Everything and nothing is happening and not happening, everywhere and nowhere, all at once, now, never and forever.

“It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect” (with the appropriate qualifications) (Metaph IV 3 1005b19–20)

- Aristotle.

When I hear "logic" assert the Principle of Identity, I say "prove it." Logic's response seems to be, it's "self-evident". That response reminds me of a frustrated parent saying "because I said so." — James Riley

To start off, this is an interesting subject and a very well written opening post.

Here's a list of philosophical definitions I posted here a few years ago.

Definitions:

• A priori truth – An assertion I want to be true but that can’t be proven, that I can’t prove, or that I’m too lazy to prove
• Atheism – A philosophical system for explaining to people who don’t believe in God why you don’t either
• Logic – a philosophical method for determining the truth without having to actually know anything
• Common sense – See “A priori truth.”
• Knowledge - There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know.
• Philosophy – The search for the truth; the meaning of life; the nature of existence; and the definitions of long, obscure words translated from German
• Clarity – Expressing what you mean in a way that makes it obvious you’re wrong
• Self-evident – See “A priori truth.”

Anyway, I share your suspicion about "self-evident." I think you're exactly right, it's "because we must agree on that before we go forward into argument. Otherwise, we can't even converse." That's what R.G. Collingwood would call an absolute presupposition. Do you agree @tim wood? On the other hand, when I say "We hold these truths to be self-evident, that men are endowed by their creator with certain unalienable rights...," it's something different. It's a statement of values. Actually, now that I think about it, maybe a value is an absolute presupposition too.

Nevertheless, it leaves me feeling somewhat an imposter to continue without a proof. — James Riley

If I may paraphrase that famous philosopher Joel Hodgson:

If you're wondering how it's justified
And other logic facts
Then repeat to yourself "It's just philosophy
I should really just relax"

In response to a demand for proof, I've also heard that a negative cannot be proven. — James Riley

This has always bothered me. Maybe you can't prove a negative is true, but you can show it's useful to act as if it is. To me, this shows how little people understand what "to know" means. I think the Hodgson paraphrase works even better here.

All the forgoing is a digression I'm trying to address in aid of another argument. I'm convinced that infinity must account for the absence of itself in order for it to be infinite. — James Riley

Mathematics is full of ideas that are absurd until we find a use for them, e.g. zero, irrational numbers, negative numbers, imaginary numbers. Infinity is useful, therefor it exists.

I think the failure of physicists to marry General Relativity and Quantum Mechanics is due to their stipulation to the Principles of Logic which they think are required to allow them to converse. — James Riley

Is this based on some specific knowledge or understanding you have? Please explain.

Any help on the Principle of Identity or the Law of Contradiction would be appreciated. — James Riley

My pet peeve is logical fallacies. I think a lot of the arguments called that are useful and legitimate.

Anyway, good post.

There's the world, and there are the tools used to make way in it. Like language and logic. A person can hurt themselves with tools not used properly. Some guidelines for their use. If it hurts, stop. If you reach a dead end, turn around. If on the wrong path, go back to the beginning or at least the last fork in the path, and start again. If you're in a hole, stop digging. And so forth.

To use the tools, know your material, know what you're trying to do. Identify the right tools and use them correctly. Avoid any confusion. And so forth. Also, do not misinterpret results. They are exactly what they are and nothing else. If you don't know, then you don't know, and that's a kind of knowledge. But a typical error is to suppose (not you, but other people) that because they do not know, then they know.

Imo, all of your confusions above result from breaking most of these rules and more besides. The good news is that you're not condemned to keep doing what you're doing; you can restart on a fresh page anew.

Thanks, T Clark. That was an enjoyable and enlightening read.

When I say "I think the failure of physicists to marry General Relativity and Quantum Mechanics is due to their stipulation to the Principles of Logic which they think are required to allow them to converse", my thought is not based on specific knowledge, or even a perfect understanding of how physicists converse, but, rather, on supposition. I assume that physicists abide the advice of tim wood, above, regarding tools and the proper use thereof. And I assume that abidance is the cause of their failure.

In following tim wood's advice, I've tried to go back to the beginning (the fundamental principles of logic) and check to make sure they stand up to more than a simple "gentleman's agreement" made to allow us all to make our way in this world, unhindered by uncomfortable, counterintuitive truths.

