suffer a setback at very critical junctures - just as we're about to solve the friggin' mystery, we hit a wall (cosmic censorship). There's more that can be said but I'll leave it at that.

Remember that by dismissing the LNC you accept ALL contradictory ideas as both being true, not just one. — Harry Hindu

Thanks for the warning! It is a big decision, a matter of life and death actually, but then I hear there are ways to defuse the principle of explosion (ex falso [sequitur] quodlibet).

So, would I be right in saying that our, especially a philosopher's, attempt to make sense of it all is, in a sense, misguided as it is not at all certain that this can be done. — Agent Smith

It seems to me that the more you try to prove - or anything else - the more energy and effort and care you have to take with definitions and understandings, as to what exactly they define and understand. That is, "local" to any problem you can have all the proof and understanding you want. Example: Because I have a book on my table, there is no hippopotamus in my den. Proof: the book is on my table and there are no hippopotami near. You don't like the proof? It works for me! So the philosopher, or the scientist, says, "It works for me." And that's it, until it doesn't. In short, we can be certain that it can be done and is done, depending on what we call certainty, or what exactly our ground is. And of course that subject to the same question.

The universe makes sense (logically).
Logically in the classical sense (categorical, sentential, predicate logic), the key premise being the law of noncontradiction (LNC) can't be violated!Why should the universe (1) make sense (2) to us? — Agent Smith

Because we stacked the deck, declaring that only what can be depicted in terms of predicate logic can be considered a real component of the uninverse.
So we can force the universe to make sense in formal logical and mathematical terms by tremendously restricting what qualifies as real to what can be logically predicated. Or we can expand our understanding g of ‘making sense’ in the direction of subjective processes of perception and intersubjective processes of language,

Why should the universe (1) make sense (2) to us? — Agent Smith

That's a very good question! :smile:
Well, I personally have no problem not knowing the meaning and purpose of the universe. It's enough for me that I can make use of it, i.e. create a meaning, purpose and uses for it.

Fire had no meaning or purpose by itself. Man has created one. (In fact, a lot ot them.)

Likewise, life per se has no meaning or purpose. We must create one for ourselves.

The Fundamental Principle of Epistemology: The universe makes sense (logically). — Agent Smith

We've discussed this type of issue several times in the recent past here on the forum. The statement "The universe makes sense," is a metaphysical statement, i.e. an absolute presupposition. As such, it is neither true nor false. It has no truth value. It's just a rule we all agree to apply because if we don't, we can't say we know anything. All in all, it seems to work pretty well.

It doesn't need to be mentioned but for the sake of clarity and arguendo,

The Fundamental Principle of Epistemology: The universe makes sense (logically).

Logically in the classical sense (categorical, sentential, predicate logic), the key premise being the law of noncontradiction (LNC) can't be violated!

I'm concerned because there seems to be no deductive proof for The Fundamental Principle of Epistemology.

Why should the universe (1) make sense (2) to us? — Agent Smith

The universe does make sense to us. I'm not sure the question as to why it should make sense to us makes sense. If the universe didn't make sense to us we would not be able to live. which of course means we would not be able to ask the question as to why the universe should makes sense.

As to the LNC, if something was both black and white all over, that would be a contradiction. But we never see anything like that. Such things seem ontically impossible, and if that's true then the phenomenal world is a world of non-contradiction.

But one particle can both be and not be in the same place at the same time. That's because LNC applies to arithmetic but (as it happens) not to superposition. So the theory goes. — Cuthbert

A particle cannot be and not be at the same place at the same time. It can be at all positions at the same time, with associated chance densities. It can't be at none of the positions at the same time, with associated chance densities. That would make the chance it's nowhere 1. How can the chance that it's nowhere be one and the chance that it's anywhere be 1 just the same? Of course there are complementary chances that it's not at that place, but that's simply the chance it's at another place. You don't make a measurement of a particle not being there. You measure the presence of particles, not their absence. In hindsight you can assign probabilities of not finding it, of not being at one place.
Isn't the LNC broken in this case? Does it make sense to say the particle is here and not here at the same time? If the chance it's not at A is 1/2 and the chance it's not at B is 1/2 too, is the chance it's not at both 1?

A particle cannot be and not be at the same place at the same time. — AgentTangarine

Yes, I am sure you are right. By "So the theory goes" I was referring to the theory which I don't subscribe to - Hermeticus's post near the start of the thread. Superposition is a distraction. A theory might seem to disprove LNC but not actually disprove it, the theory itself being the premiss at fault.

So, would I be right in saying that our, especially a philosopher's, attempt to make sense of it all is, in a sense, misguided as it is not at all certain that this can be done. — Agent Smith

I think the idea is that making sense of the universe is not a misguided project - but it is we who are making the sense of it and we are not reading off a sense that is already there. Making sense of things is a project for rational minds and the universe is not in itself and as a whole a rational mind. So another theory goes.

Why should the universe (1) make sense (2) to us? — Agent Smith

I don't think the universe should or should not make sense. It's a metaphysical presupposition (especially held in science) that 'reality' can be understood by human beings. Using science we are obviously able to develop tentative models of the world we know based on the best available evidence that can yield impressive results. But understand the universe? Not even sure this is a meaningful idea. What do you mean by understand and what do you mean by universe?

