Jim Franklin

This might be conflating two concerns, though, which is the reality of numbers and their actual existence.

Compare Plato with Aristotle. Plato held that the all forms exist in some third realm, so numbers would be counted among them. Aristotle, however, held that forms exist in particular instantiations or in minds that abstracted them from reality. (Aquinas could be said to synthesize both views in the sense that forms exist in particulars and in minds, but also have their origin in God, thus making God a sort of third realm, in a way. Neo-Platonists would view the "mind of God" similarly.)

Now, in the Aristotelian view, numbers are quantities abstracted from concrete reality (indeed, quantity is one of the categories), but they are not substantial forms, as you will not see instances of numbers as substances in the world. They're abstractions of accidental forms. Furthermore, a form needn't be instantiated actually, but can exist potentially. This is how he resolves Zeno's paradoxes. You can divide a length an infinite number of times - or in a CS context, you can apply the successor function indefinitely - but only potentially; as a matter of actuality, you have not divided a length an infinite number of times.

So, for Aristotle, you have a finite plurality of things that are potentially infinitely divisible, or a finite series of actions that can be potentially infinitely repeated or whatever.

For a contemporary realist, Aristotelian treatment of math, James Franklin…

Yes, I read it after reading the comments on this page, expecting a silly mess. But no, it was well-written, for that kind of piece - it's popular internet journalism, not a professional philosophy journal, people! For what it's worth, the 'matter is made from consciousness' view does seem unlikely in the extreme to me.

I thought it was strange the term '(philosophical) idealism' wasn't used once, as it seems that's what most of the article was describing. Maybe she didn't want to confuse people with the more common meaning of 'idealism' today (to do with ideals, not ideas). Russell was a Hegelian idealist for a few years in the mid-1890s, like a lot of British (and American) philosophers, and published a book on Leibniz in 1900. (It's probably not a great introduction to the subject, but David Stove's Idealism: A Victorian Horror-Story is a very funny long essay by the Australia philosopher, mostly ridiculing the arguments used in support of idealism, in detail. Stove's Gem - winner of his Worst Argument in the World competition[0] - is worth being able to recognize in the wild.)

[0] https://web.maths.unsw.edu.au/~jim/worst.html

> I argue that post-modern perspectivism and the individualistic or collectivistic logic which nurtures its scope can be transcended through construction of hyperperspectivistic prisms based on alogic of interrelation animated by the interdisciplinarian spirit prevailing in the field of modern science. This latter serves as the leading thread for the foundation of a new canonicity which, without losing its historical and cultural character, can make claims to truth and validity of general acceptance. The hyperspectivistic canonicity deriving from such an interrelational logic is in a position to animate a new educational model capable of overcoming both idealistic and romantic versions of Bildung.

Come on, this is self-parody.

https://web.maths.unsw.edu.au/~jim/wrongthoughts.html

None of the medievals would have been dumb enough to ask how many pure spirits could dance on a head of a pin. Like much other folklore about the Middle Ages, this is almost certainly early modern propaganda.

> The libel about angels on the heads of pins seems to be of comparatively recent invention. I have not been able to find it in any author before Erasmus Darwin (who was late enough to have written, in his Visit of Hope to Sydney Cove, on the prospects for the spread of civilisation to New South Wales), though one might suspect the Encyclopedists or Rabelais as more likely originators of the idea. [Update] No medieval writer has been exhibited who engaged in such a dispute, for the good reason that there was none.

https://web.maths.unsw.edu.au/~jim/renaissance.html

http://web.maths.unsw.edu.au/~jim/torturecardozo.pdf

"He asked them where the bomb was. The terrorists-highly
dedicated and steeled to resist interrogation-remained silent. [He] asked the question again, advising them that if they did not tell him what he wanted to know, he would kill them. They were unmoved. So [he] took his pistol from his gun belt, pointed it at the forehead of one of them, and shot him dead. The other two, he said, talked immediately; the bomb, which had been placed in a crowded railway station and set to explode during the evening rush hour, was found and defused, and countless lives were saved."

Some of the best philosophy books I've found for free online:

Thomas Aquinas' Summa Theologica. Even though you may not agree with his conclusions, it is still a remarkable piece of work.
http://www.ccel.org/a/aquinas/summa/FP.html

David Stove does a good job debunking Hume's problem of induction, which underlies what I consider wrong in most modern philosophy
http://web.maths.unsw.edu.au/~jim/davidstove.html

Liberty or Equality outlines the potential for tyranny inherent in democracy
http://blog.mises.org/6326/liberty-or-equality/