How We Know #9: Propositions

Chapter 5 is about propositions. Binswanger ventures beyond Ayn Rand, who said little about propositions. He divides propositions into classificatory and descriptive. Regarding the first he says, "Concept-formation operates by measurement-omission (to establish a range) and conceptual identification operates by measurement-inclusion (inclusion in an established range)." Descriptive propositions also work by measurement-inclusion.

The section Negative Propositions is interesting. He writes: "Negative propositions are those having the form "S is not P" -- e.g., "Lassie is not a beagle" or "Lassie is not small." Negative propositions are differentiations. Negative classificatory propositions assert that the subject is different from the existents subsumed by the predicate, and thus is to excluded from the predicate-class (Lassie is excluded from the class of beagles). ... Negative propositions work by measurement-exclusion" (179).

"Thus, negative propositions do not refer to some supposed "negative facts." Everything that exists is something. To be non-P is to have a positive identity, but one that is different than P" (179).

Interesting cases are ones about imaginary subjects. "A proposition about God, unicorns, or the integer square root of 17 is not differentiating an existent from other existents, but a valid idea from an invalid one" (180). Ayn Rand wrote some about invalid concepts in ITOE.

There is a section The Analytic-Synthetic Dichotomy. For the most part Binswanger refers to the same-named article by Leonard Peikoff in ITOE and ITOE2. Along with the analytic-synthetic distinction, Immanuel Kant made a distinction between a priori and a posteriori propositions. He said an a priori proposition is logically necessary and an a posteriori proposition is logically contingent. Peikoff is very critical of  contrasting "contingent facts" with necessary facts. Somehow "contingent" regarding propositions about the future doesn't seem to occur to him. (For example, I might have an 80th birthday.) Maybe it is not only him, but philosophers generally. Anyway, it does to yours truly. Actuaries consider future contingencies a lot.