How does nominalism have to do with mathematics?

https://thephilosophyforum.com/discussion/comment/334932

Quoting Gregory

It seems to destroy math actually.

How so?

Quoting Gregory

Nothing is exactly alike because individuality is what defines things in this philosophy.

:ok:

Reply to bongo fury

If reality has no common natures,.why should numbers share a nature necessarily?

Quoting Gregory

If reality has no common natures,.why should numbers share a nature necessarily?

Your hypothesis is nominalism. From which you draw a conclusion: nominalism.

I see this kind of argument here not infrequently. :roll:

Quoting Gregory

In articles on Russell and others, the word nominalism comes up sometimes. I have never known what it has to do with math. It seems to destroy math actually. Numbers can never act an exact way if they don't share a nature. Chaos theory would cover all branches. With the physical sciences, nominalism says you have to test each two objects that seem identical to see if they act different. Nothing is exactly alike because individuality is what defines things in this philosophy. Personally I like it. Any nominalists out there?

overly simplified definition of chaos theory:
the branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes in conditions, so that small alterations can give rise to strikingly great consequences.

It isn't that chaos theory isn't right, its that if you don't understand it, you may apply it to philosophy the wrong way.

There is absolute truth but absolute truth is very often hard to figure out. Nominalism and also on the other end Plato's realism are over simplifications of reality in my opinion. A car's behavior can be predicted, because to a strong extent (not absolute) a car reacts to Newtonian Physics.

Physicists who came after Newton made more exact discoveries of what reality is and the equations corresponding to that. As time goes on, predicting what a car will do, might come even closer to the absolute truth. I would argue the absolute truth is alot like an asymtope in that it will not exactly be reached but it will be reached in the sense that we'll say "good enough".

Quoting Gregory

If reality has no common natures,.why should numbers share a nature necessarily?

Their universality, if they have a mind-independent existence. I'm pretty sure numbers being real would entail that nominalism is false. Maybe there aren't tree universals, but three of anything would be the same exact number.

Hume pointed out that we can't say where force comes from, hardly knowing what force is in itself. He says things hardly need to make materialistic sense on earth, let alone at its source. If a human mind could somehow squeeze out the thought that 4 equals 9 and 1+4+9+20=12, then Humes thought would be complete

There seems to be only two valid forms of relativism. 1) nothing is true except that nothing is true because that is true. I like that serpentine move, speaks of nothingness. 2) everything is true. Speaks of a Eleatic substance to me

Quoting jgill

I see this kind of argument here not infrequently. :roll:

What, exploring of apparent implications under threat of reductio ad absurdum in order continually to clarify, revise and construct? If only!

https://thephilosophyforum.com/discussion/comment/397746

Quoting Gregory

If reality has no common natures, why should numbers share a nature necessarily?

Numbers construed how? As fictional characters, or concrete quantities?

Quoting bongo fury

Numbers construed how? As fictional characters, or concrete quantities?

Aren't they only fictions? I am not doing what jgill says. I'm offering an alternative, not proving a point per se

Quoting Gregory

Aren't they only fictions?

If you like. Although wasn't Frege and Russell's logicist project roughly (I think I'd better stress the roughly) about construing them as kinds of quantities? And then isn't there also the option of treating equations as pure syntax?

But ok, settling on the popular course of deferring literal translation of our grown-up math talk just as we do with our Romeo and Juliet talk, and just agreeing to play "pretend", what then is your question? Which numbers or classes of numbers are you supposing do or don't share a nature, and under what assumptions?

Quoting Gregory

I am not doing what jgill says.

I hope I didn't misrepresent @jgill; his description just put me in mind of a possible contribution to that other thread.

Quoting Gregory

If reality has no common natures,.why should numbers share a nature necessarily?

Sorry, guys. My point is that an assumption of nominalism in physical nature is not required if one speculates about nominalism of numbers and other math concepts. Go directly to the question of whether nominalism exists in math. :cool:

Reply to jgill

I get your point. Math and physical world seem separate with regard to the question of nominalism.

Reply to bongo fury

Russell wrote a lot of pages trying to prove one plus one equals 2. The final proof is not until Volume II, 1st edition, page 86. I like to get into those discussions and see what can be doubted. What if for an alien's brain, 2 plus 2 equals 100? I can see how that could work. Is our for of rationality necessary? Nominalism seems a stride in that direction

A consistent position of relativism is what I'm after, as I said above. I think 1 plus 1 equals anything or everything except 2. That's where Greg's at, reading Hegel

Quoting Gregory

What if for an alien's brain, 2 plus 2 equals 100? I can see how that could work.

Ok, is that like their Romeo copping off with their Tybalt, and it working as drama, perhaps... or it being canonical?

Or is it, after all, a matter of their having a system of symbol-pointing that we could reasonably interpret as equating certain (or all) quadruples with certain (or all) centuples, in some way that works for them?

Maybe 1 does not equal one because a nothing is identical, as nominalism says. So there is only one 1, one 2, ect. and math crumbles before philosophy. Wouldn't it result in there being only one number?

Quoting Gregory

and math crumbles before philosophy. Wouldn't it result in there being only one number?

Yes! And I alone know what it is. :nerd: