I agree. "Infinite" is a property attached to an object, such as "large house" or "infinite number".

As "large" doesn't exist as an object, "infinite" doesn't exist as an object. — RussellA

If that is the case, then it seems barmy to talk about different size of the infinite sets.

I said math and philosophy have different way of doing things
— Corvus

They certainly do, which is why I’m wondering what a thread on mathematics is doing on a philosophy forum. — Joshs

Mathematics must have been believing in Philosophy's assistance in clarifying the tricky concepts. :snicker:

Yes, for example as in "infinite number" where "infinite" is a property of "number". — RussellA

There is no such a thing as "infinite" number. See this is an illusion, and source of the confusion.
Infinity is a property of motion or action, nothing to do with numbers. Infinite number means that you keep adding (or counting whatever) what you have been adding (or counting) to the existing number until halted by break signal (as can be demonstrated in computer programming).

A set containing 3 numbers can be made infinite, when it is in the counting Loop 1, 2, 3, 1, 2, 3 .... ∞ Therefore a term "infinite number" is a misnomer. I bet my bottom dollar that you will never find a number which is infinite, because it doesn't exist. If it did exist, then it is not an infinite number.

Umm... that's a school math book. Have you even studied a math course in the University? They are a bit different. — ssu

I have a few university Calculus and Algebra and Trigonometry books lying around here, and they are full of questions and answers. Studying math means you read the definitions in the books and work on the questions for the answers purely using your reasonings.

And if you study philosophy, you will similarly (hopefully) be given a exam where you have to answer too. — ssu

No. That is not the case. If you study philosophy for the degree, you must read, and write dissertations which you must defend it at a 'viva voce'.

Math and Science pursues the answers in the answer book.
— Corvus
What answer book? — ssu

Have you not read a single math book? If you read any math book, it will have Exercises and Examples after or in the middle of a chapter. The answers for the Exercises will be either at the back of the book, or as a separate Answer Book that you must acquire, if you needed it.

What answer book?

I think mathematics is especially interested in logic. I would dare to say that math is part of logic. — ssu

Sure, not denying that at all. They are all parts of each other we could say that. They are all inter-related too. But the methodologies they employ and the ideas of their goals might be different depending on the folks who are doing them.

Just look at ↪Lionino wrote above. Now I don't know if he is a mathematician, but at least he totally understands that philosophy is part of mathematics. — ssu

Never said math is not part of philosophy. That is what you are saying for some reason.
I said math and philosophy have different way of doing things.

We don't. He proved that they are the same size. — TonesInDeepFreeze

From the point of the set N, it looks like it is. But from the point of the set P, it looks like it is only a half set to N. What's going on?

? :yikes:

I don't get your point here. — ssu

Math and Science pursues the answers in the answer book. You are either right or wrong. Philosophy is more into your arguments and logic for the answers, hence there is no such thing as the answers in the answer book i.e. truth and falsity they pursue are different in nature.

I will likely make a thread about the Grundlagenkrise in the coming weeks. — Lionino

Blimey I was going to make a thread about "Science as a superstition".

I think you got it a bit wrong. Those who are obsessed about truth or falsity are mathematicians. Even if they sometimes have different axiomatic systems, then it's about right or wrong in that formal system. — ssu

I think you got it wrong too. Philosophers don't care about the truths and falsity as the answers in the answer sheets. Philosophers are more concerned with the truth and falsity in the concepts, propositions, and logic.

It's the Philosophers who are interested about a lot more. Things like morals or aesthetics, which obviously aren't about truth or falsity. — ssu

Yes, Philosophy used to be the parents of all sciences and mathematics. It is the mother of all subjects, and we cannot deny the fact.

In Philosophy, they tend to analyse concepts and propositions for truth or falsity. That's what they do. End of the story.

But maybe the mathematicians and scientists do things differently. They don't ask what the concepts mean as long as they are in the textbook. They just accept them, and work on.

