Metaphysician Undercover

OK, but the question was, how does your giving a rule populate a set? Do you apprehend the issue. Suppose I decree, as you suggest, that all red thing...

In order to consider the smallest possible square, we need some ontological principles, principles of physical existence which would dictate how small...

I think that's all well and good, because no two objects are exactly the same, and the difference between this object and that object is never the sam...

Thanks for the information. I know that mathematical definitions are called axioms. The problem that I have been trying to shed light on, is that some...

As the purveyor of a vast quantity of rubbish, you're foolish to call for such restrictions. You might as well request yourself to be banned.

This is the difference between an intelligible object and a sensible object. The intelligible object is apprehended directly by the intellect, while t...

I don't think that this is the proper way to represent language, as such a continuum, because we need to account for the significant difference of int...

You're as bad as Banno with your divine proclamation. "I have collected all the natural numbers" and therefore you have collected them. Stipulating th...

So the contradiction remains unresolved. That a set could have an infinite cardinality is what I dispute, as contradictory. "Infinite cardinality" con...

Until you demonstrate that "set of natural numbers" is not self-contradictory, such claims are nonsense. And to say that something infinite is not ind...

Exactly, this is what the quotation is saying, "infinite" in calculus and algebra is different from "infinite" in set theory. Set theory has transfini...

Before we close this discussion MindForged, remember the reason why I first engaged you on this thread. It was this statement: I didn't agree with you...

That is what is nonsense. There is no such thing as "the size of the natural numbers", unless the natural numbers are not infinite.. If the natural nu...

Seems that way doesn't it?

Neither did you include anything which should be there. I didn't see any odd numbers. Where's this collection you're referring to? It's easy to speak ...

If you knew the precise cardinality of an infinite set, you'd be able to tell me the relationship between the cardinality of a finite set and that of ...

You don't seem to understand the issue. You have stated that the cardinality of the set of naturals between 1 and 100 is 100, and that the cardinality...

OK, then I suggest you quit using "transfinite", because you are only introducing ambiguity. Why then did you say: "The cardinality of the set of natu...

Are you going to make your divine declaration "I have collected all of the odd numbers", and therefore you have collected them?

I've noticed that no one has reached the end of pi yet, why do you think that you can reach the end of the odd numbers?

Care to prove that?

OK, now we're getting somewhere. You were not talking about "infinite", or "infinity", you were talking about transfinite numbers. Why didn't you say ...

That would be a never ending task, so you'd never have that collection. Perhaps you like to think that the impossible is possible Banno, but that's co...

Try looking at it this way Mindforged. Let's assume that a collection may be infinite and then describe what it means to be a collection, keeping in m...

Actually, I define terms like "set" "collection", "object", and "infinite", in the ways normally accepted in philosophy. It's your argument which does...

That's the problem with those mathematicians who believe in contradictory things like "infinite sets". They believe in these "inconceivable" concepts ...

I've explained to you how "infinite set" is clearly contradictory. Also it's quite obvious that the waythe concept of "imaginary numbers" treats the n...

Honestly, I don't think mathematicians care about contradiction within they're work. What is important is that the prescribed methods work. Mathematic...

Let's say "the earth is round" is a proposition. If I claim that what this proposition means, is that the planet we live on, is the shape of a circle,...

The problem is that spheres are only conceptual, just like infinities. So the question is, does a concept, like "infinity", have actual existence. I'm...

You haven't actually grouped those stars into a collection though. That collection is completely imaginary, in the mind only . That's the point of the...

If it's an object then it exists. To be an object is to exist. There is no non-existent object, that's contradiction. You're just trying to find a sem...

That's false. To put something into a set is to assign it some sort of existence. If Harry Potter characters are non-existent then the set of Harry Po...

There is no such "set". The moments after the present moment have not yet come into existence so you cannot collect them into a set, nor can they be m...

Take any set of a series of natural numbers, 1 - 10, 1 - 20, 2 -40, whatever. If that set has two or more members, then the subset of the even numbers...

To me you have just demonstrated the logical deficiency which the concept of "infinite" introduces into set theory. You have demonstrated that the set...

I see no clear definition of infinity here, just a rambling description of a particular type of set, which you call an infinite set. That description ...

Care to provide that "clear" mathematical definition of infinity?

What's wrong with the idea that the universe has a boundary? That seems to be a natural and intuitive idea, the universe being a thing, and things hav...

Language, thought, and communication, are just like morality, success requires effort. To think that being moral comes naturally to a human being is t...

My opinion, for what it's worth, is that the shoutbox is generally full of posts with low quality philosophical content, and if left on the front page...

It all looks like metaphysics to me. You have described a separation, a distinction between the object of thought and the good ("significance", what i...

No. a statement, sentence, or a proposition (as a type of statement), is a collection of words which needs to be interpreted. And then, what is taken ...

Yes, that is what I mean. I define subjective as of the subject, and objective as of the objective. Judgement is something that subjects do therefore ...

I think that the idea with the microdosing of acid is that you are not really supposed to notice effects. If depression is the problem, then there is ...

Check out some Inuit throat singing.

I'm saying that inductive reasoning does not determine purpose. For example, every day that we see the sky, it is blue, so we conclude by inductive re...

Anyone try microdosing LSD?

OK, I'll see what I can do. Consider the existence of an object. It has a temporal extension past and future. From this perspective the present is irr...

Why not? I think you have this backward, believing in it is what convinces you of it. That's known as "faith". One has faith in Jesus (believes in Jes...