Notes on Nature of Philosophy

From Platos Footnote. Massimo Pigliucci’s new book 4/4/2016 11:57 AM

Introduction (not skipped)

I will defend the proposition that progress in science is a teleonomic (i.e., goal oriented) process along definition (i), where the goal is to increase our knowledge and understanding of the natural world. --seems reasonable to me Consider first mathematics (and, by similar arguments, logic): since I do not believe in a Platonic realm where mathematical and logical objects “exist” in any meaningful, mindindependent sense of the word (more on this later), I therefore do not think mathematics and logic can be understood as teleonomic disciplines (fair warning to the reader, however: many mathematicians and a number of philosophers of mathematics do consider themselves Platonists). Which means that I don’t think that mathematics pursues an ultimate target of truth to be discovered, --so what about Gödel? Peter Unger and Lee Smolin’s ‘The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy’ (2014), http://smile.amazon.com/The-Singular-Universe-RealityTime/dp/1107074061?ie=UTF8&keywords=The%20Singular%20Universe%20and%20the%20 Reality%20of%20Time&qid=1459792337&ref_=sr_1_1&sr=8-1 --we read Lee’s end-of-physics book in Martin Perl book club. His anti-string theory book. Seemed a bit overheated and unfair to me. http://smile.amazon.com/Trouble-Physics-String-TheoryScience/dp/061891868X/ref=asap_bc?ie=UTF8 --would Alien mathematicians ‘invent’ the same mathematical objects we do? Like the natural numbers? The assumption that they would ‘discover’ the same regularities we do lies behind ET searches (for what that’ Smolin immediately proceeds to reject the above choice as an example of false dichotomy: it is simply not the case that either mathematical objects exist independently of human minds and are therefore discovered, or that they do not exist prior to our making them up and are therefore invented. Smolin presents instead a table with four possibilities:

yes has rigid properties? discovered yes

existed prior?

existed prior ? no evoked

has rigid properties? fictional no

invented

Smolin goes on to provide an uncontroversial class of evocation, and just like Wittgenstein, he chooses games: “For example, there are an infinite number of games we might invent. We invent the rules but, once invented, there is a set of possible plays of the game which the rules allow This means we have to say that all the facts about it became not only demonstrable, but true, at that moment as well … Once evoked, the facts about chess are objective, in that if any one person can demonstrate one, anyone can. And they are independent of time or particular context: they will be the same facts no matter who considers them or when they are considered” --does Gödel’s theorem apply to chess? I think Gödel would claim chess exist in ideal Platonic reality. --how does a game differ from a set of axioms? We can explore the space of possible games by playing them, and we can also in some cases deduce general theorems about the outcomes of games --the space of possible games sounds kind of platonic Here is Smolin again: “There is a potential infinity of formal axiomatic systems (FASs). Once one is evoked it can be explored and there are many discoveries to be made about it. But that statement does not imply that it, or all the infinite number of possible formal axiomatic systems, existed before they were evoked. --Smolin has added some subtly to the discussion. I doubt it will change many minds. --I as usual just don’t know… --I got back and forth on whether Gödel’s theorem is profound or just an elaborate version of “This sentence is false.” In fact, many FASs once evoked imply a countably infinite number of true properties, which can be proved” (p. 425). -And for real numbers presumably uncountable infinity, but maybe they can’t be proved? mutatis mutandis? mu·ta·tis mu·tan·dis m(y)o͞oˈtätəs m(y)o͞oˈtändəs,-ˈtātəs,-ˈtandəs/ adverb adverb: mutatis mutandis 1. (used when comparing two or more cases or situations) making necessary alterations while not affecting the main point at issue.

"what is true of undergraduate teaching in England is equally true, mutatis mutandis, of American graduate schools" --lovely word. Science writers should learn from it!