The actual meaning of mathematical existence is that it's whatever working professional mathematicians say it is. You don't accept that, but that is how it works. — fishfry
You have the same objection to football, baseball, Chinese checkers, and whist? You reject playing poker because the only Queen you know is Elizabeth? Nihilism. Childish rejection of the very concept of abstraction. — fishfry
What I reject, is not the concept of abstraction, but the childish notion that an abstraction is an existing object — Metaphysician Undercover
nd what is completely absurd is an otherwise educated individual who cannot grasp that there are terms of art, and what they mean as terms of art is just what the people who use them as such say they mean, period. — tim wood
For example, I have a chair. By your standards, that's incoherent because "chair" is an abstraction.... — tim wood
. What do you say of a chair? "Chair" is certainly an abstract noun. Actually, all nouns expect for proper names are abstract. Where do you go with that?What I reject, is not the concept of abstraction, but the childish notion that an abstraction is an existing object — Metaphysician Undercover
Because I have not seen any resolution to these questions, I would not say that a "rule" has any existence at all. — Metaphysician Undercover
What fishfry has finally started to realize above, this principle: "if mathematicians say it exists then it exists", is a faulty principle. — Metaphysician Undercover
I hope you see the problem with this. You're saying, if we (mathematicians) agree that it exists then it exists, without any definition of what it means to exist. In any other field, no one would agree that such and such "exists", unless there was a definition of "exists" and some evidence to show that the thing actually exists. For example, would some biologist come in with a fictitious life form and ask the other biologists, can we agree that this life form exists, so that it can be a real existent life form? Or would a physicist propose the existence of a fictitious particle? — Metaphysician Undercover
On the other hand, the ideas/concepts represented under the name "empty set" certainly do exist. They're functional and purposeful. So also is my imaginary hippopotamus friend: he exists too, but also not at the store. — tim wood
What do you say of a chair? "Chair" is certainly an abstract noun. Actually, all nouns expect for proper names are abstract. Where do you go with that? — tim wood
I would say that the laws of Mathematics and Logic are normative principles pertaining to conduct regulation so as to make the world easier to describe and manipulate.
These normative principles cannot be given a logical justification on pain of circularity, rather their justification stands or falls with their general overall usefulness. — sime
Think of mathematicians sitting around a table and creating a game, discussing the pieces that are played, the environment in which they are played, and the rules that are agreed upon. Once done, would you then say, "The game does not exist."? You fail to recognize that math is a social endeavor, frequently deriving from observations of the physical world, but just as frequently not. — jgill
From this perspective, would you say the rules are the axioms? I would say no, there are ill-defined patterns of thought that precede the establishment of the rules, and that might be the subject of study and formalization at a later time - as is the case of the foundations of mathematics. — jgill
Physicists thought one day there must be atoms. Then they discovered the atoms are made of protons and electrons and neutrons. Then they discovered the protons are made of quarks. Now they think the quarks are made of strings. Do any of these abstractions exist? Yes they do, in the sense that they are part of an abstract mathematical theory that explains the experiments we're capable of doing at any moment in history. — fishfry
Physicist invent new existing things all the time. And de-exist things to. The luminiferous aether was once regarded as existing, till Michelson and Morley couldn't find it and Einstein did away with its necessity. — fishfry
A scientific entity has existence when it's a necessary ingredient of a successful physical theory. — fishfry
I gather you call "real" only what is "really out there." But if the 20th century taught us anything, it's that the existence of such a thing as "real things out there" is an assumption and not a fact. I believe if I'm not mistaken this is called scientific realism. It's only an idea. We could kick it around. But you have no logical basis for claiming it's true and everybody else is wrong. The days of Euclidean geometry and Newtonian physics are gone. Now we know the world consists of probability waves that are everywhere at once till we measure them. What can that mean? We don't know. But you claiming that you personally know what things are real, is a delusion on your part. Since you called me delusional the other day, which I can live without. — fishfry
Because we use the language as if there is an existent thing referred to by "game", "rule", or "concept", we fall under the illusion that there is such existent things. — Metaphysician Undercover
Nothing really exists because there are no entities of sufficient purity that they are not compositions of things, many of which fail to exist themselves. — jgill
Right, how could a thing which is composed of parts which do not exist, itself exist? — Metaphysician Undercover
It doesn't work though, because it doesn't explain how I'm here when no one's looking. So my real, true existence, is not supported by that fiction. That it is, is a delusion. — Metaphysician Undercover
It doesn't work though, because it doesn't explain how I'm here when no one's looking. — Metaphysician Undercover
Notice what you're doing: you're defining an extension to real numbers and real arithmetic. This doesn't magically transform infinity into something it's not (it's not a real number) it just means that the concept of infinity within your extended system, is coherent.Here's my definition of infinity, and for simplicity I'm only referring to positive infinity: infinity is a number, but it has a characteristic that all real numbers do not possess. Namely, it is a number that is greater than any particular real number. All the rules of arithmetic applicable to real numbers do not carry over to use of infinity. Examples: infinity plus a real number is infinity: infinity divided by infinity is not equal to one: infinity subtracted from infinity is not equal to zero. — Michael Lee
The problem is, as I demonstrated, the concept of "empty set" is self-contradicting. — Metaphysician Undercover
Non-existent things provide no support. — Metaphysician Undercover
This simply your "take" on language. It has nothing to do with the definitions, purposes, and functionality of the idea as used by its users and represented by them in this phrase as term of art. — tim wood
You would deem the mathematics "supporting" the moon landing and Mars' vehicles non-existent. You would also label the very thoughts you post here non-existent. — jgill
The thoughts which were used to produce those symbols are events which are in the past, and no longer have existence. — Metaphysician Undercover
But those who read and interpret those symbols revive those thoughts and give them renewed existence. — jgill
Thus, like monks reading and reciting scripture, were an order to so illuminate and pronounce mathematical works with unflagging resolve those thoughts would exist forever.
Hemingway's thoughts exist unendingly, for someone, somewhere is reading them now. — jgill
There is no continuity of existence between a thought at one time and a thought at a later time, so the two are not the same thing. — Metaphysician Undercover
the new thoughts are not the same thoughts as the old thoughts — Metaphysician Undercover
Nonsense. Take the Pythagorean Theorem: a2+b2=c2a2+b2=c2
The original thought occurred millennia ago, and it has been transmitted through the intervening years both by a variety of symbols and word of mouth. It remains essentially the same in Euclidean geometry, which by and large is the world in which we live, even though there are other forms of geometry. — jgill
"The word 'thought' may mean: a single product of thinking or a single idea." (Wiki)
The PT is an idea transmitted down through the ages. Thought = Idea. Your definition of "thought" is far too narrow. You clearly want to keep all your thoughts to yourself. :roll: — jgill
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