"INFINITY definition =1. time or space that has no end: 2. a place that is so far away that it cannot be reached:" - the Cambridge English Dictionary.

It implies that if you know what it is, then you don't know what it is. If you don't know what it is, then you know that you don't know. It is a paradoxical concept, which has to be branded as a contradiction in Philosophy.

Sure, we know that at least a world exists, the world being our mind. But we do not know whether there is an outside world (brain in a vat), that is usually what people talk about when we say the world exists or not. — Lionino

Once you closed eyes and blocked your ears and nose, from the moment, your beliefs and inferences based on your memory of the facts, takes over on the existence of the world outside of you.

Sorry I can't understand, I think this sentence has some words missing. — Lionino

Seeing wave of gravity and saying it is time or space time is like saying, an eclipse is God's facial expression. Just a metaphor or simile whatever you call it. :) Are you a French or Greek?

Here is a finite definition of an infinite set: "A given set S is infinite iff there exists a bijective function between S and a proper subset of S." Furthermore, such a bijective function can be stated finitely.

Here is an example. Take the set of natural numbers ℕ = { 0, 1, ··· }. Now take a proper subset of ℕ containing only even the numbers, ℙ = { 0 , 2 , ··· }. These two are equinumerous because there is a bijective function f : ℕ → ℙ, given by f(n) = 2n.

The proof that "f" is bijective is finite. So is the proof that ℙ is a proper subset of ℕ. — DanCoimbra

Great post, thanks. How do you prove then N is different size to P?

We adduce a sentence G that is is true (to be more precise, it is true in the standard model for the language of arithmetic) if and only if G is not provable in T.

Then we prove that G is not provable in T. So G is a true sentence that is not provable in T. Moreover we show also that ~G is not provable in T. So T is incomplete. — TonesInDeepFreeze

Could you demonstrate and prove the provability and unprovability of G in real arithmetic sentences in T?

Well, you can see gravitational waves insofar as you observe them by checking the spatial distortion that they cause. Maybe that is what they were getting at but I did not see that thread. Not sure what the connection is with what I said though. — Lionino

Maybe they did. But whatever they saw, equating it to time or spacetime sounds bizarre.

For someone who defends physicalism, they are. — Lionino

It would be a form of totemism in disguise for science. Seeing an eclipse, and saying that must a God annoyed at something. A similar logic.

I would say no because those facts could be a fabrication of the mind. — Lionino

The fabrication of the mind is the world. No? I am sure when one dies, his world dies too, because he can no longer fabricate anything anymore.

There cannot be such a thing as a ‘epistemic entity’ because it is, when taken literally, a contradiction in terms: an entity implies something within the ontology of reality, and epistemology pertains solely to knowledge (and specifically not ontology). — Bob Ross

How would you know if something is an entity without knowing what it is?

Ok, so ‘□∀M -> □∃T’ is ‘it is necessary that every motion is ??? and that entails that it is necessary that there exists a time”. That doesn’t make any sense to me. — Bob Ross

That is not propositional logic. It is an EL (Epistemic Logic) operator which means, Agent "knows". It could have been "K" for knows in general, but the box implies knowing via observation.

‘∃M1t1∃M2t2 →□Ag,T,M’ means ‘there exists a motion and time such that there exists another motion and time’ and that entails ‘it is necessary that there is an agento, time, and motion’. Again, I don’t know what this is trying to convey. — Bob Ross

If there was Motion1 to Motion2 with time1 to time2, then the Agent knows Time generated from the Motion via Observation. This is what it means.

One can talk about infinity conceptually, as one does in mathematics, without reference to its empirical verifiability. — DanCoimbra

"Let us not forget: mathematician's discussions of the infinite are clearly finite discussions. By which I mean, they come to an end." - Philosophical grammar, p483. Wittgenstein.

