fishfry

I misunderstand many things. My apologies if that is the case in this instance. LOL at the Annie Hall reference, one of my faves.

We're entirely in agreement. My mistake if I thought otherwise.

I'm a Platonist when it suits me, and a formalist when that suits me. My derivation of the theorem 2 + 2 = 4 in Peano arithmetic was purely a formal e...

Wait, what? Did Ahab and the Pequod exist before Melville existed? Of course it's an interesting fact that Moby Dick is based on a true story. The wha...

Good news. I'm working on a reply in case it takes a while. I do think you're failing to distinguish between: * The philosophical question; and * The ...

Fiction. Facts are true even before we know them. The sun was a flaming ball of gas long before we discovered that fact. But fiction comes into existe...

If it's true that all we need to know is axioms, then the question becomes, which axioms? We know that in math, at least, axioms are insufficient to c...

It was a typo, a Freudian one if you like since I agree that this particular error makes you totally right and me totally wrong. I get that. From my e...

If I use the word same instead of equal does that satisfy you? The fact that you say you read my post and this is your complaint means we're done. You...

Is it possible you missed this? https://thephilosophyforum.com/discussion/comment/328116 Also you claimed that the law of identity does not apply to n...

I provided a direct proof from first principles. You might have questions or specific objections. But to claim I did not provide a proof means you hap...

It was neither physics or engineering. It was politics. Even at the time people asked why should we send men into space when we had so many social pro...

Now I did not say that and I hope you can see that I did not say that. I will forgive your rhetorical excess but I will most definitely respond. I am ...

Interesting case. It reminds me of the days of Dr. Kevorkian. He became the face of assisted suicide. But he operated in a very gray area. Some of his...

The world has been in a state of inevitable environmental disaster since Malthus. The predictions never come true. Some think the notion that there ev...

f = ma is essentially a definition. A very clarifying definition to be sure, but it's not a fact or a theorem. It's a definition. That is my understan...

I take no responsibility for and neither endorse nor necessarily agree with anything written by anyone on this site but myself; nor do I necessarily d...

What do you make of the 1919 eclipse that confirmed Einstein and disproved Newton? https://en.wikipedia.org/wiki/Eddington_experiment

Perhaps you can clarify this point for me then. The law of identity is that a thing is equal to itself. Why wouldn't this apply to numbers? A rock is ...

Newton took a lot of flack at the time. His law of gravity told us what gravity does; but not what it is. He famously said that "I frame no hypotheses...

Yes thanks for making that point. In fact Russell and Whitehead famously took 400 or whatever pages to prove that 1 + 1 = 2 directly from logic; and p...

Me? Wasn't sure about the quoting. Newton's instruments only followed Newton's laws to a certain degree of approximation. They follow Feynman's laws -...

Of course this is false. Newton looked through a telescope that he himself had made. He was a master lens grinder. That's peripheral to the discussion...

I can't respond to this. You're factually wrong. There's only one set {0,1,2, pi}. There isn't "another" set that happens to have the same elements an...

I have already confessed to not reading the post and only lazily making one of my standard hobby horse points. Did you want me to confess again? Is th...

I responded primarily to the title of the OP without reading much of the post, and without reading the other responses in the thread. If I misconstrue...

You could never prove them. For one thing they're not "true," if by true you mean that the universe actually works that way. We know that for objects ...

Let me remedy that omission. Before I start I hope we're agreed that there are two levels to this discussion: 1) The philosophical point that 2 + 2 is...

I was going to reply to you later but just ran across this, which could not be more false. I have repeatedly explained to you that the axiom of extens...

You oughta see the political forums.

I think I understand your point but I have some counterpoints. I believe you are saying that when we say 2 + 2 = 4 we are saying two things: One, that...

That's the heart of Banach-Tarski and it's purely syntactic, nothing to do with spheres. It's amazing. I hope you will look into this. I have a little...

You hit a lot of really cool topics. I'll keep my answers brief. I hope we can focus on one or two things instead of branching out into too many diver...

That's why they call it pure and applied math! And likewise the theory of computation. I hope you will agree that although Turing machines have an unb...

I was skimming your reply looking for a point of reference, something I could understand. I came to this. I think it's a point of irreconcilable diffe...

My quarks are really annoyed at this! They have a rich inner life, you know. At the very least, by virtue of being the constituents of the atoms that ...

I walked through this in detail a few posts ago. In the Peano axioms they are both the number SSSS0. In ZF they are both the set {0, 1, 2, 3}. = { ?, ...

Of course 2 + 2 is the same thing as 4. I cannot imagine the contrary nor what you might mean by that claim. But more importantly, they are the same s...

I wonder if by actual you mean physical. In math the axiom of infinity gives actually infinite sets; that is, infinite sets all of whose elements can ...

What do you make of infinite-dimensional spaces? An example would be the set of all continuous functions from the real numbers to the real numbers. Th...

National borders are historically contingent. Surely this is a trivial point, not a profound one. The US was the US before and after the Louisiana pur...

Isn't that the anthropic argument used by physicists? That the universe is fine-tuned for life? It comes up in multiverse theory. Point being that it'...

You made the statement that ZFC allows two different things to be equal. I said I know of no such example and you have not backed up your claim or put...

What's interesting about Banach-Tarski is that it's a purely syntactic paradox. The free group on two letters has a paradoxical decomposition, and thi...

Like I say, I'm not in a position to defend panpsychism intellectually, since I haven't studied the literature. It's just a personal belief, and one n...

The first time I saw it was in Stan Wagon's book, The Banach-Tarski paradox. I found it confusing and had to devote brain cycles to figuring out what ...

@"Mephist" and I had a monumental pages-long conversation about constructive math a while ago. You might find it interesting. All in all I learned far...

I'm glad I could turn you on to this paper. I saw a little category theory back in grad school many moons go, then left math. When the Internet appear...

Yes I do understand take this philosophical objection. If I say 2 + 2 = 4 then if they are the same object they're the same. I'm saying nothing! If I ...

I agree with you re installed base or established mindshare. There are substantial developments in new foundations these days, category theory and hom...