Every proposition is simple
Following a suggestion from Rubenstein (2025), one can defend the very counter-intuitive hypothesis that there are no conjunctive propositions by arguing that whenever we seem to assert a conjunction what we are actually doing is distributively assert a pair of proposition and not a proposition that is a conjunction. The same for any other propositional attitude. Thus, there is no need to postulate conjunctions. However, following a many-ist strategy from Thunder (2025), it is possible to extend the argument so that nothing but elementary propositions exist.
According to Champollion (2015), the following are examples of sentences with distributive predication:
- John, Peter and Bill carried a briefcase.
- All the men carried a briefcase.
The notion of distributive predication has been developed to account for “the behavior of predicates when they occur with plural definites, noun phrases headed by distributive quantifiers like every, and noun phrases coordinated by and.” (Champollion 2015). The basic idea here is that a sentence like (a) is logically equivalent to a conjunction like (c):
- John carried a briefcase, Peter carried a briefcase and Bill carried a briefcase.
However, the notion can be extended to any other sort of plurals, quantifiers or coordinations. Thus, we should call cases like (a) and (b) cases of conjunctive-distributive predication, to distinguish them from other sorts of distributivity, like disjunctive-distributive predication as in sentences like:
- John, Peter or Bill carried a briefcase.
- One of the men carried a briefcase.
Here, a sentence like (d) would be equivalent to a disjunction like (f):
- John carried a briefcase, Peter carried a briefcase or Bill carried a briefcase.
But, of course there is nothing special about conjunction or disjunction. As a matter of fact, we can extend the notion of distributivity to any sort of logical operation and not only to plain pluralities but to sequences as well, regardless of whether we can find them in the wild in natural language. Consider the following example:
- It is true that if John carried a briefcase, Peter carried a single folder.
- I know that if John carried a briefcase, Peter carried a single folder.
It is clear that the truth and belief predicates in these two cases are not predicated either conjunctive-distributive or disjunctive-distributive. Is it predicated in some other form of distributivity? One may be tempted to say that not, because the conditional is not a plurality, but this would be question-begging against our hypothesis. The point here is that it is natural to extend the notion of distributivity so that we can say that (g) and (h) involve conditional-distributive predication over the sequence of John carried a briefcase and Peter carried a single folder.
Furthermore, there is nothing special about conjunctions, disjunctions and conditionals. This strategy can be extended to any logical combination, so that for any complex sentence S of logical form F(p1, p2, … pn), any predication over S is F-distributive over the sequence <p1, p2, … pn>. Thus, no need to postulate complex proposition is required.
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ResponderBorrarI didn't get it, it seems that something is missing. Saying "a and b" is the same as saying "a", then saying "b" (supposing I'm consistent with my past self). You get the same as conjunction by producing a sequence of assertions. But the same logic doesn't work with disjunction: saying "a or b" is not at all the same as saying "a", then saying "b". So what kind of production, if not a sequence of assertions, allows one to express a disjunction? There doesn't seem to be any.
ResponderBorrarGreat question, yet I think I have an answer: Your criticism seems to be confusing two senses of "a sequence of assertions": On the everyday sense, it means making an assertion and then another, in subsequent times. But I was using it here in the set-theoretical sense in which it only means an ordered pair. My claim here is that a sequence of assertions, in the second sense, is neutral regarding what we can say or do with them. Does that help?
BorrarI see. Now I have a follow-up question: if you want a full logic, you cannot be satisfied with only one operator, but if you juxtapose atomic propositions, how do you know if this is a conjunction or a disjunction? Or do you want to build everything from the sheffer stroke?
Borrar