GrandMinnow

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I see that you are confused about the most basic aspects of mathematics, language and reasoning. On certain points, your understanding is not even at ...

I did not say there is a circumstance in which '2' and '1' do not denote numbers. '2+1' is a compound term made from the constants '2' and '1' and the...

The denotation of 'the father of Jane Fonda and Peter Fonda' is Henry Fonda. The denotation is not Jane Fonda nor Peter Fonda nor the sibling relation...

You are repeating yourself without arguing specifically to the point I made. You argue by mere assertion. My point stands. Given your pattern of ignor...

https://plato.stanford.edu/entries/logic-intensional/ And a classic brief introduction to the subject is: Introduction To Mathematical Logic, pages 1-...

Aside from your lack of understanding of use/mention, I suspect that another big obstacle for you is that you don't understand that usually mathematic...

When we say that n is even we mean that n is a natural number such there exists a natural number k such that n = 2k. But, yes, that does imply that a ...

But you don't know anything about the formulation of classical mathematics. But your account of the meaning of mathematics is not compatible with the ...

The chairs are objects. And the mathematical object that is the number of chairs is the number 6. And the set of chairs also is an object, and it has ...

Please do not misrepresent what I said. I said explicitly that '1' and '2' do each refer to a distinct object. My remarks should not be victim to misr...

What is meant by whom? What is meant by mathematicians is not what is meant by you. I haven't said here what is necessarily correct. There are formula...

I am telling you the terminology and framework of ordinary axiomatic mathematics. 'qualifier' is not the terminology used. Of course, you may set up y...

sqrt is an operation. sqrt(2) is the object that is the result of the operation applied to the object 2. sqrt is the operation, and 2 is the argument ...

Algorithms that execute to completion do so in a finite number of steps. As far as I know, what you may have in mind is not an algorithm but rather it...

Equivalence classes of Cauchy sequences. This has been mentioned to you previously in this thread (1) We don't assume they exist. We prove they exist....

'The reals' means 'the real numbers'. We construct the set of real numbers. It doesn't make sense to debate whether a real number is a number. Mathema...

My rough impression is that professionals in the field of philosophy of mathematics usually do know about mathematics. Which philosophers in, say, the...

Whatever you have in mind linguistically is irrelevant since the sentence is linguistically perfectly correct. Even more simply: There is a unique obj...

I didn't write "E!x^". It doesn't make sense. I wrote "E!x x^2 = 2".

"There exists an object that has the property that its square is equal to 2" is perfectly fine English.

E!x x^2 = 2 is a theorem of ordinary mathematics. Anyway, I made my point that existence is not a predicate..

In casual discussion, mathematicians may say things like "the square root of 2 exists". But in a more careful mathematical context, we don't say that....

Infinitesimals are made rigorous with non-standard analysis derived with techniques of model theory or with internal set theory.

You don't know what set theory is. You don't know about the symbolic logic in which set theory is formulated. You don't know what the language of set ...

I addressed that already. You blew right past it.

I don't think in a framework of "infinite processes being completed or not completed". The notion of "an infinite process being completed or not compl...

It's worth noting that the challenges in the first post of this thread have been met. But hell if I know whether the poster understands that by now.

1. Is flush with critiques of a subject while he is unwilling to inform himself of the basics of that subject by even reading an introductory textbook...

I appreciate that threads are open to posting by both well informed and less informed posters. That doesn't entail that misinformation, misconception,...

That is a central point that I have made twice now. You have not responded.

A possibility occurs to me: When people who don't study the actual mathematics of set theory hear about such things as the axiom of infinity or encoun...

As I alluded previously, your "reinterpret an axiom" has no apparent meaning (surely not rigorous) other than as a vague personal notion. Axioms are f...

You're talking about how you'd like mathematics to be, but you do it entirely in a castles-in-the-air manner without regard to even a minimal understa...

The context of modern logic and mathematics involves formal axiomatization. Anyone can come up with all kinds of philosophical perspectives on mathema...

I meant to write " does not require ." I edited my post just now upon reading your post and realizing that I mistakenly left out the word 'not'.

The proof that there is a real number x such that x^2 = 2 comes later in the history of mathematics. It is found in many a textbook in introductory re...

We separate two questions: (1) Is there a real number x such that x^2 = 2? (2) Supposing there is a real number x such that x^2 = 2, is that real numb...

There are myriad ways to spout nonsense, fallacy, and misinformation such as yours, but fewer distinctive ways to state accuracies. So I am at a disad...

In order to meaningfully discuss incompleteness, you need to read a textbook in mathematical logic. Without such background, your notions and terminol...

(1) By 'alphabet' in this context we mean the set of symbols of the formal language. The concern is not with the number of alphabets, but rather with ...

Note: I make use of some of the sharpenings of certain notions and specifics that came after Godel's original paper. (1) Godel-Rosser pertains to syst...

(1) There is nothing incorrect in what you quoted. (2) Since not just Wikipedia (which itself is not a reliable source on mathematics and certain othe...

No, the left side does not represent an operation. The left side represents the value of an operation with an operand pair. The value of the operation...

You're confused. If the left and the right refer to the same thing, then the formula is true (or satisfied). And when the left and the right refer to ...

No, the laws of identity are not violated in mathematics, no matter what we take the ontological status of the referents to be. Or, please state preci...

I didn't say that they necessarily refer to the same object. I said the formula is satisfied when they refer to the same object. The fixed semantics f...

In the vast ordinary sense in mathematics, an equation (an identity statement) is a formula of the form: T=S where 'T' and 'S' are terms. The equation...

Points to make clear: (1) Ordinary mathematics, formally and informally, uses the law of identity. This is the use of first order logic with identity ...