"The universe is under no obligation to make sense to you." ~Neil deGrasse Tyson

(E.g. read Zapffe or Camus.)

This "law of noncontradiction" has essentially been disproven by the principle of quantum superposition.
— Hermeticus

Then the LNC has both been proven and not proven. Remember that by dismissing the LNC you accept ALL contradictory ideas as both being true, not just one. — Harry Hindu

:100:

A more modest approach would be - "We haven't found a way to describe superposition without apparent contradiction. Therefore we haven't yet found a good way to describe superposition. But we're working on it." — Cuthbert

:fire:

"If you think you understand quantum mechanics, you don't understand quantum mechanics." ~Richard Feynman

Why should the universe (1) make sense (2) to us? — Agent Smith

(1) The universe "makes sense" because
(2) we are aspects of the universe who must make as much sense of it (via myths, metaphysics, arts, histories, natural sciences, etc) as we can in order to help ourselves survive and our descendents thrive despite the universe.

"The more the universe seems comprehensible, the more it also seems pointless." ~Steven Weinberg

The universe does make sense to us. I'm not sure the question as to why it should make sense to us makes sense. If the universe didn't make sense to us we would not be able to live. which of course means we would not be able to ask the question as to why the universe should makes sense. — Janus

1. If the universe didn't make sense (to us), we wouldn't exist.

2. We exist.

Ergo,

3. The universe does make sense (to us). [1, 2 MT]

The Anthropic Principle (AP) arose out of the question "why are the properties of the universe such that it allows (intelligent) life?" The AP answer is that there's nothing to explain because there's a multiverse out there and we simply happen to be (it's a fluke) in a universe which is life-friendly (comprehensible).

In other words

1. Yes, the universe is comprehensible (we wouldn't exist if not)

2. There is no reason why the universe is comprehensible. It's just a probabilistic outcome.

As to the LNC, if something was both black and white all over, that would be a contradiction. But we never see anything like that. Such things seem ontically impossible, and if that's true then the phenomenal world is a world of [...] — Janus

The LNC is the foundation of classical comprehensibility; it's a litmus test for sense as opposed to nonsense. Nonsense is a much broader concept (incoherence is a bigger world than mere inconsistency).

We must create one for ourselves. — Alkis Piskas

Comprehensibility is not something we can project/impose onto something that is inherently incomprehensible unless you mean, by that, pareidolia/apophenia. Interesting to say the least!

See Janus' argument (above).

I don't think the universe should or should not make sense. — Tom Storm

Why? Anyway, The Fundamental Principle of Epistemology (FPE) is one we work under. I'm looking for a proof (deductive) for the FPE. See Janus' post (above).

What's the :100: for? Any relevance to the OP?

Please weigh in on Janus' post and my reply to him/her (above) - I like his/her argument. It's a variation of the Anthropic Principle.

↪180 ProofWhat's the :100: for? Any relevance to the OP?

@Harry Hindu aptly corrected @Hermeticus' self-refuting claim and thereby defended the OP.

1. If the universe didn't make sense (to us), we wouldn't exist. — Agent Smith

False. The universe doesn't "make sense" to bacterium and they survive ("exist") in exponentially greater magnitudes than all humans ever born.

I more or less said as much in my previous post in reply to your two-part question from the OP. Not an "Anthropic Principle" in the least.

Quantum superposition has already been logically described without contradiction using Tensor Products in Categorical Quantum Mechanics, a form of Linear Logic . Linear logic is para-consistent, so doesn't permit the derivation of anything from A and not A, otherwise known as ex contradictione quodlibet.

False. The universe doesn't "make sense" to bacterium and they survive ("exist") in exponentially greater magnitudes than all humans ever born.

↪Agent Smith I more or less said as much in my previous post in reply to your two-part question from the OP. Not an "Anthropic Principle" in the least. — 180 Proof

I mulled over this matter as best as I could and here's what came out from my that:

Comprehension requires a thing (C) that can be comprehended and (O) a comprehender. Comprehensibility is about C and not O. Thus, even if a bacterium fails to comprehend, the universe is/can still be comprehensible.

What aided me in that understanding, if it is one, is looking at comprehensibility as simply patterns which if you think about is nothing but laws of nature. Isn't it true that sussing out the universe is, either in part or in whole, discovering the laws of nature (patterns)?

Janus argument then becomes:

1. We exist implies the universe is comprehensible (patterns)
2. We exist
Ergo,
3. The universe is comprehensible (patterns).

The Anthropic principle is a response to the pressing question:

4. Why are the properties of the universe such that (intelligent) life is possible & actual?

4 is another way of asking:

5. Why is the universe comprehensible?

After all it's comprehensibility (patterns/laws) that make the universe suitable for life.

The response based on the Anthropic principle is that this universe which is comprehensible is just one of many possible and actual universes (the multiverse); in other words there's no reason why the universe is comprehensible (Nothing to see here! Move on, move on!)

That's my take on the issue. I could be wrong of course. Correct me if I am.