I was taught that in logical argument, the parties must chase all the premises back to that point upon which everyone is agreed before they can go forward (i.e. the beginning or a fork in the path). I'm simply refusing to agree with logic's premise, and demanding that it meet its burden of proof with more than a "because I said so." Perhaps I'm just not a gentleman.

I get there because I always get a "Duh!" feeling in my gut whenever I hear how quantum theory has come up with some new idea, like spooky action at a distance, for example. It seems to me that if my a priori truth (as you defined such truths above) were to be accepted, if all the tools were tossed, and all the rules were broken, and we started anew with my understanding of All, then "Duh!" would be the wedding of the two camps.

One might argue such a definition of All would have our brains fall out in open mindedness; we could not converse or make our way in the world. Even if that were true, I see no harm in assigning a small cadre of physicists to look into it. After all, it seems to be their camp which is frustrated. While they are skipping along their investigative way forward, they might send a party back to make sure they didn’t get off the trail at the beginning. Of course, by my definition of All, there would be nothing wrong with that if they did. Indeed, it would be necessary. It would not even be a waste of time to waste their time.

But if my definition of All were correct, I don’t think it means our brains would fall out or we couldn’t converse. I just think people smarter than me (physicists) would have some “AHA!” moments we could all enjoy and benefit from after the dutiful dumbing down for public consumption.

All the foregoing, and my tossing out the rules, had me generating what I thought were interesting opinions on particle physics, singularities, matter, dark matter, energy, dark energy, and time. But I’d sure like to nail down why I’m wrong about my foundation before I continue building on it.

Anyway, thank you for your gracious and understanding response. It is impossible for wise to complain about stupid. And, while you might have made fun of me and I’m just too stupid to know it (not saying you did; it’s just that it flew over my head, as it was probably supposed to, if indeed you did), at least you didn’t complain. A soft broke horse is a better horse.

you might have made fun of me — James Riley

I absolutely wasn't trying to make fun of you. I did try to be funny. The list of definitions I included is from a thread of philosophy jokes I started a couple of years ago.

I assume that physicists abide the advice of tim wood, above, regarding tools and the proper use thereof. And I assume that abidance is the cause of their failure. — James Riley

I assume I'm no more sophisticated in advanced physics than you are. It is my understanding that the reason quantum mechanics and relativity don't fit together is that they describe two different worlds. Unfortunately, there is only one world. There is no doubt in my mind that they will be able to be reconciled eventually.

more than a simple "gentleman's agreement" — James Riley

Don't underestimate the power of those gentleman's agreements. I have made the argument many times that most of the questions addressed on the forum, and in philosophy in general, are metaphysical questions. By which I mean that they set the stage for our understanding of the world but they are neither true nor false. They are useful in a particular situation or not useful.

meet its burden of proof with more than a "because I said so." — James Riley

To me it is the essence of philosophy that everything eventually goes back to "because God said so," "because X said so," "because we agreed that it was so," "because I said so," or "just because." Ultimately, there is probably one additional step back - "because that's how our minds work. How they have evolved to interact with the world."

I see no harm in assigning a small cadre of physicists to look into it. After all, it seems to be their camp which is frustrated. While they are skipping along their investigative way forward, they might send a party back to make sure they didn’t get off the trail at the beginning. — James Riley

You've lost me a bit. Is this cadre going back to reevaluate the underlying assumptions in order to find why we can't reconcile relativity with quantum mechanics? That's being done. I think it's hard, because both theories work very, very well to describe the phenomena they cover. And now we've reached the point, likely gone beyond the point, when I don't know what I'm talking about.

All the foregoing, and my tossing out the rules, had me generating what I thought were interesting opinions on particle physics, singularities, matter, dark matter, energy, dark energy, and time. But I’d sure like to nail down why I’m wrong about my foundation before I continue building on it. — James Riley

Maybe I'm lost again. Those entities - matter, time, particles, etc. - are physical phenomena we have observed or at least are trying to observe. They are not logical entities. What rules are you throwing out again?

Some advice - If, when you want to respond to a particular post, you click on the "reply" arrow that shows up when you run your curser next to the time stamp at the bottom of that post, your reply will be tagged and the person you are replying to will be notified.

Even better, if you want to reply to some particular text, you can highlight that text. A black "quote" button will show up. If you click on that, the text you highlighted will be copied down to the reply you are writing with a tag which notifies the person you are replying to.

I have a feeling that taking any of the ideas I've discussed here any further will divert the discussion from what you are trying to achieve here. You and I have very different philosophies.

I've been beating my head against the wall reading Hegel for quite some time now... — James Riley

Ah. There's the problem.

