5.2 Splitting Up Topics
Some of the topics just look disjunctive, no matter how hard I tried to get rid of disjunctiveness. And this affects the categorisation.
Consider, for instance the Sets and Grue topic. This just looks like it is made up of two parts - discussion of set theory, and discussion of the grue paradox. And while both of these are connected to Nelson Goodman, and more generally involve technical challenges facing a certain kind of mid-century empiricist, they aren’t really connected to each other. The set theory discussion looks like it should go in either Metaphysics or Logic; the grue discussion looks like it should go in Epistemology or Philosophy of Science. But putting the whole topic in any one of these four seemed mistaken.
Fortunately, there is a nice technique to resolve this problem. And it involves yet more applications of the LDA model. Take the articles that are in this topic (i.e., have a higher probability of being in this topic than in any other), and use the LDA technique to sort them into a two-topic model. I’ll call this a binary sort in what follows. So instead of taking all 32261 articles and sorting them into 90 (or more) topics, just take the 555 articles and sort them into 2 topics. If we’re lucky, one side of the sort will be the set theory articles, and the other side will be the grue articles.15
And it turns out we are more or less lucky in just that way. Here are the keywords and paradigm articles for topic 1 in this binary sort.16
- grue, green, emeralds, examined, projectible, verisimilitude, entrenchment, projectibility, emerald, entrenched
- Sydney Shoemaker (1975) “On Projecting The Unprojectible” Philosophical Review 84:178-219.
- Simone Duca and Hannes Leitgeb (2012) “How Serious Is The Paradox Of Serious Possibility?” Mind 121:1-36.
- Neil Tennant (1994) “Changing The Theory Of Theory Change: Towards A Computational Approach” British Journal for the Philosophy of Science 45:865-897.
- Ilkka Niiniluoto (1998) “Verisimilitude: The Third Period” British Journal for the Philosophy of Science 49:1-29.
- W. Balzer and V. Dreier (1999) “The Structure Of The Spatial Theory Of Elections” British Journal for the Philosophy of Science 50:613-638.
- Stephen Mulhall (1989) “No Smoke Without Fire: The Meaning Of Grue” The Philosophical Quarterly 39:166-189.
- Peter Schroeder-Heister and Frank Schaefer (1989) “Reduction, Representation And Commensurability Of Theories” Philosophy of Science 56:130-157.
- Graham Oddie (1981) “Verisimilitude Reviewed” British Journal for the Philosophy of Science 32:237-265.
- Herbert Keuth (1976) “Verisimilitude Or The Approach To The Whole Truth” Philosophy of Science 43:311-336.
- Hans Rott (2000) “Two Dogmas Of Belief Revision” Journal of Philosophy 97:503-522.
- Paul Teller (1969) “Goodman’s Theory Of Projection” British Journal for the Philosophy of Science 20:219-238.
- Bernard Berofsky (1968) “The Regularity Theory” Noûs 2:315-340.
- John Henry Harris (1978) “Strong Scientific Theories” Philosophy of Science 45:182-205.
- Barry Ward (2012) “Explanation And The New Riddle Of Induction” The Philosophical Quarterly 62:365-385.
- Wolfgang Spohn†‡ (2005) "Enumerative Induction And Lawlikeness*" Philosophy of Science 72:164-187.
- frege, membership, pure, null, abstraction, plural, boolos, mathematics, ordinal, russell
- Øystein Linnebo and Agustín Rayo (2012) “Hierarchies Ontological And Ideological” Mind 121:269-308.
- Stewart Shapiro (2003) “Prolegomenon To Any Future Neo-Logicist Set Theory: Abstraction And Indefinite Extensibility” British Journal for the Philosophy of Science 54:59-91.
- Keith Hossack (2000) “Plurals And Complexes” British Journal for the Philosophy of Science 51:411-443.
- Kit Fine (1998) “Cantorian Abstraction: A Reconstruction And Defense” Journal of Philosophy 95:599-634.
- Vann Mcgee (1997) “How We Learn Mathematical Language” Philosophical Review 106:35-68.
- George Boolos and Peter Clark (1993) “Basic Law (V)” Proceedings of the Aristotelian Society (Supplementary Volume) 67:213-249.
- Michael B. Kac (1997) “The Proper Treatment Of Singular Terms In Ordinary English” Mind 106:661-696.
- Thomas Müller (2005) “Probability Theory And Causation: A Branching Space-Times Analysis” British Journal for the Philosophy of Science 56:487-520.
- Louis Osgood Kattsoff (1936) “Postulational Methods. Iii” Philosophy of Science 3:375-417.
- Brent Mundy (1986) “Optical Axiomatization Of Minkowski Space-Time Geometry” Philosophy of Science 53:1-30.
- Alan Berger (2002) “A Formal Semantics For Plural Quantification, Intersentential Binding And Anaphoric Pronouns As Rigid Designators” Noûs 36:50-74.
- John Hawthorne and Gabriel Uzquiano (2011) “How Many Angels Can Dance On The Point Of A Needle? Transcendental Theology Meets Modal Metaphysics” Mind 120:53-81.
- Kit Fine (2005) “Class And Membership” Journal of Philosophy 102:547-572.
- John Wisdom (1928) “Mctaggart’s Determining Correspondence Of Substance: A Refutation” Mind 37:414-438.
- Jaakko Hintikka and Gabriel Sandu (1992) “The Skeleton In Frege’s Cupboard: The Standard Versus Nonstandard Distinction” Journal of Philosophy 89:290-315.
The first subtopic isn’t exclusively articles about grue, but the keywords suggest that they are going to be a big chunk of what’s there. And the second subtopic looks like set theory. The binary sort worked.
So now instead of asking how the articles in this topic should be classified, we can ask the two questions of how the articles in these subtopics should be classified.17 And while neither question is trivial, they seem at least a bit more tractable. Ultimately, I ended up putting set theory in Logic and Mathematics, and grue in Philosophy of Science. Just why I made those choices is for later sections, but for now I just wanted to show how the subtopics were generated.
There is one more thing we can note about this binary sort - the model is very confident in its answers. In the original 90 topic model, there is precisely 1 article that the model gives a probability greater than 0.99 to being in a particular topic.18 In the binary sort I just described, 57% of the articles are such that the model gives them a probability at least 0.99 of being in one particular topic. Now obviously it’s easier to be more confident in a two-way sort than a ninety-way sort. But this gives us a check of how disjunctive the model itself things the topic is. And I’ll use that to check whether it really makes sense to split a topic up in this way.
One advantage of doing things this way rather than looking for a more and more fine-grained model of the whole universe is speed. It would be somewhat interesting to see what happened if we sorted the 32261 into 120 topics. But that would take something like 12 hours on a good personal computer. The binary sort I described in the text takes well under 12 seconds.↩︎
An embarrassing admission: Due to a coding error, I ended up using 1954 for the seed for these binary sorts, not 22031848 like I’ve used for everything else. I only realised this after I’d done so much work building on them that it would have been too much to go back and change it - especially since the value of a random seed shouldn’t matter too much. But it was annoying to have had this change slip in.↩︎
Just to be clear, I’m using ‘topic’ for the elements of the 90-way partition that the original model generated, and ‘subtopic’ for elements of the 2-way partition that these new binary sorts generate.↩︎
It’s Contextualism, Hawthorne’s Invariantism and Third-Person Cases by Anthony Brueckner.↩︎