TonesInDeepFreeze

That's good. Though, it's logically true anyway. Next is to fix line 3 of Argument A.

Liar paradox: If "This sentence is false" is true, then "This sentence is false" is false. and If "This sentence is false" is false, then "This senten...

Whatever you mean to say, if you want me to understand it (especially to understand it exactly) then you need to rewrite it without a number between a...

I can't make sense of that with the numbers interposed as written. I don't know what is meant by interposing a number between an adjective and what it...

He didn't.

To begin with in all that, what's your definition of "real thing"?

I don't like that tree. The order and proximities seem incorrect and haphazard in places.The Venn diagram is better.

As As a taxpayer, I'm quite happy for my share - my .00002 cents - to have contributed to your research. More, if I had it to give.

There's an interesting angle on this. In the language of PA we can express. Sentence S can't be negated. It's false, but it can be stated in the langu...

Bottom line for your exercise: 'This sentence can be negated' is true and not paradoxical. 'This sentence can't be negated' is false and not paradoxic...

Your exercise is not in a mathematical context, which is okay, but it's worth noting comparison with mathematics (I'm simplifying here). Consider: Thi...

Putting '(1)' between 'this' and 'statement' is not coherent. And putting '(2)' between 'this' and 'statement' is not coherent. Maybe you mean: If "th...

P.S. In Argument A, 2. does not need to be taken as a premise. 2. follows from 1. by UI.

If you wish to revise further, then please state any further amended arguments in new posts, so that my replies are still pertinent relative to the po...

That's a major re-edit of the OP after several edits. Before I reply, is that your final edit?

Every sentence can be negated, simply by putting a negation sign in front of the sentence. Doing that is purely a syntactical operation. It does not m...

I think you mean you would be surprised. That seems reasonable. On the other hand, if an outlandish or "out of thin air" existence claim is asserted, ...

You mentioned "sufficient evidence". I'm wondering whether we would deem my knowledge of kangaroos to be sufficient to have a reasonable belief that t...

"There exists a fish with blue fins and a green body." I don't assume that is true and I don't assume that it is false. "There exists a striped kangar...

Interesting that Algebra dominates. I would have thought it would be Analysis and its offshoots.

There is a difference between "S is false" and "I disbelieve S." "S is false" in many contexts raises expectation of demonstration that S is false. Bu...

One more time: We are in a context of everyday English. Then, I have given a mathematical representation of that everyday English sense. A mathematica...

Why do you keep saying I've avoided the question when I have not, when, indeed, I have answered several times and with copious explanation and detail?...

Possible outcomes: ExBx Black dog found before end. $500 and get to go home early. Black dog found at end. $500. Black dog not found. Wasted time tryi...

For any given consistent system S, there are infinitely many theorems and infinitely many non-theorems.

I'd be curious what the percentages are for each of the branches. To not have it too Balkanized, it would have to be large groupings like: Foundations...

That chart seems to capture discovery not proof. For example, the min in row 4 is 1 only because we discover that there is a black dog and give up try...

Here are some more problems with that article: (1) The sqrt(2) proof does not make clear its indirect form. Indirect in clear form would be to assume ...

That was a while ago. But you're still asking! There you even correctly posted yourself that you surmise that I agree that if we count 2 objects then ...

Not in the real world. I eat the whole pie all at once. Math needs to correspond to reality!

Definitions: x is rational iff x equals a ratio of integers x is irrational iff ~ x is rational Theorems: x is irrational iff ~ x equals a ratio of in...

I took out what I previously posted in this message. My questions were not needed.

Proof that certain reals have infinite expansions does not rely on assumptions that patterns repeat. No, it is not endless. Proofs in mathematics are ...

No, it is proven. Perhaps you might say that the axioms are arbitrary. But, given the axioms, proof that some reals have infinite decimal expansions i...

As mentioned, 'proof by contradiction' is not the right term. And such cases can more comprehensively be described as 'deductively proving'. We may pr...

Right, case-by-case in an indeterminate domain. The ordinary proof that the square root of 2 is irrational is not a proof by contradiction. Assuming P...

Be careful with the terms 'proof by contradiction' and 'indirect proof'. This is the form of proof by contradiction (indirect proof): Assume ~P Derive...

I've answered that already a few times. To have a non-empty count, of course there exist the objects counted, and in you example, these objects are bo...

For a consistent formal (I always mean 'consistent formal' in this context) system S, there is an infinite enumeration of the proofs. So it is linear,...

No, what have truth values are statements. What have a truth values are the statements "There exists a natural number that is the successor of 0" and ...

I asked whoever said that numbers have truth value(s)? Or is it your own claim that numbers have truth value(s)?

Whoever said numbers have truth value(s)?

The second one is reasonable. The first one is a mess.

Too literal about the word 'religious'? It is used as cudgel. So it is good, as a starting point at least, to point out that it is not literally true.

It was not 'rationalistic'; it was 'over rationalistic'. And it's not that I find it so insulting, but that it is ad hominem.

Godel discusses formal theories. What does "provable from the ground up" mean in regards to Godel's incompleteness theorem?

" and are critically different.

Of course I don't. I listed a good number of the major features of religion. I don't relate to mathematics with any of those features.

Oh please, a minor pedantic shift in the way one casts an ad hominem doesn't erase it's affect as an hominem.

And that doesn't deserve the mangled version you posted earlier. It's not clear what "line to be drawn" means there. And every formula is provable in ...