Here's a tired old example for you to think about. Suppose you attempted to play chess against an opponent who moved the pieces anywhere. How would the game go?

Suppose that opponent then said he saw no reason why he should move the pieces as stipulated; after all, the rules are mere "I told you so".

Abandon the law of noncontradiction and anything follows: p & ~p ⊃ q.

Accepting a contradiction is the same as accepting any and every other proposition. Hence, doing so obliterates further discussion.

You've lost me a bit. Is this cadre going back to reevaluate the underlying assumptions in order to find why we can't reconcile relativity with quantum mechanics? — T Clark

Yes. That's what I would like to know is being done. If there is a group of smart people going backwards, instead forwards, to the very beginning, with the goal of launching an all out assault on the fundamental principles they thought were in stone, re-testing to make sure they are indeed in stone, and infallible, and that their comrades at the front, pushing forward with physics, are still on the right track, then I would sleep better at night. I'd prefer if these people were some of those who have been to the front, and who have run into a contemporary wall in physics, so they can know their exercise is not merely academic. I want their heart in it.

I know I am certainly not qualified to do more than simply say "prove it" when logic trots out "self-evidence" or "can't prove a negative" as it's sole response to my challenge. I would hope that people smarter than me would either upend the principles or, if the principles are sound, then at least come forward with something better than anecdote, or something akin to "Well, Jim, if you don't agree, I can't talk to you any more."

To hearken back to a previous post, if the principles hold, I would hope they'd at least return from their ventures and show me a sock. And in anticipatory argument, that sock would be a proof, and that proof would not merely be anecdote; and that proof would not merely reference to how frustrating, difficult, or impossible life would be if we had to place chess with those who don't know our rules.

Maybe I'm lost again. Those entities - matter, time, particles, etc. - are physical phenomena we have observed or at least are trying to observe. They are not logical entities. What rules are you throwing out again? — T Clark

Those physical phenomena are aspects of the two theories that, to date, have not been wed. I'm suggesting the failure to wed them could be, at least in part, due to the approach to the phenomena being based entirely on logical entities (gentlemen's agreement) that have not yet themselves been proven and which could thus be inadequate to the task. Maybe the rules being used really aren't the rules.

What if the frustrating place we find ourselves is due our having adopted a premise that should not have been agreed upon in the first place? As an analogy, Socrates' (Phaedo) discussion of the corporeal versus his discussion of the perfect soul; it's not unlike logic being corporeal (of this world), whereas the perfect soul is "All" and not so limited. Maybe reality is the opponent moving chess pieces around the board in violation of all the rules the body thinks it knows. Perhaps those who fail to play by corporeal rules know multiple, infinite worlds that we have not fathomed. It would seem to me the answer *might* start with the all out assault on what we think we know and how we got here.

Your advice on quotes, and how to do them, was much needed. I had early on thought to educate myself on this but I was too intimidated or lazy to research the features of the board and how that was done. Your concise placement here is greatly appreciated.

In conclusion, I just came here looking for a sock.

If there is a group of smart people going backwards, instead forwards, to the very beginning, with the goal of launching an all out assault on the fundamental principles they thought were in stone, re-testing to make sure they are indeed in stone, and infallible, and that their comrades at the front, pushing forward with physics, are still on the right track, then I would sleep better at night. — James Riley

Do you know enough about physics to know whether the evaluation you are discussing is already being done? Do you know what the fundamental principles underlying current physics are? I guess what it comes down to is, do you know enough about modern physics to be able to ask the question "What's the matter with modern physics?"

In conclusion, I just came here looking for a sock. — James Riley

Would you recognize a sock if they showed you one?

Do you know enough about physics to know whether the evaluation you are discussing is already being done? Do you know what the fundamental principles underlying current physics are? I guess what it comes down to is, do you know enough about modern physics to be able to ask the question "What's the matter with modern physics?" — T Clark

Would you recognize a sock if they showed you one? — T Clark

Physics is not the question. The question is logic. I'm assuming physicists are abiding science, and it's traditional adherence to the fundamental principles of logic. It is the principles of logic that I question. If I am wrong on that, and physicists have found a sock, then yes, since it is a logic sock they would have found, I would recognize it. But I've not heard of it. I came here, to a logic forum, in search of it. So far, no joy.

On the other hand, if physics or any other study for that matter, had disproved a fundamental principle of logic in pursuit of their own inquiries, I think it would have been Earth-shaking news that rocked the world. Again, I've not heard of it. I suspect I would not have to come here looking if it existed. But crickets.