Welcome to TPF~ :cool: :up:

How would a difference in size be established between them when there is no counting involved? And if there is counting involved, how would infinity be reached? — Philosopher19

Doesn't infinity mean endless? i.e. unreachable eternal continuation in concept?
If it was reachable, then it wouldn't be infinity. Any set or size would be unknowable, if it were infinity. Therefore talking about different size, set or number of infinity, is it not a nonsense?

Sure. But we can see also Quine's point that analytic expressions are meaningless, because the meanings of the words change through time. And most of all, there is no logical explanation why words have the meanings.

For example, the word bachelor's meaning "an unmarried adult male", Quine asks who on earth gave that meaning to bachelor, and why? Meanings of words are totally contingent and changeable. A single words can have also multiple meanings too which adds to the confusion. Hence without the empirical perception which reflects the situation, analytic words themselves have no meanings.

But a physicalist will say that there is only the ink down on the paper, and that any content represented by it exists as chemical reactions in our mind. — Lionino

It seems like some form of superstition. A couple of days ago in one of the new thread here, the OP was claiming that he witnessed the actual wave of gravity with telescope, and it must be the physical existence of spacetime. It sounded like some religious beliefs of some cult folks claiming the earthquakes and hurricanes are act of the angry God or something.

So for physicalists, facts are physical or there are no facts; — Lionino

We are not denying the existence of physicals or substances, but they themselves are not facts or minds.

otherwise it would depend on whether you are talking about the type or the token, or whether the guy you are asking is an idealist, or what the fact is talking about. — Lionino

Wittgenstein said in TLP "The world is the totality of facts.", and it sounds interesting. It also sounds a kind of Solypsism. It cannot be said, but it presents itself. One's perception of the world is limited by one's knowledge of the facts of the world that one knows. The facts includes certain possibilities, impossibilities and logic that operates in the world. Could the facts one knows about the world he faces, and lives in, be the ultimate reason to believe in the existence of the world?

Zen is known for this, for example the book Zen Mind, Beginner’s Mind.
Also, the Tao Te Ching can be read and (somewhat understood) by nearly anyone in an hour.
In mystic Christianity, Jesus’s encouragement to become as children… etc etc. — 0 thru 9

Zen would be a knowledge that is impossible to demonstrate due to the nature of the knowledge, which is subjective and intuition based.

I have no idea what Tao Teching would be. Never heard of it in my puff.

For Jesus and Christianity, I know very little too. Only thing I know is that Jesus has died, but resurrected in 3 days (hence the Easter day). After the resurrection, we don't know where on earth he has been living. This cries for an esoteric inquiry.

I read a little about the underground religious sector stemmed out of Christianity called Gnosis, which is heavily into pagan rituals. These folks would be deeply into esoteric knowledge.

But it seems evident that none of these folks above would agree to demonstrate their esoteric or mystic knowledge even if they knew what they are.

I gave some examples and here is a compiled list:

Brain; (thoughts, thinking) — Mark Nyquist

It looks like a good name for a function in A.I. programming. You could write more details of procedure in the function specifying the variables, constants, inputs and outputs for the different external events fed into the function, and the procedures within the function could go through preset calculations and operations based on the set algorithms from the input and outputs from the hardware sensors in the AI agent.

The functions can be called from various parts of the main program carrying out tasks for the different physical and mental events. When fully implemented, it would be an interesting project or demonstration how AI can simulate the brain functions for generating and interacting with the input and output from the external world, and for all those different mental events and operations.

Cool. What program language are you using for creating the AI system?
Any data structure in hand for the project?

1. G is provable. So G is unprovable
2. G is not provable

So, there is G in the theory T

Have I got it right? — TheMadFool

Shouldn't G be in the form of arithmetic calculus propositions for the incomplete theorem to apply?

But what would be the point of the formalised analytic data, if it is only dictionary nature unable to interact with the external world events and inputs?

