I see no philosophy nor mathematics in your latest replies to me. It appears you've simply gone off the rails in your crackpot ways. Oh well, maybe ne...
Then you'd have to reject the axiom of extensionality, and all axioms which follow from it, and set theory in general. As I explained, allowing that t...
The sense of "identity" I am concerned with is that stated by the law of identity, "a thing is the same as itself". Do you agree with this formulation...
That's nonsense, you cannot read "1+1" as "2" because that's obviously a misreading. There is an operation signified by "1+1" and this implies that th...
The problem being, that contrary to your claim, there are no things denoted in mathematics therefore mathematics is not "extensional" in the way of yo...
Like Tones' you refuse to stick to mathematics, committing the folly @"Banno" pointed to, a pretense of mathematics. Until you define and demonstrate ...
Sorry Michael, I cannot follow you. You've strayed from mathematics, just like Tones did with the example of Twain=Clemens. Your example, like Tones' ...
The values returned are the same. What is represent by the right and left sides is not the value itself, but the operation. Therefore the "=" signifie...
We can go with that position if you want. It is irrelevant to the rest of the post, which demonstrates that "the value" of the right side, and of the ...
No that is clearly not the case, because these two procedures are completely different. They are said to result in the same value, 2, but the operatio...
Of course, we are not talking about the symbols, we are talking about what the symbols represent. In your example, "A" represents something, and "B" r...
Big problem with consistency when the use of "=" is not consistent. In the sense that axioms are a representation of what mathematicians are doing, th...
It should be evident to any well trained philosopher, that set theory is just terrible philosophy. I think that is what bothered Wittgenstein about ma...
I don't see any issue with bijection in principle. But when it is proposed that the quantity of a specific set is infinite, bijection would be impossi...
You have this wrong. A study of the history of mathematics will reveal to you that the axioms come about as a representation of usage. We could start ...
Yes, and as I've shown over and over again, that definition of "=" is not representative of how "=" is actually used in mathematics. Therefore it is a...
I love the new Lounge. It's a very vibrant, happening place, reflective of our society. The news is blaring at the top of the room but no one pays any...
This is clearly incorrect. We can imagine things without a concrete instantiation. That's how artists create original works, they transfer what has be...
Similar, but I wouldn't call it "picturing". Anyway, the point is that this "picturing" does not require a "concrete instantiation", which I assume im...
"Mathematical antirealist" is also a "rule". It states an ontological principle, or rule. It is a rejection of mathematical objects. The rules of set ...
I agree. I didn't say you need to believe in the truth of the principles you employ. However, it's hypocrisy to say "I'm a mathematical antirealist" a...
The issue is with the premises (axioms) of set theory. If you are "mathematical antirealist" you ought to reject set theory on the basis of the axioms...
The key point here, is that imagination does not require sensation of whatever it is that is imagined. But you claim understanding a concept requires ...
I would definitely disagree with this. There is a big difference between seeing, hearing, touching, or otherwise sensing an "object", thereby describi...
There goes the lounge! How can one lounge in the lounge with all that shit flying around? I say take that shit and corruption to the parking. Might be...
Of course, that's known as fiction. This evades me. How do you think of a number as a natural concrete object? Are you talking about the numeral, or t...
I interpret that as 'mathematics is extensional and that's how intensionality is relevant'. Whatever it is you are trying to say here, it appears to b...
The issue is a little more complex than how you represent here, but this is a good indication of why "set theory" is not applicable to mathematics. In...
The issue is not whether or not some mathematicians define "=" as meaning 'is identical to', as a premise for a mathematical theory, or some other pur...
Lying requires intent, which GPT lacks. Here's the example I gave Banno in the other thread. You and I are each one. Together we are two. We can symbo...
That mathematics consists of "objects" with identity is Platonist metaphysics. In this metaphysical theory, mathematical ideas like numbers are object...
It appears to me, like the quantum nature of energy demonstrates quite conclusively that the reality of space and time cannot be infinitely divisible....
Did you not understand the example I gave you in the other thread? I suggest you go back and read that post you made for me when you fed that example ...
I do not think I was ever subjected to new math. I simply learned at a very young age not to follow rules without a reason for doing so. I was not int...
I think there is a very close relationship between "mathematics" as the principles, rules etc., and the application of those principles. As Plato said...
I think the obvious point to start with is divisibility. Generally, mathematics provides that a quantity, any quantity, can be divided in any way. We ...
That's a specific, restricted definition of "incompleteness". The term is slightly different in physics for example. So this is an example of what I a...
I disagree. The "math boys" here at the forum tend to respond with 'go read some math texts' to anyone who disagrees with them on fundamental principl...
The point I was making is that concepts like infinity, incompleteness, and even computability, extend beyond mathematics. So, the mathematical approac...
You have this inverted. These are actually philosophical issues which have a bearing on mathematics. The way that a particular mathematician deals wit...
It's interesting that you title the thread "the art of thinking". I believe the key to bringing anxiety into the category of beneficial is to provide ...
I would say that is one interpretation of "dark energy", but here would be a number of possible interpretations. What I meant is that "more internal s...
Hi Dan, I see you're new here, so welcome to this space. I don't think it's proper to say that expansion means "more spatial structure" between intern...
Now, now, let's have fair representation. I balk at the claim that "1+4=5" implies that "1+4" refers to the exact same thing as "5" does. And, I have ...
I really don't think "truth" in this way is relevant. This is more of an issue of pragmatics, mathematics is a tool. You wouldn't say that one saw is ...
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