[quote]pat wrote:
[quote]smh_23 wrote:
[quote]pat wrote:
Well then I would still have to resort to saying that the mechanism by which something is obtained does not preclude the object.
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Right, I understand the claim. Mathematics exist and do not supervene on the physical. The rest of your post is a series of re-statements of this claim.
What is missing is evidence. On what evidence do you affirm that mathematics exist–actually exist–as a set platonic, non-physical ideals? On what evidence do you claim to know that it is not the case that mathematics supervene on the physical “material”–I use the term widely here–of the brain and its physical perception of the physical world it inhabits?
Note that analogy will not substantiate your claims. You drew an analogy involving continents. But it does not logically follow from “human conception of continents <---- physical continents, which exist outside the mind” that “human conception of mathematics <---- *non-physical mathematics, which exist outside the mind.” There is no necessary logical entailment in the analogy (as there just about never is: Analogy makes for poor philosophy).
*Note that the analogy doesn’t even work internally, because continents are physical entities whereas mathematics, in your view, are not.
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Well Kant posed this same problem the unlovable son of a bitch he was, he did have good points.
But first, I would highly contend that analogy makes poor philosophy. I have read my share of philosophy books and treatises and whatever other agonizing thing a dead guy can write. I cannot honestly think of one at the moment that did not use analogies. Maybe Aristotle? Jesus used them exclusively to make points.
Analogies not only make great philosophy, they make the subject matter tolerable. I may have made a bad analogy, but it doesn’t make all analogies bad.
Anyhow, the problem with the metaphysical is that no matter how we try, we have no choice but to interact by means of the physical.
There are many ways I think to attack it.
The many worlds hypothesis is one. The idea that a proposition would be true whether or not there where any human minds to to know it. In a possible world with no physical beings with minds exist, would a proposition still be true? Do the objects of the proposition still exist?
So with math, what are numbers? What are functions? ← not rhetorical.
Another approach is to take a look at the physical itself. In as much as Kant was right, so was Berkeley who proposed nothing physical exists, they are all objects of a mind. Berkeley has a university named after him, if Kant does I don’t know it. So who was right?
In as much as we cannot extrude our physicality from the examination of metaphysical objects as Kant says. We cannot prove the physical actually exists as Berkeley says.
As for the analogy, the point was objects exist whether we know it or not. One may not know anything about continents and indeed there was a time where that was true, yet they exist. Math also exists whether we know it or not. If nobody knew it, would it still exist? I believe the answer has to be yes. After all math wasn’t made, it was discovered. Nobody is credited with creating math, people are credited with discovering it. I don’t think it a matter of semantics.
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Jesus wasn’t a philosopher in the relevant sense. He said philosophical things, but he didn’t do formal philosophizing.
Anyway, the aphorism is that all analogies limp. Analogy can be useful in explaining something that isn’t clear, but it is generally a weak form of argumentation. This is because argument from analogy is not good at demonstrating logical necessity.
Anyway, I still don’t see a single reason to believe that mathematics exist and do not supervene on the physical. The question of whether or not mathematics were discovered or invented–surely you know that this is a question of much contemporary debate. If you believe that it is certain that the debate is settled in your favor, why do you believe it? By this I mean: On what specific evidence do you affirm that mathematics exist as some sort of platonic non-physical ideal?