In that case it would remain hidden from us because it is beyond our abilities to comprehend it. — Fooloso4

When the mysteries are revealed then they are for the initiated no longer mysteries. — Fooloso4

Sure. My point was that in either case, the knowledge is not for demonstrating to public whether you are able to comprehend it or not. Even if you were a new initiate to the secret society, they will make you to work from the bottom to the top with dedication and hard work for acquiring the knowledge. They won't demonstrate the mystic knowledge, and show you the whole lot at one go, just because you joined their school or club.

https://en.wikipedia.org/wiki/Cyc — PL Olcott

That looks an interesting project. :ok:

No, the observed motion was a change in the fabric of spacetime. — MoK

It sounds like a voice from the deepest well of confusion. Will leave you to it. :yawn:

No, time is a component of spacetime. Spacetime was first claimed to be a substance by the general theory of relativity. It is also confirmed by observation of gravitational wave and lens. — MoK

You are confusing the observation of the wave with time as a substance. Observed motions are not time itself.

Because nothing is a condition in which no thing exists. Something is a condition in which at least one thing exists. Therefore, nothing to something is a change as well. — MoK

Nothing is a condition, and something is a condition too. So a condition to a condition means nothing has changed.

No, time is a substance and nothing is a condition in which no thing exists. Therefore, the premise is correct. — MoK

What do you mean by substance? Is it a physical object you can see and touch?

No, nothing is not something. The conclusion also follows from the premises. No time, no change. Time does not exist in nothing. Therefore, nothing to something, that is a change, is not possible. — MoK

Until you clearly define what nothing, something, change and time is, the conclusion is nonsense. The first thing wrong is the concept of time, which doesn't exist in the actual world.

All of the knowledge of the actual world is defined as the stipulated meaning of terms and stipulated relations between terms in an inheritance hierarchy knowledge ontology specified as Rudolf Carnap / Montague grammar meaning postulates. The term Bachelor(x) is stipulated to mean: Adult(x) & Male(x) & ~Married(x) defined in terms of the constituent parts that comprise it. — PL Olcott

Still doesn't change the fact that it doesn't add any new knowledge or facts into the concept unless it was used with the real world situations or observations.

That would depend on what you mean by the term. As I understand it, it is knowledge gained through some kind of transcendent experience. It is known only to those who have had this experience. Some attempt to bring about this experience in one way or another by an altered state of consciousness. Others claim that it is something that happens to you without regard to what you do. Not ever having had such an experience I cannot evaluate it. I cannot say whether it reveals something about the world or human beings or the individual. I do not know to what extent it is an interpretation of what happens.

The term mystical is also used to mean what lies beyond both experience and explanation, that is to say, beyond knowledge. The arche of existence or that there is anything at all. — Fooloso4

The standard definition of "Esoteric" is very unusual and understood or liked by only a small number of people, especially those with special knowledge:, which suggests intentional hidings of their knowledge into their own circles, societies or cults. Therefore demonstrating the intentionally hidden knowledge for the circle members or initiated followers only to the uninitiated, outsiders or public would be contradicting the meaning of the concept as well as their intentions, gist, purposes and ideas for the esoteric and mystic knowledge.

In general esoteric knowledge is totally different type of knowledge from the general philosophical knowledge in methodology, objects and beliefs, and the main difference being the hidden exclusiveness of the knowledge only for the chosen few.

An analytic expression x is any expression of language verified as completely true (or false) entirely on the basis that x (or ~x) is derived by applying truth preserving operations to other expressions of language that are stipulated to be true thus providing the semantic meaning of terms. — PL Olcott

Problems with analytic expressions are possible tautology. They tend to repeat what is already contained in the subject of the expressions e.g. "A bachelor is an unmarried male." viz. they don't increase or add new knowledge.

Yes, my reaction exactly. The most intriguing thing about this paradox is that a lot of people don't mind reasoning with something that is empty of meaning... Probably because they did not check that it actually has meaning prior entering this logic loop. — Skalidris

An ambiguous statement disguised as a paradox.

