There is a temptation to find modal logic non-trivial; do not fall for it
- Quine
Quine, being an empiricist, just did not care about anything that could not be observed, and anything that could be observed would be possible (p → it is possible that p). Thus modal logic is irrelevant. Quine sides with Diodorus, who says that any possibilities are trivial (which Aristotle disagreed with).
Donald Davidson shared Quine’s view that anything meaningful in philosophy could be defined with first-order predicate logic.
Analytic vs synthetic statements; there exist a priori synthetic judgements, that are necessary but synthetic, according to Kant. A lot of people disagree and say that synthetic judgements are inherently a posteriori.
If a judgement is truly analytic it is necessarily true.
This is kind of what was called logical vs deductive necessity in our Logic course.
Synthetic vs. analytic is a fake distinction, and what is analytic in some cases is synthetic in others, and vice-versa - Quine’s solution to some problem I guess.
Kripke <3
Taught as a logical empiricist, broke with the tradition. Sees a strange tension between the Quinean dogma and the commitment to scientism.
The notion of science revolves around the notion of natural law. Science is most interested in the laws of nature.
A law is a modal notion. There is necessity in it. Most laws of nature are ‘genuine discoveries we make,’ they are not analytic. They are a posteriori, but it would be strange to say that they are contingent.
So now we have to use the logical means Quine doesn’t want us to use.
There are genuine a posteriori necessities, according to Kripke. We discover them in science, and this basically forces us to abandon the Quinean framework.
Instead, Kripke takes up the notion of possible worlds. This is a Leibnizean notion, he was perhaps the first to have the idea. He believes God chooses the most unique world, and Leibniz computes that using calculus.
Kripke, unlike Leibniz, is not too interested in the theological dimension. We can compare possible worlds. For Leibniz, God can do this.
A possible world is a consistent set of propositions.
w1: p, q, r, s
w2: p, ~q, r, s
w3: p, ~q, ~r, s
if the set of all possible worlds is { w1, w2, w3 }, then p is necessary and s are necessary, while q and r are possible.
5.61 Logic fills the world: the limits of the world are also its limits.
We cannot therefore say in logic: This and this there is in the world, that there is not.
For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world : that is, if it could consider these limits from the other side also.
What we cannot think, that we cannot think: we cannot therefore say what we cannot think.
?
God I wish Aristotle abstained from writing the metaphysics. Blaming him for the fall of the West.
Some things (f.e. umbrella terms) do not have essences, so no rigid designator.
Don’t write multiverses that’s just a logical claim
Kripke? More like bloodke
The thin red line - the only true possibility of the branching temporal modal logic. Basically the thread going through every actualized possibility.
(Some think) Descartes was the first to rely on thought experiments;
Metaphysicians just can’t stop making shit up (very literally).