I've always appreciated the cartoonist and their ability to reduce a complex issue to one or a few cells. I cannot draw for the life of me. But if I could, I would imagine this: A parade down the middle of a boulevard, the leader of which would be a King, a crown on his head and scepter in hand, buck-naked and the word "Logic" on his crown. All the many people line the way, with high acclaim for his wonderful clothing. A little boy points and asks "Momma, why is the King naked?" To which his mother responds "But he is not! He has a beautiful, regal outfit!"

Edited to add: It could be any area of study, not just physics. I chose physics because their inability, but desire to marry two theories is, I think fundamentally important to philosophy.

It is the principles of logic that I question. If I am wrong on that, and physicists have found a sock, then yes, since it is a logic sock they would have found, I would recognize it. — James Riley

I don't see the fundamental issues in physics as logical errors. Somebody tell me I'm wrong.

On the other hand, if physics or any other study for that matter, had disproved a fundamental principle of logic in pursuit of their own inquiries, I think it would have been Earth-shaking news that rocked the world. Again, I've not heard of it. I suspect I would not have to come here looking if it existed. — James Riley

Physics doesn't prove or disprove logical principles. I don't think it can, by definition. It uses them as tools.

I chose physics because their inability, but desire to marry two theories is, I think fundamentally important to philosophy. — James Riley

Inability so far. I don't think physics is ever important to philosophy. I do think that philosophy is important to physics, although you won't find many physicists who agree. From what I've read, I think many physicists believe that a solution to the QM/relativity problem will require a radical revision of physics comparable to the changes that happened when relativity and QM were developed in the early 1900s. I don't see that as a philosophical change.

I don't see the fundamental issues in physics as logical errors. Somebody tell me I'm wrong. — T Clark

You may be correct, but I'm not talking about the fundamental issues in physics as logical errors. I'm talking about the fundamental principles of logic being in error. I assume physicists are logical, no? If not, then bingo! There's my answer. Now all I need to do is learn how physics got around logic and explain that to logicians how their fundamental principle(s) is flawed.

Physics doesn't prove or disprove logical principles. I don't think it can, by definition. It uses them as tools. — T Clark

I don't think physics proves or disproves logical principles either. I think physics uses logical principles to make physical proofs. I'm asking about the tool (logic), not the machine (physics) that is being worked upon.

Physics would be important to philosophy (the logical branch thereof) if a cadre returned from an assault on logic having found it to be wanting. Likewise, they would be important to philosophy (the logical branch thereof) if they returned with a sock the logicians had never found. In the latter case, the logician might simply say "I told you so." And that is true, they did. Be they did not prove it. The mode of travel can matter. I used to be jealous of those people who, after my long cognitive slog to a place, I find already there, having arrived on the wings of intuition. But then I remember I have found along my way; the truth is often counterintuitive. While others may wonder what took me so long, I’d rather arrive knowing what I don’t know. We may be in agreement; we may be in the same place. But if I must have company, I choose those who arrive by foot.

I *think* that a principle of logical argument is that the burden of proof is upon the proponent. — James Riley

That is false. It is self-refuting. Note, that claim - that the burden of proof is upon the proponent - is itself something you (or someone) is proposing. And thus they have the burden of proof. And any attempt they make to discharge it, will involve making proposals. And thus it will never be discharged. That claim is therefore equivalent to claiming that nothing can be shown, including that nothing can be shown. Which is self-refuting. (I assume you have heard of this 'principle' from the internet - from a youtube video, or wikipedia or some such? That is, you've heard of it from wholly unreliable sources).

The basic principle of intellectual inquiry is that the burden of proof is on the one whose claim conflicts with appearances. It's known as the principle of phenomenal conservatism or sometimes the principle of credulity.

Note, it is not self-refuting, for it itself appears to be true. And thus we have reason to believe it is true and the burden of proof is on the person who thinks that principle is false.

But it means that when you say this:

When I hear "logic" assert the Principle of Identity, I say "prove it." Logic's response seems to be, it's "self-evident". That response reminds me of a frustrated parent saying "because I said so." — James Riley

You are mistaken. The best and only evidence you can ever have that a proposition is true, is that it is either itself self-evident to our reason, or it is implied by something that is. Your parents, of course, are not Reason and thus when they say "because I say so" this does not constitute evidence in support of what they have said. (For an analogy: if I simply write an extra zero on my bank statement, that does not make me ten times richer. However, if the bank writes an extra zero on my balance, then I really am ten times richer).