If someone claims to have mathematical knowledge it can be demonstrated. Can the same be said of someone who claims to have mystical knowledge?
— Fooloso4
:nerd: :up: — 180 Proof

But Fooloso, wouldn't you agree if mystical knowledge is demonstrated, then it would be no longer a mystical knowledge?

Time is not ontological entity. Time is epistemic entity.

That doesn’t make any sense, unless you are just conveying that time is just the form of experience. — Bob Ross

It says what it means. It is a simple and clear statement which reflects the nature of time. I am not sure if it needs explanation.

□∀M -> □∃T
∃M1t1∃M2t2 →□Ag,T,M

I don’t know what this is supposed to be conveying. — Bob Ross

M = Motion
t = time
Ag = agent

Your pseudo-syllogism doesn’t produce a logical contradiction and, thusly, doesn’t prove the logical impossibility of nothing becoming something. Your argument, in its form (as best as I could infer), is:

P1: T ↔ C
P2: E → C
P3: N → !T → !C
C: E → (C & C!) — Bob Ross

Time is not ontological entity. Time is epistemic entity.
□∀M -> □∃T
∃M1t1∃M2t2 →□Ag,T,M

P1) Time is needed for any change — MoK

Time doesn't exist in the actual world. Time is a priori condition for perception and experience in Kant, and I believe it is correct. Changes take place totally unrelated to time. Time has nothing to do with changes. Human mind perceives the duration or interval of something starting and ending, and that is all there is to it.

Time is simply a civil contract to say that it is 1 year for the earth to rotate around the sun, and 1 day for the earth to rotate itself to the same point on the geographical location. Without those planetary movements, the time as we know it wouldn't exist at all. It follows that changes don't need time. So we could say that changes generate the perception of time.

P2) Nothing to something is a change — MoK

A change is from something to something else. Why is it nothing to something?

P3) There is no time in nothing — MoK

An ambiguous statement.  This cannot be accepted as a premise for its ambiguity.  Time is a concept and a priori condition for perception and experience.  Nothing is a concept to denote a state of non-existence.  You must define what "nothing" means before making the statement for consideration.

C) Therefore, nothing to something is logically impossible. (From P1-P3) — MoK

Can nothing be something? Then it can be possible for nothing to something. Hence the conclusion would be wrong. Because "Therefore, nothing which is something is logically possible." would be right.

But if nothing is not something, or if it is a state of non-existence, then the conclusion would be ambiguous, and invalid, because it doesn't clarify what "nothing" is, and it doesn't follow from the premises. There is no necessary logical connection from the premises to conclusion.

Could be, but still does not explain how they had predicted the upcoming solar flares years in the future. — Ege

It must have had been some type of Astrological prediction they had. I don't know the details of the methods, but here is the Wiki article on it.

If 'This sentence is false.” is true, then since it is stating that the sentence is false, if it is actually true that would mean that it is false, and so on.
Language conveys information and I can’t extract relevant information from this sentence, this is why I do not understand why people manage to reason logically with it. — Skalidris

For example, the liar paradox “this sentence is false” simply appears meaningless to me and I do not enter the logic of: If 'This sentence is false.” is true, then since it is stating that the sentence is false, if it is actually true that would mean that it is false, and so on. — Skalidris

The statement is unclear to be true or false. "This sentence" doesn't indicate which sentence it is describing or declaring about. From the statement, it is implied that there must another sentence before it, for the statement to be qualified to conclude "False", but it is not clear, whether it is the case, or "This sentence" means the sentence itself.

If it is the sentence before it, then it is missing, and if it is the sentence itself, then it doesn't indicate why it is false.

Therefore, if someone uttered the statement, it would beg the question, "Which sentence do you mean?"

A "first cause" is "first" in relation to a specific chain. There may be a multitude of different chains. The "first" of one chain may be prior in time to the "first" of another chain. Therefore the assertion "there can be no cause prior to a first cause" is illogical. — Metaphysician Undercover

:up: I was going to write the similar content of the post long before, but yes that is the crucial point.