What is the basis for reason? And mathematics?

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Skepdick
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### Re: P=P is a Contradiction

raw_thought wrote: Wed Sep 23, 2020 5:49 pm https://en.wikipedia.org/wiki/Taxicab_g ... stance.svg
Look at the example from your own link! It shows that the shortest distance from point A to point B is still a single straight line.
Nobody is denying that. What YOU are misunderstanding is what "straight" means in a TaxiCab geometry.

raw_thought wrote: Wed Sep 23, 2020 5:49 pm
Of course if you arbitrarily say that one can only move back and forth and never in a diagonal straight line of course the distance will be longer.
Idiot. The geometry is arbitrary, not the distance.

raw_thought wrote: Wed Sep 23, 2020 5:49 pm
I can even claim that I live 4,000 miles from New York, 2,000 miles from New York, 1,000 miles from New York or any distance ( except shorter than a single straight line from my house to New York ) But I hope you see that that is silly.
It's not at all silly! It's how geometry works! You need to tell us HOW you are measuring the distance between New York and wherever you stay.
raw_thought wrote: Wed Sep 23, 2020 5:49 pm
it is obvious that you have not shown me a square circle.
It's obvious that I have, and that you don't understand why.
raw_thought wrote: Wed Sep 23, 2020 5:49 pm
I cannot believe that we are debating if the shortest distance between 2 points is a single straight line!
We are not debating that. You are trying to impose an Euclidian geometry on the debate. WHY?
Skepdick
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### Re: P=P is a Contradiction

raw_thought wrote: Wed Sep 23, 2020 5:50 pm https://en.wikipedia.org/wiki/Taxicab_g ... stance.svg
Taxicab geometry - Wikipedia 2020-09-23 19-38-55.png (53.85 KiB) Viewed 314 times
Skepdick
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### Re: P=P is a Contradiction

raw_thought wrote: Wed Sep 23, 2020 6:06 pm And since , the shortest distance between 2 points is always a single straight line. Your link does not show a square circle!
There's no point in re-explaining this to you.

Clearly you don't understand the difference between the general notion of a geometry and the particular notion of an Euclidian geometry.
Last edited by Skepdick on Wed Sep 23, 2020 6:52 pm, edited 1 time in total.
Skepdick
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### Re: P=P is a Contradiction

raw_thought wrote: Wed Sep 23, 2020 6:22 pm Sure in a city where diagonal lines are arbitrarily forbidden you cannot drive from some point A to point B in the shortest distance.
They aren't "arbitrarily" forbidden. Physical matter gets in your way!

Walls, buildings. You literally cannot drive THROUGH that stuff with a car: a geometry is imposed on you.

raw_thought wrote: Wed Sep 23, 2020 6:22 pm But that doesn't mean that there is no shortest distance. It means that to take the shortest possible distance between 2 points you will have to trespass people's property. That is a question of law, not geometry.
Which is why I explained to you that the shortest distance between Buenos Aires and Shanghai is right through Earth's core. 12000km or thereabouts.

That's not a question of trespassing - it's a question of digging. Would you like a shovel, or do you prefer to fly there?
raw_thought
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### Re: P=P is a Contradiction

Suppose you are a taxi driver and you are angry that you cannot go from point A to point B directly because there is private property and buildings in the way. You get political power and you have those buildings declared public areas and have them removed and then put in a street that is the shortest route. Trying to overturn geometrical rules and the basic postulates of math is silly and futile.
raw_thought
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### Re: P=P is a Contradiction

https://en.wikipedia.org/wiki/Taxicab_g ... stance.svg
OK , you are a taxi driver and want to take the green arrow because it is obviously the shortest route. Unfortunately, the streets are perpendicular and only run in a east/west and north/south direction. Solution 1. Talk to city council and try to get a street that follows the green route put in. Solution 2. Change mathematical rules ( for example that the shortest distance between 2 points is a single straight line ) . What solution seems more reasonable to you? Yes, it is hard to get government to satisfy your needs. But isn't solution 2 ridiculous???
raw_thought
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### Re: P=P is a Contradiction

The reason that I said that I can say that I am 2,000 miles from New York, 3,000 miles from New York or say any distance (that is the absurd consequences of taking your absurd position and a classic logic move. You assume that your opponent is correct and then show how it implies absurd conclusions that even he cannot accept ) ) is that... Well ok an example might help better. Since buildings and private property alter geometry according to you, lets say that the only route from here ( North Carolina ) to New York is to first go to California and then to Canada, any other route has mountains in the way etc. One doesn't say, wow the laws of math are arbitrary. One says that the shortest route from Goldsboro North Carolina to New York is 496 miles and we cannot take that route because mountains are in the way.
raw_thought
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### Re: P=P is a Contradiction

Please note that I am not saying that mountains are blocking my path to New York City. I am saying that even if they were that would not alter the fact that I am 496 miles from New York City.
Skepdick
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### Re: P=P is a Contradiction

raw_thought wrote: Thu Sep 24, 2020 1:29 am One doesn't say, wow the laws of math are arbitrary. One says that the shortest route from Goldsboro North Carolina to New York is 496 miles and we cannot take that route because mountains are in the way.
Idiot.

