predication and genus

What is the basis for reason? And mathematics?

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ficino
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predication and genus

Post by ficino » Thu Oct 12, 2017 3:24 pm

If there is a genus F, then is it the case that for all x, if x is F, x must be in the genus F? (In asking this question I leave out the problem of analogical predication of names of God.)

Thank you, f

wtf
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Re: predication and genus

Post by wtf » Fri Oct 13, 2017 1:50 am

What is a genus in this context? There's a technical term genus in math, but it's quite far removed from anything your question might possibly be about.

If you mean some sort of logical or conceptual category, your question suffers from vagueness. For example if by genus you mean set, then you run into Russell's paradox. But it by genus you mean proper class, then what you say is true. If x is F then x is in F.

I totally fail to understand what God has to do with this.

ficino
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Re: predication and genus

Post by ficino » Fri Oct 13, 2017 3:29 am

Many thanks for answering.

I am thinking of genus as in Aristotle's Categories and throughout his works. In Ari, a genus is a "kind," which is divided into species by various differentiae. I.e. "There are kinds in the sense in which plane is the kind of plane figures and solid of solids; for each of the figures is in the one case a plane of such and such a kind, and in the other a solid of such and such a kind; and this is what underlies the differentiae. Again, in formulae their first constituent element, which is included in the essence, is the kind, whose differentiae the qualities are said to be." Metaphysics V.28, 1024a36-b6. So, e.g. "biped," of which "man" is a species. Or "color," in which white/pale is a species.

I'm wondering whether, if we say there is a genus of movers, the First Unmoved Mover must be in the genus of movers if it is to be a mover. Aquinas does not want God to be in any genus. But he also argues to God's existence by identifying God with the First Mover. And in Aquinas' argument from motion, doesn't the First Mover need to be in a genus of movers for the argument to go through? It doesn't seem to me that one can say that the First Mover is supreme in an ordered series of movers AND deny that the First Mover is in a genus of movers. So the First Mover seems not to be identical with Aquinas' God.

I'm sorry, I don't know enough to know the difference between "set" and "proper class"! And I am mystified by the Wikipedia link, but thank you for linking it. You can see that my background is not in math or modern logic.

wtf
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Re: predication and genus

Post by wtf » Fri Oct 13, 2017 3:52 am

ficino wrote:
Fri Oct 13, 2017 3:29 am

I'm wondering whether, if we say there is a genus of movers, the First Unmoved Mover must be in the genus of movers if it is to be a mover. Aquinas does not want God to be in any genus. But he also argues to God's existence by identifying God with the First Mover. And in Aquinas' argument from motion, doesn't the First Mover need to be in a genus of movers for the argument to go through? It doesn't seem to me that one can say that the First Mover is supreme in an ordered series of movers AND deny that the First Mover is in a genus of movers. So the First Mover seems not to be identical with Aquinas' God.
This seems out of place on the philosophy of math subforum. It has nothing to do with math. I noticed that you usually post in the religion section. Perhaps that might be the right place for your question. Questions about God and first movers are not any part of math.

But since we're here, why must there be a first mover? The standard mathematical counterexample is the negative integers ..., -4, -3, -2, -1. In this model, each number has a predecessor (or "mover" if you like) yet there is no first mover. This model comes up all the time in discussions about William Lane Craig's cosmological argument. You could if you like think of each number as an "event" that is "caused by" the event immediately to its left. Every event has a cause, yet there is no first cause.

That's the thing about math. Given any metaphysical or physical theory, math can whip up a model. Math itself is agnostic about what's true. Math is a toolkit for building models so that we can talk about them with precision. But it doesn't tell you whose model is the right one to describe the state of our world.

ficino
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Re: predication and genus

Post by ficino » Fri Oct 13, 2017 3:28 pm

Thank you. I've only posted 6 times on here, or thereabouts. But I'll try moving this to the religion subforum. I posted here because I thought the question of predication and genus had to do with logic.

Averroes
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Re: predication and genus

Post by Averroes » Fri Oct 13, 2017 6:06 pm

Thank you. I've only posted 6 times on here, or thereabouts. But I'll try moving this to the religion subforum. I posted here because I thought the question of predication and genus had to do with logic.
It is alright ficino, it is not only a math subforum, but also a logic subforum. And the OP has a place here. Give me some time I will reply to you if God wills. Do not worry.

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Harbal
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Re: predication and genus

Post by Harbal » Fri Oct 13, 2017 6:11 pm

Averroes wrote:
Fri Oct 13, 2017 6:06 pm
I will reply to you if God wills.
What possible objection could God have?

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attofishpi
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Re: predication and genus

Post by attofishpi » Sun Oct 15, 2017 11:07 pm

Harbal wrote:
Fri Oct 13, 2017 6:11 pm
Averroes wrote:
Fri Oct 13, 2017 6:06 pm
I will reply to you if God wills.
What possible objection could God have?
No, it's willy not wonte.

wtf
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Re: predication and genus

Post by wtf » Mon Oct 16, 2017 2:02 am

ficino wrote:
Fri Oct 13, 2017 3:28 pm
Thank you. I've only posted 6 times on here, or thereabouts. But I'll try moving this to the religion subforum. I posted here because I thought the question of predication and genus had to do with logic.
I did some Googling and evidently this is something to do with ancient logic. I don't mean to discourage anyone from talking about classical logic. I don't know anything abut it and can be of no help. What I read does not seem to have anything to do with math as I understand it, but maybe it did back in the day. The examples are triangles being part of the genus polygon, So the examples are mathematical even if I don't recognize it as the kind of math I know. So maybe there's some philosophical aspect that's beyond my limited knowledge.

If anyone wants to explain more about this I'm certainly interested in learning. I still don't see the connection to God.

ps -- What is "analogical predication of names of God?" I would like to know what that means so that I can learn something. I do remember a story by Arthur C. Clarke called The Nine Billion Names of God.

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