A lurker awakes!

Aristotelian realism is the middle way between Platonism and nominalism. Mathematicals are real, contra nominalism, fictionalism etc.; but they are features of physical things, not a separate realm of Forms, contra Platonism.

I would not call A-realism naturalist, since we are not interested in whether cats or dogs can recognize a quantity (it seems they can) but in understanding it, a characteristically extra-physical act. But they are no more non-natural than colors or 'the son of Diares' (a stock example of Aristotle).

As far as general Platonism goes, a robust theist should have no problem stuffing all Forms into God's mind as His ideas.

'Intuit' is a funny word here. Intuition can also mean a gut feeling or mental grasp that is less than full understanding. (Again, think of higher animals and their powers of recognizing but not understanding quantities.) A very young child discovers that a person doesn't disappear in the game of Peek-a-boo, but to invoke intuitionism to explain it seems overkill.

It is no big problem that much of our mathematics is strictly unobserved. (No Euclidean straight lines just sticks; no true spheres just oblate spheroids, etc.) The mathematician may please his humor that he is accessing some Higher Realm by his insight, but he is being modest; he can as easily be described as accessing the contents of his imagination.

James Franklin is one of the clearest contemporary voices for Aristotelian realism. Some of his articles are available online. (btw, JSTOR is available free even if you are not connected to a university.)

Thanks to the originators of this forum, I've enjoyed the reading.

C Kirk Speaks (yes, that's really my surname)

Chris Kirk wrote:

A lurker awakes!

Aristotelian realism is the middle way between Platonism and nominalism. Mathematicals are real, contra nominalism, fictionalism etc.; but they are features of physical things, not a separate realm of Forms, contra Platonism.

I would not call A-realism naturalist, since we are not interested in whether cats or dogs can recognize a quantity (it seems they can) but in understanding it, a characteristically extra-physical act. But they are no more non-natural than colors or 'the son of Diares' (a stock example of Aristotle).

As far as general Platonism goes, a robust theist should have no problem stuffing all Forms into God's mind as His ideas.

'Intuit' is a funny word here. Intuition can also mean a gut feeling or mental grasp that is less than full understanding. (Again, think of higher animals and their powers of recognizing but not understanding quantities.) A very young child discovers that a person doesn't disappear in the game of Peek-a-boo, but to invoke intuitionism to explain it seems overkill.

It is no big problem that much of our mathematics is strictly unobserved. (No Euclidean straight lines just sticks; no true spheres just oblate spheroids, etc.) The mathematician may please his humor that he is accessing some Higher Realm by his insight, but he is being modest; he can as easily be described as accessing the contents of his imagination.

James Franklin is one of the clearest contemporary voices for Aristotelian realism. Some of his articles are available online. (btw, JSTOR is available free even if you are not connected to a university.)

Thanks to the originators of this forum, I've enjoyed the reading.

C Kirk Speaks (yes, that's really my surname)

 
How can you get JSTOR for free? I've been trying since forever!

Etzelnik wrote:

How can you get JSTOR for free? I've been trying since forever!

A free personal account is available, though it is limited in number of articles on your 'shelf' and you cannot easily print them: I've done it the hard way, saving an image of each page and then making a little folder for them.

(I tried to give a link, but i'm too 'fresh' on this site. Go to JSTOR dot org; click 'Login'; find and click 'Register for a MyJSTOR account')

Maybe you cannot because you are not in the US?

C Kirk

Daniel, much thanks for the welcome.

I do wonder why Franklin says so little about unrealized mathematicals, except that maybe he sees no problem with it at all. My position would be to assert that we - well, mathematicians - invent our own mathematicals, even the simplest ones, although we get these ideas from the real mathematicals of the world. Then we apply those imaginary mathematicals to the real mathematical features we observe, adjusting where necessary. Sometimes it takes a while, as the discovery that Euclidean space isn't quite physical space. Note the discussions in De Anima II.6–7, DA III.1–3, and De Sensu. Once we have a healthy stock of such ideas, we can invent wholly new ones. Am I really to invoke rifling through God's mind, or wandering around the Platonic Realm, to speak of n-dimensional space for instance? Evidence that we are not accessing such higher realities directly is that our mathematics is neither complete nor consistent, per Goedel. If the Goedel fits, it's yours.

There is a theological argument to make against Platonic-style intuitionism. Consider the end of the 'First Day' in Galileo's heliocentric Dialogues. There he claims that (in limited ways) we can know *exactly* what's in God's mind concerning mathematicals. That seems very hubristic (Simplicio calls it 'bold, even daring'), and counter at least to the analogical theory of the so-called names of God. Whatever our knowledge is, it is not exactly like God's.

C Kirk (Speaks, my last name)

Alexander wrote:

[1] Do we have to claim that we are perfectly accessing the higher realities? [2] Do we even have to claim much competence in accessing them? If not, that significantly blunts your criticism. [3] As far as Gödel is concerned, from what I know, he argued that the consistency of mathematics could not be proven. That doesn't mean mathematics is not consistent - just that we aren't in a position to prove that it is. [4] Again, I'm not sure we have to claim that we know exactly what's in God's mind. [5] We can say that abstract entities exist first in the mind of God. [6] This does not entail that they exist in exactly the same way in which we "perceive" them. [7] Indeed, given divine simplicity, it seems obvious that God cannot know mathematical truths (or any truth, for that matter) in exactly the same way as we know them.

Reply [5]:
Yes. That seems in fact where Platonism ended up historically as the Platonists became Neo-platonists. (And even with the master himself: what else is the One of Plato's Cave analogy but the Platonist God, from Whom all Forms flow?)

R[1,2,4,6]:
Intuitionism as usually understood is supposed to be just that perfect mental sight of a mathematical; in fact isn't 'to perceive' just one of those verbs of success? A defective perception of a rabbit in the grass as a gopher isn't a rabbit perception; at best it's a sizable-rodent perception.

R[3]: I thought Goedel proved that *no* mathematical system complex enough to be interesting could be *both* complete and consistent. Make it full and rich with useful and interesting concepts, you can generate contradictions; make it perfectly consistent, it is impoverished and of little use. That's been my understanding of the Incompleteness Theorem.

R[7]:
Divine simplicity to me makes all sorts of trouble for theist style intuitionism.

Chris Kirk