[BillSPrestonEsq]

my calc 2 teacher puzzled over that a little bit, said, basically, oh well, it works, shrugged and went on, my previous teacher didnt have a problem. He believed in a God (deist)

[Chrysostom]

Hmmm... I had returned to check on the thread and I seem to have found a thread to which I may be able to contribute.

(Donny) The metaphysical problem for atheists in mathematics is the argument of monism vs. pluralism. Radical monism states that there is one substance out of which all reality is made. The problem with this theory is that it destroys mathematics. For mathematics to work, there must be a plurality of things. If there is no difference between 7 and 9, mathematics is useless.
Pluralism, which opposes monism, states that there are only particulars and no abstract concepts. For example, we may see or experience five books or five cakes, but not an abstract “fiveness” separate from these experiences. The problem with this theory is that 5, | | | |, V, or five are all symbols or representatives, not the actual numbers. However, according to pluralism, these different symbols are different, because there is no abstract concept of “fiveness” that they represent. The result is that mathematics is destroyed, because this abstract concept is required for math (especially algebra). Mathematic proofs and equations are made up of symbols. They correspond to other symbols, and therefore represent the same thing as those other symbols. For example 5 * 6 = 30 and five groups of six is thirty both represent the same thing, but what is that thing? Without the abstract concept of “fiveness”, “sixness”, etc., they cannot represent the same thing, for the symbols are obviously different. “Six” looks different than “6”, yet according to math, they must represent the same concept or math is rendered useless. Thus, the abstract concepts of math must correspond with the particulars of math.

(Me) Your author hasn't examined 1) bundle theorists, 2) individuation through bare particulars, or 3) Strawsson's transcendental individuation. Your author also doesn't understand some distinctions monists (of sorts) can make. For instance, one might say that there is only one substance, but that there are many forms, modes, accidents, etc. of that substance.



Your discussion of the laws of mathematics points to the problem of the uniformity of nature and the problem of the one and the many.



(Donny) The final theory is that mathematics is just language. We have defined the symbols 6, +, 3, =, and 9 so that 6 + 3 = 9. The glaring problem with this is that it still fails to explain why these symbols actually correspond and working empirical reality

(Me) Nobody holds this or the logic view any more. By the middle of the 20th century, it was realized, to the defeat of the logical positivists, that mathematics isn't just a tautology or language construct (which people generally thought for centuries before that), especially given that some mathematical truths were discovered that couldn't be expressed in language. It was also realized that mathematics doesn't reduce to logic. Quine, for instance, thought that math reduced to logic plus set theory, and from this analogy tried to naturalize epistemology. You won't find any philosopher these days that thinks that math is a tautology, truist language construct, or expansion on logic.

[Chrysostom]

(Donny) I would like an answer, Jerry. a priori or a posteriori for math?

(JerryLove) Math was understood after seeing the evidence that proves its applicability.

(Me) I can't really think of any philosopher that thinks math is a posteriori (although someone might!). Jerry's response doesn't commit him to either side, though.

For a basic, though not precisely technical, definition of a priori, use this: knowledge that requires only competence with the concepts involved. Thus, Jerry might easily become competent with mathematical concepts from experience but still have a priori knowledge of mathematics.

* edit *

I take that back. I can think of a number of philosophers that think many truths of mathematics is a posteriori (for instance, Descartes and 2+3=5 or four-sided squares), but none recently.

[Chrysostom]

(JerryLove) Want to talk math now? Or are you incapable of typing anything but the same old propiganda about transendentalism.

(Me) Donny's post is an instance of attempted transcendental argumentation. He has given an example in which he thinks the atheist worldview cannot account for knowledge (math). He thinks that the atheist must ultimately appeal to induction to make his case, but again raises the red flag on induction. That brings sufficient reason for Jordan to bring up the Humean problem of induction.

[Chrysostom]

Since we're talking about philosophy, I had a joke for you.


Kant lived all his life in a tiny town, was never married or had children or did much of anything exciting. He died with a philosophically fruitful but generally bland life. However, this is not the worst death a philosopher might die.

For instance, Descartes was in a tavern, and the bartender asked him, "Want another beer?" Descartes's response was his demise: "I think not." (ba dum, ching)

Berkeley died an even sorrier death. His girlfriend stopped seeing him


If you didn't understand those jokes... ah well. Descartes thought, "I think, therefore I am" in his second meditation. Thus, the joke says that he didn't exist anymore because he didn't think -- "I think not."

Berkeley's idealism led him to interesting conclusions. For instance, to Berkeley, nothing existed unless it was perceived by a mental substance. Thus, the joke goes, when his girlfriend stopped seeing him, he stopped existing, as he was unperceived.

I realized that the former commits a logical fallacy and the latter ignores Berkeley's use of God and distinction between sensibles and mental substance. Give me a break, though... it's funny!

[+Donny]

(Me) Your author hasn't examined 1) bundle theorists, 2) individuation through bare particulars, or 3) Strawsson's transcendental individuation. Your author also doesn't understand some distinctions monists (of sorts) can make. For instance, one might say that there is only one substance, but that there are many forms, modes, accidents, etc. of that substance.

Well, the book was actually a history of mathematical theory. It had only a short section on the philosophy of math.

(Me) Nobody holds this or the logic view any more. By the middle of the 20th century, it was realized, to the defeat of the logical positivists, that mathematics isn't just a tautology or language construct (which people generally thought for centuries before that), especially given that some mathematical truths were discovered that couldn't be expressed in language. It was also realized that mathematics doesn't reduce to logic. Quine, for instance, thought that math reduced to logic plus set theory, and from this analogy tried to naturalize epistemology. You won't find any philosopher these days that thinks that math is a tautology, truist language construct, or expansion on logic.

IIRC, didnt a philosopher try to logically prove 1+1=2?



I got your first joke with descartes.. try using that at a comedy club and see how quick you get thrown out

[MonkeeSage]

How does that Berkleyan sonnet about the tree in the quad. go?

A little tree, unpercieved, hidden amidst the quad;
though by human eye unseen, exists;
percieved in the mind of God.

(Something to that effect, anyways, heh).


Shelumi`El
Jordan

S.D.G

[Chrysostom]

(Donny) IIRC, didnt a philosopher try to logically prove 1+1=2?

(Me) Leibniz offered an attempted derivation from the definitional stipulation that 1+1=2. Centuries later, his proof was realized to have formal, semantical errors. However, even if one can definitionally show the truth of some basic arithmetical truths (for instance, the use of the plus sign), we haven't examined all of math.

[JerryLove]

However, even if one can definitionally show the truth of some basic arithmetical truths (for instance, the use of the plus sign), we haven't examined all of math.

Except that all math can be accomplished using iterations of addition, compariason, and binary inversion. Proving those three proves pretty much all of the lower and middle math.

[MonkeeSage]

Originally posted by JerryLove
Except that all math can be accomplished using iterations of addition, compariason, and binary inversion. Proving those three proves pretty much all of the lower and middle math.

Except no one has ever seen any future iterations, meaning that we haven't examined all of math, meaning that the problem of induction is ever in front of us.


Shelumi`El
Jordan

S.D.G

[JerryLove]

Particularly hard for Christians for whom the nature of the universe can change at the whim of God