That is false. It is self-refuting. Note, that claim - that the burden of proof is upon the proponent - is itself something you (or someone) is proposing. And thus they have the burden of proof. — Bartricks

I got the principle from a logic professor 40 years ago who taught me that logical argument places the burden of proof upon the proponent. This was followed by the practice of law based thereon, where the burden of proof is upon the proponent. The "someone" who proposed it is not me, or the professor, or the law. The "someone" who proposed it is logic itself, or more particularly logical argument. I didn't get it from the internet. In fact, the internet did not even exist when I got it.

Regardless, even if it were not a principle of logical argument, that would not in itself make it self-refuting. To be self-refuting it would have to be inconsistent. Placing the burden of proof upon the proponent is no more self-refuting than what appears to be a gentleman's agreement, without proof, regarding the law of identity or the law of contradiction. Logic makes those proposals, not me.

The basic principle of intellectual inquiry is that the burden of proof is on the one whose claim conflicts with appearances. It's known as the principle of phenomenal conservatism or sometimes the principle of credulity.

Note, it is not self-refuting, for it itself appears to be true. And thus we have reason to believe it is true and the burden of proof is on the person who thinks that principle is false. — Bartricks

It would seem the "principle of phenomenal conservatism" or the "principle of credulity, or what "appears to be true", while not self-refuting, are certainly no more authoritative than the even more fundamental and credible principles of identity or non-contradiction. In fact, these principle you cite are weaker, in that they smack of anecdote and the idea that "because once, always." They, at their best, would be a corollary and further down the road even than the fundamentals. But I don't believe even logic would cite them for any starting point. Check that! Maybe it would if it was trying to distract, or hide from an assault on it's principles. Maybe a principle of logical argument is different from the basic principle of intellectual inquiry?

No, self-refutation doesn't require inconsistency, at least not in the content of what has been asserted. If I sincerely say "it is raining, but nobody believes it is" then my statement is self-refuting, but it is not inconsistent. There is no contradiction contained in it. Yet I have refuted myself for in saying it I demonstrate its falsity.

Similarly, the claim that nothing can be shown is like this: any attempt to show it to be true assumes its falsity.
Anyway:

It would seem the "principle of phenomenal conservatism" or the "principle of credulity, or what "appears to be true", while not self-refuting, are certainly no more authoritative than the even more fundamental and credible principles of identity or non-contradiction. — James Riley

Yes it is, because our evidence that the principle of non-contradiction is true is that it appears to be. That is, our reason represents it to be. How would the principle of non-contradiction possibly have more rational authority than the principle of phenomenal conservatism?

If I sincerely say "it is raining, but nobody believes it is" then my statement is self-refuting, but it is not inconsistent. — Bartricks

I perceive two problems with this. First, if a statement is self-refuting it is inconsistent with the truth. Second, I believe there is a logical fallacy called argumentum ad populum or something like that. The fact nobody agrees with you about the rain matters naught to the truth of the matter asserted.

How would the principle of non-contradiction possibly have more rational authority than the principle of phenomenal conservatism? — Bartricks

Because the latter is dependent upon subjective observation, while the former is based upon what logic would claim to be empirical truth ("A" cannot = "-A").

Night night.

The law of noncontradiction applies to logic, not to reality. There is no restrictions in reality, but restrictions in logic. Logic is all about restrictions.

The law of noncontradiction applies to logic, not to reality. There is no restrictions in reality, but restrictions in logic. Logic is all about restrictions. — Yohan

Hi Yohan. Can you extrapolate on that for me. It sounds metaphysical, or like metaphysical realism. Maybe an example?

The QM scientist stands in his lab and sees a patent violation of "X" sitting right there on the table in front of him. This patent violation of "X" is called "Y".

Where Logic says "X" and QM sees "Y", and where QM is a disciple of Logic, QM has a problem.

QM can continue to search for why "Y" is wrong, or QM can make Logic prove "X". After all, Logic is the proponent of "X" and therefor, by Logic's own rules, Logic has the burden of proof. So far, the best Logic has come up with is this:

""X" is self evident, and I can't prove a negative. You must not question me. Rather, you must continue trying to figure out why "Y" is wrong and you must use "X" to do it."

No, the proposition 'it is raining and no one believes it is raining' is self-refuting, but not inconsistent with truth. For it is possible for it to be true. It itself contains no contradiction.

