Rucker’s Mindscape

In his book Infinity and the Mind  (which you can read online at his website), Rudy Rucker puts forward the notion of what he calls the “Mindscape.”  He writes:

If three people see the same animal, we say the animal is real; what if three people see the same idea?

I think of consciousness as a point, an “eye,” that moves about in a sort of mental space.  All thoughts are already there in this multi-dimensional space, which we might as well call the Mindscape.  Our bodies move about in the physical space called the Universe; our consciousnesses move about in the mental space called the Mindscape.

Indeterminacy and Borges’ infinite library

Jorge Luis Borges’ “The Library of Babel” (from his collection Labyrinths) famously describes an infinite library, comprising books which together represent every possible combination of characters in the alphabet in which they are written.  Most of the books are gibberish, just as, if you emptied a bag of Scrabble letters onto the floor and looked at the patterns that resulted, almost none of what you’d see would count as a genuine word or sentence.  But because every possible combination is there, many intelligible books are there too.  In fact, every possible such book is there, so that the library contains all knowledge, every truth there is about everything.  For any of these truths, though, the trick is to find it somewhere in this infinite, bewildering Babel.

Pop culture roundup

Two or three of my readers have expressed interest in my posts on movies, popular music, and pop culture in general.  And I’ll bet at least twice that many are interested.  So, for you fans of pretentious pop culture analysis, here’s a roundup of relevant posts and articles.  For the most part I’ve included only those that are fairly substantive.

David Foster Wallace on abstraction

In his book Everything and More: A Compact History of Infinity (he had a way with titles), David Foster Wallace has some wise things to say about abstraction.  To orient ourselves, let’s start with the definition of “abstract” he quotes from the O.E.D.: “Withdrawn or separated from matter, from material embodiment, from practice, or from particular examples.  Opposed to concrete.”  So, for example, a billiard rack or a dinner bell is a concrete, particular material object.  Triangularity, by contrast, is a general pattern we mentally abstract or separate out from such objects and consider apart from their individualizing material features (being made of wood or steel, being brown or silver, weighing a certain amount, and so on).

Materialism subverts itself

A naïve understanding of materialism attributes to it a naïve understanding of matter.  Matter, common sense says, is more or less the way it appears to us in ordinary experience.  It is solid, colored stuff that always tastes, smells, sounds, and feels a certain way.  Materialism, on a naïve understanding, is the view that everything that exists is like that.  Even unobservable particles are assumed to be tiny solid, colored objects that have their own tastes, smells, sounds, and feels to them.  Like little stones or marbles.

Naturalism versus Katz’s Platonism

Naturalism holds that there is nothing more to reality than the world of concrete entities causally related to one another within space and time.  Since this is the realm studied by the natural sciences (such as physics, chemistry, and biology), naturalism can also be characterized as the view that the subject matter of natural science is all that there is.  Naturalism thus denies the existence of God, of angelic intellects, of immaterial souls (whether conceived of along the lines of Descartes’ res cogitans or in some other way), and of Platonic Forms and other abstract objects. 

What is mathematics about?

I commend to you James Franklin’s latest article “Mathematics as a Science of Non‑abstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics.) 

The access problem for mathematical Platonism

Mathematical Platonism takes numbers and other mathematical objects to exist in a third realm distinct from the material and mental worlds, after the fashion of the Forms of Plato’s famous theory.  A common objection to this view, associated with philosophers like Paul Benacerraf, is epistemological.  In order for us to have knowledge of something, say these philosophers, we must be in causal contact with it.  But if numbers are abstract objects outside of space and time, then we cannot be in any such contact with them, because they would be causally inert and inaccessible to perception.  So, if Platonism were true, we couldn’t have knowledge of them.  Yet we do have such knowledge, which (the argument concludes) implies that Platonism is false.  This is known as the “access problem” for mathematical Platonism.

Augustine on divine illumination

Plato held that the Form of the Good makes other Forms intelligible to us in a way comparable to how the sun makes physical objects visible to us.  He also took our knowledge of the Forms to be inexplicable in empirical terms, since the Forms have a necessity, eternity, and perfection that the objects of the senses lack.  His solution was to regard knowledge of the Forms as a kind of recollection of a direct access the soul had to them prior to its entrapment in the body.

Frege on objectivity

It can be an interesting exercise every now and then to reread something that had a profound effect on you earlier in life.  In my case, Gottlob Frege’s grand 1918 essay “The Thought” is a piece that I find always repays renewed study.  I think I first read it almost 30 years ago, and it was one of several philosophical works on thought and language that began to break the hold on me of the metaphysical naturalism I had picked up as an undergraduate – though that was a slow process, taking a decade fully to unfold.