The the shortest route from Buenos Aires to Shanghai is 12000km and we cannot take that route because the planet is in the way.

The geodesic between Buenos Aires and Shanghai is 19000km.
The geodesic between Goldsboro and New York is 496 miles.

Your thought is so raw you are incapable of spatial reasoning.
wtf
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### Re: P=P is a Contradiction

Immanuel Can wrote: Sun Sep 20, 2020 4:43 am But my real interest in doing so was to speak about the law of identity, which is a truth without which no mathematics would be possible. So I'm sure you can get behind the law of identity.

Fair enough?
Yes and no but mostly no. First, I don't actually have much interest in the subject. I agree with you that the law of identity is a law of logic that is assumed throughout math; and so that like a fish never thinking about water, mathematicians never think about the law of identity.

So in this sense I agree with you.

But I found your response somewhat disingenuous; so much so, in fact, that although my natural inclination is to just let this whole subject go; I find that I am compelled to respond.

You never took responsibility for, or addressed my questioning, of your use of the word "tautology." In so doing you are interpreting my objections in a completly wrong manner and totally misunderstanding (accidentally or deliberately) what I'm saying.

Like I say it's not a big deal either way; but you continue to avoid taking responsibility for what you plainly said.

I'll respond to the individual points now.

Immanuel Can wrote: Sun Sep 20, 2020 4:43 am
Oh, I see where you got confused. You thought the word "trivial" had to have meant "useless." It did not: by it, I meant "obvious" or "circular," not "useless."
No, I understood you to say that tautologies are obvious and thereby useless. In which case you are wrong, since Wiles's proof of Fermat's last theorem is a tautology. It's a theorem that holds in every model of the axioms from which it's derived. And since FLT is most definitely NOT trival or obvious in any sense of those words, it follows that you are wrong about tautologies.

But instead of simply acknowledging this totally simple point and moving on, you just change the subject. You IGNORE the fact that I've written you now two lengthy posts challenging your use of the word "tautology." You simply ignore it.

I find this baffling.

Immanuel Can wrote: Sun Sep 20, 2020 4:43 am If you check, you'll find that there is more than one definition for "trivial" in the dictionary. And the term "trivially true" is an idiom, meaning, "true, but in a way that adds no new information." So when we say that something is "trivially true," we mean that it is true, but not in any way that is surprising.
In your original statement that I objected to, you said that P = P is trivial because it is a tautology. But that's wrong. Fermat's last theorem is a tautology but is highly nontrivial. So now you're changing the subject.
Immanuel Can wrote: Sun Sep 20, 2020 4:43 am Now, P=P is as obvious a truth as one can possibly get. But since the second P adds no new information to the first P, we can say it's "trivially true." Or to put it another way, it's a "truism."
I will say here that I am not a logician, so I take no position on whether the law of identity is true or not, obvious or not, trivial or not. As I say as a math-oriented person I just take the law of identity for granted. But if I put on my logician hat, I don't think it's obvious at all. After all you are literally not the same person you were a microsecond ago. Your cells all regenerate after a few days. And so forth. Or we can say, "I'm not myself today." That is a perfectly correct English usage; yet it violates the law of identity.

So I don't think the law of identity is particularly true; and even if it is true in some particular domains, it's far from clear to me that it's "obvious." It's something we ACCEPT WITHOUT PROOF in order to get logic and math and science off the ground. I think the law of identity is a rather a profound statement because (1) it is essential to rationality, science, and civilization; yet (2) it is manifestly false!

So there. That's my two cents on the law of identity. But even so ... I am not talking about the law of identity. I don't CARE about the law of identity. I am asking you to defend or explain or correct your statement that the law of identity is trivial by virtue of its being a tautology. That claim is as false as false can be.
Immanuel Can wrote: Sun Sep 20, 2020 4:43 am I now see that you've been getting excited over a mere misunderstanding of usage.
I'm simply disappointed to watch you change the subject and either deliberately or inadvertently pretend I'm "excited" over something you just made up as you wave your hands and ignore, YET AGAIN, what I am saying to you.

Immanuel Can wrote: Sun Sep 20, 2020 4:43 am And maybe that's my fault for assuming people would understand the implications of my use of the idiom "trivially true." But I trust this clears all that up.
You mean you thought I would be fooled by your entirely changing the subject and ignoring what I've been saying? Well I guess that didn't happen.

Immanuel Can wrote: Sun Sep 20, 2020 4:43 am Now, look back at the top of this thread. What is the claim? That P=P is not a truth at all; that it is, in fact, a "contradiction." That is clearly false. It was to that claim that I was referring.
Well that's why I wasn't following the thread. I don't tend to follow some of these, let's call them off-beat threads that pop up on this forum. Which is exactly WHY I responded to what you wrote without bothering to read what came before.

But why should that matter? The paragraph you wrote, where you said P = P is a tautology hence trivial, is false on its face. I somehow I have failed to convey that this is my concern; then the fault is on me for poor communications. So let me just say this again.