Here is another view that is possibly true, but self-refuting: there is no reason to believe anything.

Again, possibly true. But any attempt to defend it would undermine itself as to defend a view is to attempt to show that there is reason to believe it.

As to what you say about the principle of phenomenal conservatism - well, I do not follow you. What reason do we have to think the law of non-contradiction is true save it appearing to be?
And if that is true, howdoes that not demonstrate that its truth is even more basic?

I mean, a first storey is more basic than a second as you can't have the latter without the former. Well likewise the principle of phenomenal conservatism is more basic than the law of non-contradiction for we are not justified in believing the latter unless the former is true.

a principle of logical argument is that the burden of proof is upon the proponent.
— James Riley
That is false. It is self-refuting. — Bartricks

You've neglected the "logical" in logical argument. Which means you did not trouble to try to understand what you were reading - or what you're writing about.

No, you don't know what you're talking about or what I'm talking about. But thanks for your input.

The law of noncontradiction applies to logic, not to reality. There is no restrictions in reality, but restrictions in logic. Logic is all about restrictions. — Yohan

Yes. I think this is at the heart of this discussion.

@James Riley - is the failure to recognize the difference between reality and a representation of reality, i.e. logic, one of the logical errors you are talking about?

No, the proposition 'it is raining and no one believes it is raining' is self-refuting, but not inconsistent with truth. — Bartricks

It is not self-refuting. If I say "1 apple plus 1 apple makes for 2 apples, but Bartricks disagrees" I have not said something self-refuting. The fact Bartricks disagrees with something reflects on Bartrick, not the fact. Otherwise, everything Bartricks disagrees with would be self-refuting. Quite the contrary.

to defend a view is to attempt to show that there is reason to believe it. — Bartricks

Not true. Devils advocates defend views to defeat them. We did it in the law all the time.

What reason do we have to think the law of non-contradiction is true save it appearing to be?
And if that is true, howdoes that not demonstrate that its truth is even more basic? — Bartricks

The law of non-contradiction is a fundamental principle of logic which I have been calling out. I agree with you. Other than it's appearance, what proof is there that it is true? It is a basic, fundamental principle of logic whether it is true or not.

Well likewise the principle of phenomenal conservatism is more basic than the law of non-contradiction for we are not justified in believing the latter unless the former is true. — Bartricks

That is not logic. The fundamental principles of logic hold themselves out as truth, notwithstanding observation.

No, you don't know what you're talking about or what I'm talking about. But thanks for your input. — Bartricks

According to your rule, I'm correct until and unless you disprove my claim. Good luck with that!

A devil's advocate is still trying to show that there is reason to believe the view they are advocating for.

I still do not understand what your point is in respect of the law of non contradiction or any other law of logic for that matter. Our evidence they are true is that they appear to be. That isn't a problem.

No.

The basic principle of intellectual inquiry is that the burden of proof is on the one whose claim conflicts with appearances — Bartricks

And when things appear differently to different people?

I would think if everything appeared the same way to everyone people wouldn’t even argue.

This seems to just put the burden of proof on whoever is disagreeing with you (as they clearly conflict with what appears to you to be the case). Cheeky.

is the failure to recognize the difference between reality and a representation of reality, i.e. logic, one of the logical errors you are talking about? — T Clark

I'm not sure I understand this. My failure to understand may be due to definitions. Logical thought is a tool set used to aid in understanding reality. Where representations of reality are used, logical thought likewise applies to those representations. If there is a logical error in the tools themselves, then it is a failure of those tools to abide the standards which those tools impose upon everything in reality (or representations of reality) that they are utilized in working on.

Our evidence they are true is that they appear to be. That isn't a problem. — Bartricks

Apparently that is not a problem for you. I think there is a philosophy for that, but I can't recall what it is. For others, like logical thought itself, they demand proofs beyond appearance.

If it appears to you that it appears to Helen that the burglar had a red hat on, and it appears to you that it appears to Sam that the burglar had a blue hat on, then other things being equal you have as much reason to believe the burglar had a red hat on as a blue one.

The law of non-contradiction appears to be true. That is, the reason of most people represents it to be true. That's an appearance: a rational appearance.

It is precisely because of this that we understand that conflicting appearances cannot all be accurate. Indeed, to take some appearances to be conflicting is of a piece with taking their representative contents to be contradictory.

In this way we learn that one or other or both appearances are inaccurate.