Philosophy of Mathematics

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Philosophy of math was one of my favorite subjects. It helped that my prof had a masters in math and her Phd in philosophy.

I fall into the logicism camp at least as far as I understand math. Mathematics works like logic (and probably is reducable to logic) - it’s a formal language with stipulated rules - a model that seem to map very well onto our world. Mathematical objects are useful fictions that help us organize the world around us.
 
I understand what you are trying to say. I don’t think that “God is math” is true in the same way that “God is love/truth” though. Love and truth are all-encompassing entities. Math has a more limited scope. It’s kind of like saying that I am my left finger.
 
Isn’t math like color? It is accidental rather than substantial, a quality of a thing rather than the thing itself. Or rather, an abstraction systemarized and with its own formal logic of a quality of a thing.
 
As others have pointed out, viewing math as only a quality of nature runs into problems with much if the more esoteric disciplines within mathematics.

Additionally, yes mathematical concepts manifest in instances of other things. Why does that imply they don’t exist separately.
 
I understand your criticism, but I don’t agree. Love and truth do not fully define God. Yet “God is love” is acceptable. God doesn’t have parts–here’s God’s love over here. And over here is God’s truth.

As Augustine muses at the beginning of Confessions. Somehow God is infinite, yet omnipresent. Thus God’s infinity is indivisible and fully present in every point of space and time. He has no parts.
 
I honestly can hardly parce that article. Would you care to detail your opinion a little more clearly please?
 
Does logicism imply nominalism or are you stating those as separate beliefs?

I don’t think “math is logic” implies “math isn’t real”.
 
Math is one way we model the natural world.

Take for example electromagnetic theory. We model both electrical and magnetic fields as a field of vectors and therefore can describe through these vectors how an EM field behaves but it doesn’t tell what exactly an EM field is.

Same thing with photons. We can describe their behavior in terms of either waves or particles but what are they exactly?
 
I assure you that the life of many mathematicians has little to do with using math to explain physical phenomena.

Math can’t be ‘just’ a model. The math used in the sciences can be expanded by logic necessity into mathematics so esoteric it doesn’t represent a single thing.

I would also point out it seems a little peculiar to say “math is one way we model the natural world”. I can’t think of another way we model it. How can such a pervasive fact of nature be just a tool?
 
Did I say math was only used to model physical phenomena?

NO.

I never said that. Read my post again.
 
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I thought I remembered you being in the “math is just a tool” camp, based on your posts yesterday.

My apologies.
 
No problem.

Sorry for snapping at you.

Now, what field of math are you studying?
 
My concentration is numerical methods. Funny enough though, the past two summers I’ve done work on statistical modeling. (Although heavily computer aided so it still fits).

I’ve taken a lot of numerical partial differential equations and computational fluid dynamics. That would be a fun field to find work in.
 
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Nice.

I am more partial to differential geometry especially the Poincare upper half plane. I must confess to being ignorant of statistics.

When I was at university I worked as a research assistant for some physical oceanographers. They do a lot of modeling of ocean phenomena using computational fluid dynamics.
 
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Ok thanks, something to keep in mind. I don’t like to run around touting this (I hate it when people act like school or education is some sort if competition), but since it’s relevant, I’m a dual math/chemical engineering major, so I hope to find CFD work related to that.

Yeah… I’m about as ignorant about geometry as the average high school graduate. I’ll get away without even having taken abtract algebra since it never fit into my tight schedule. (I’m taking a graduate level linear algebra course instead).
 
What do you mean by “real”?

Math is certainly real - we use it all the time.

Mathematical objects are constructs and abstractions of logic. And in the same way as logic, I don’t think math needs to exist in our ontology to do what it does. A lot of people see the unbending truth of math as from there think that math must have some special reality in our world but I don’t think that follows. Language is the same way when I think about it.

Something like English is human-made, it’s real in that it’s used but it isn’t an immutable truth. And yet some day two billion years from now when humans are all dead and gone (let’s just assume for the sake of argument we don’t last that long and the universe is still chugging along) certain propositions of English can and will still be true. For instance, a yard will alway be three feet - it always has been and it always will be. At some points, at regular intervals, in that bleak future the sentence “today is Tuesday” will be true. Even without us.

Math works the same way, or, I find the least problems with what math is thinking of it that way. It’s a formal language - with subjects and operators and functions - and we have found that it maps onto our world nicely. Logic works the same way, and even natural languages do.
 
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chessnerd321 said:
How can you recognize that there are two apples if there’s no such thing as “2”. Further, how can you recognize the relationship between 2 apples and 2 oranges? The commonality you distill from the two situations exists outside the mind. 2 apples is the same number of things as 2 oranges whether or not someone takes note. It seems to be the two-ness of the apples is a particular instance of two, which is a general attribute of nature, in this case quantity.
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Well, I don’t the exact mechanism in our brain which allows us to recognize things in reality.
chessnerd321 said:
Your analogy of direct relationship falls appart quickly when it comes to more esoteric mathematics. What possible physical meaning can John Conway’s surreal number system have? It might be applicable in some way I admit, but not in a meaningfully direct way. If we can take what we abstract from reality and it leads logically and necissarily to something not reflected in reality then we’ve discovered a truth beyond physical reality. But it seems just as real, derived from the truths reality gives us.
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All abstract objects are feasible to exist in reality.
 
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