When you wrote that P = P is trivial because it's a tautology, did you mean that or did I misunderstand that or are you simply perhaps mistaken about what a tautology is?

Here is the original quote.
Immanuel Can wrote: Thu Sep 17, 2020 2:11 am P=P is also a tautology. The fault is not that it is wrong, or tells a lie; it's that even if true, it's utterly uninformative of anything new. It adds no value to our thinking at all.

You're wrong. You're flat out wrong. Replace the string "P = P" with the string "Wiles' proof of FLT" and you will see why.

Peace brother. I'm sure this is an honest misunderstanding.
Immanuel Can
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### Re: P=P is a Contradiction

wtf wrote: Fri Sep 25, 2020 5:00 am
Immanuel Can wrote: Sun Sep 20, 2020 4:43 am Oh, I see where you got confused. You thought the word "trivial" had to have meant "useless." It did not: by it, I meant "obvious" or "circular," not "useless."
No, I understood you to say that tautologies are obvious and thereby useless.
Ummm...no.

That's not what I said. Please read the very sentence above, the one you already quoted, and read carefully. You'll see I say, "Not useless," just "circular" or "obvious."
I find this baffling.

That's because you did indeed misread, and because I have zero interest in pursuing the abstract mathematical curiosities. So I make no comment on them. My only interest was in the law of identity, with which you agree, and is a supposition of all mathematics.

So what are we still talking about? I haven't a clue.
Peace brother. I'm sure this is an honest misunderstanding.
Okay. It seems so. All over a misunderstanding of the implication of the word "trivial," apparently.

Peace.
Immanuel Can
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### Re: P=P is a Contradiction

wtf wrote: Fri Sep 25, 2020 5:00 am Yes and no but mostly no.
Peace brother. I'm sure this is an honest misunderstanding.
I double-checked.

"Triviality" in maths and in logic mean two different things. Your concerns are about maths, mine about logic. So we're not using the word the same way.

Ironically, that would be a violation of the law of identity -- the logic version. And since we both believe in that, we don't want to do that.
wtf
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### Re: P=P is a Contradiction

Immanuel Can wrote: Fri Sep 25, 2020 9:19 pm
That's not what I said. Please read the very sentence above, the one you already quoted, and read carefully. You'll see I say, "Not useless," just "circular" or "obvious."
FLT is circular or obvious? You don't know what a tautology is.

In logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. [My emphasis]

https://en.wikipedia.org/wiki/Tautology_(logic)

You are STILL ignoring what I'm saying to you.
Immanuel Can wrote: Fri Sep 25, 2020 9:19 pm "Triviality" in maths and in logic mean two different things.
I have said NOTHING about the word triviality. NOTHING NOTHING NOTHING.

NOR is there ANY such formal definition of triviality in either logic OR math. I call bullshit. You are a crank.
Immanuel Can wrote: Fri Sep 25, 2020 9:19 pm Okay. It seems so. All over a misunderstanding of the implication of the word "trivial,"
Still lying. You are confused about the word tautology and you won't even engage with what I'm saying. You won't even ACKNOWLEDGE what I'm saying. Is your reading comprehension faulty? English not your first language? Sanity not your first mode of existence? What is your major malfunction?

I said NOTHING about the word trivial. NOTHING. You keep pretending I did in order to avoid responding to my pointing out your error.

You used the word tautology in such a way as to make your assertion flat out false. And you won't even engage with the point.

I see that I initially confused you for a sane person. My error. You're a nutball and a crank.
Immanuel Can
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### Re: P=P is a Contradiction

wtf wrote: Sat Sep 26, 2020 10:01 pm I have said NOTHING about the word triviality. NOTHING NOTHING NOTHING.
wtf wrote: Sat Sep 26, 2020 10:01 pmOn the other hand, even if you are saying that P = P is trivial and adds no information, even that is wrong.
Apparently, in your world, "nothing" means "something."

Sorry. I have no idea what you're foaming on about. My sole point was that the law of identity is not optional. You already wrote:
wtf wrote: Sat Sep 26, 2020 10:01 pmI don't actually have much interest in the subject. I agree with you that the law of identity is a law of logic that is assumed throughout math; and so that like a fish never thinking about water, mathematicians never think about the law of identity. So in this sense I agree with you.
So we are agreed. What you're saying about tautologies in maths is not interesting to me, and not relevant to the question of logic.

Apparently, I can't explain that to you, for some reason. But that's fine.
I see that I initially confused you for a sane person. My error. You're a nutball and a crank.
Well, I am content to mark our disagreement without impugning your character or intelligence.
Last edited by Immanuel Can on Sun Sep 27, 2020 12:42 am, edited 1 time in total.
Skepdick
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### Re: P=P is a Contradiction

wtf wrote: Sat Sep 26, 2020 10:01 pm NOR is there ANY such formal definition of triviality in either logic OR math...

You keep pretending I did in order to avoid responding to my pointing out your error.
There's no formal definition of "error" in math or logic either.