“2 + 3 = 5” is a sort of tautology. Numbers are a figment of our reasoning process; they don’t exist in the same sense as a cat or a mat

Sorry Brad but your assertion is a kind of futile semantic exercise

So, its being a tautology is irrelevant to whether or not such objects exist.

Point swell taken Brad. However in no way does the equation confer objectivity

I'm not sure what you mean by this.

The equation 2 + 2 = 5 or for that matter any mathematical “tautology”.

What does your statement 3+2 = 5 mean if the terms 3, 2, and 5 do not exist? Would they not exist at least by virtue of their definitions?

Pris it’s purely a semantic matter.

This is just a test, only a test!

-- Updated April 24th, 2012, 12:49 pm to add the following --

I repeat, it’s all a matter of semantics--------

And what does saying that explain?

It asks why waste a lot of words that can be interpreted to mean nearly anything

in the hope people will take that for profundity?

No pris, only that it might stimulate some thinking in that direction. Profound I’m not, but Intuition strongly suggests that much of the apparent disagreement amongst us lies in that direction

Well I think if mathematical objects exist, they cannot be mental objects, since that would be to say they are dependent on thought

Brad does that mean that if there were no Universe numbers wouldn’t exist

When the Big Crunch occurs and there is only one of it all, is the number 1 the only one existing

In my brain, and yes it’s a relatively small one, Intuition suggests numbers have no reality beyond a process of electrons shifting around amongst cells

Pris in #24 expresses it far better than I

Each and every concept is true to some degree.Truth is quantifiable.

Aha! Bel my very favorite participant has nailed it. In other words, she is saying, as I understand her, and I concede I could be mistaken, as I have long maintained with virtually no support whatever, that nothing is entirely anything while everything is partly something else

Personally I feel that if something exists in space and time it is more true than any abstraction from the tangible world of things .

Einstein could not have better expressed it nor in fewer well-chosen words. Bel I sometimes wish I were single once more, much younger, and you lived nearby

Only however if I could take with me my present “smarts"

So nothing is entirely true while everything is partly so: 2 + 3 = 5 is partly false in the sense that numbers exist only as a figment of thought process and have no absolute “existence” like the rock sitting there

….while I’ve long wondered whether our concept of numbers might fall flat in the face of infinity. For instance if there are an infinite number of numbers then how can there also be an infinite number of even ones, and odd too, etc, and somehow doesn’t this call into question the legitimacy of infinite universes

Lo! the very idea of infinity itself might be invalid, merely a sound emanating as a result of interaction amongst brain cells transmitted by an evolutionary constriction of the humanoid breathing mechanism

While I conceded that her concept somewhat negates aspects of my own argument it is only because her thinking so far outweighs mine

I would also incidentally describe myself (and my No. 2 Son) as a Socialist if “Apodictical Existential Pantheist” didn’t sound more impressive

humans have six legs.

I presume you mean entirely false. What if the fetus contains an extra set of dormant leg cells; how many legs does a woman have who is pregnant with twins

Perhaps not good examples but over the enormous range of possible examples you cannot draw a dividing line beween those good and those bad

Of course such thinking multiplies indefinitely the conditions required of the statement: “Humans of the world we know don't have six legs, assuming by “human” you mean …... while “leg”is defined as ……... until it requires an infinite number of words to bestow truth upon it. Indeed if the Universe is infinite forever and anything that can happen, will happen……….

the statement itself is paradoxical

Yes but only if you maintain a distinct dividing line between paradoxical and not

Your problem here is that you are using a property of finite sets on infinite sets.

I’ll have to take your word for it, I’m not a mathematician, my reactions purely spontaneous

—but I'm not sure what you meant about the legitimacy of infinite universes.

Forgive me Pris but it’s hard to express some of these intuitional insights. It might prove for instance that an infinite Universe is impossible, calling into question the entire concept of infinity

…....just Intuition babbling on

just change it to all humans have six legs.

I imagine a race of six-legged humanoids in a distant galaxy who don’t consider us “human” so you still have to attach conditions. Lawsuits have been conducted and won on the basis of such apparent absurdities

I'm not prone to argue.

Good one Pris, I must remember it

The statement [all humans have six legs] is false if there is a single human who doesn't have six legs.

Let me reiterate that six-legged Marty who considers himself human but doesn’t consider us so sees the statement as true. So you have to specify at least that what you mean by “human” excludes, say, anything not earthbound. You will have to continue adding conditions until what you’re saying is, “ 'All humans have six legs' is false” provided that which I callI call human has fewer than six legs” which is of course a tautology


Naturally I’d have to specify that Marty doesn’t consider one of his kind who has lost a leg, as human.

Pris we simply view the Megillah differently. Yours is black and white with definite outline while mine is fuzzy gray in all diretions

Alas, well, the fuzzy object with indefinite outline does after have a faint stripe here and there and maybe even a small touch of color

seems to be that no definite statements can be made about anything

I’ll have to concede however that some seem more definite than others

-- Updated April 27th, 2012, 11:05 am to add the following --

No, I don't. It may be true that my circle of acquaintances is not quite as extensive as yours, which seems to extend to alien life forms,

Pris while I don’t know any of them personally their existence is almost a certainty while surely some of them are six-footed

The idea we’re alone is absurd. A very conservative estimate places our number at six sextillion but it must surely be much higher than that as just recently it’s been suggested that there are more planets than stars

Existence of the abstract is intermittent depending entirely upon apprehension by a living person.

Well put Eric, according to the general principle that nothing is entirely anything while everything is partly something else so there’s no distinct dividing line between the abstract and the concrete. Thus we have a rock at one extreme and God at the other with The Catholic Church and Costco somewhere between