Greg wrote:

the modality of the "should" is probably more like natural necessity; the more plausible reading (from what you are reading) is probably that "summer should be like summer" means "we ought to behave as though it is summer".

There's an ambiguity in the English language (in fact, it is a linguistic universal that all languages share this ambiguity) between the deontic sense of the word "should" and the epistemic sense of the word "should." You are interpreting my post with the epistemic sense of the word "should," when I am using it in the deontic sense.

When we say that "summer should be summer," are we saying that "of all the possible things summer could be, in the best possible world, summer is summer"? Let's suppose that there exists some "summer+" where instead of being like your typical summer in a continental climate with warm weather, "summer+" also causes all sentient inhabitants of the season to experience warm, pleasant nostalgia. Would it be better for summer to be more like "summer+," or instead to be like plain old summer? If it is better for summer to be like "summer+," then can we truly say that "summer should be like summer" when, instead, it should be like "summer+"?

Sorry if this seems terribly confusing, but I don't know how can I explain my thought in a clearer manner.

KevinScharp wrote:

Not so. To talk about this, I need to be a bit less sloppy than I was being. The main issue here is what follows from a contradiction, not whether any contradictions are true. In classical logic and lots of other logics, every claim follows from a contradiction. This rule is called ex falso, but it has come to be called explosion recently. There are lots of logics that reject explosion, and in these logics, you can reason with contradictions without them "blowing up" the system. LP is one example, but all the relevance logics like R or E have this feature as well. And there are strong reasons to adopt a relevance logic that are totally independent of the semantic paradoxes. In these logics without explosion, you can do lots of normal reasoning like conjunction intro and elim, most have modus ponens. They have double negation elimination. Some have disjunctive syllogism and conditional proof (it depends on the proof theory on the latter). So there's a wealth of reasoning that doesn't depend on rejecting contradictions. One important question I have asked in my own work is: can one get by with one of these logics in every way one might want? I've argued that the answer is No.

(1) Relevance logic is just modal logic in disguise.
(2) Paraconsistent logics don't actually solve paradox because, counter-intuitively, they're strictly weaker than classical logic. Yes, if I impoverish my system so that I can't talk about certain things, then I will end up with the result that I can't talk about certain things, and some of those things just might be paradoxes, but this isn't because you actually solved the paradox. You just impoverished the system. It's not unlike how psychiatrists treated mood disorders with a lobotomy, observed the patient was not as moody as before, and declared success.

You see, there's actually a reason why philosophers for the past 2,000 years have adopted classical logic: because classical logic (an

KevinScharp wrote:

(e.g., virtual particles in quantum field theory)

The Schrodinger equation is completely deterministic. The initial conditions completely determine the evolving state of the quantum potential. If "nothing" causes the virtual particles to come into being, then the evolution of the SE can't be determined by initial conditions, meaning that the SE is not deterministic. However, this contradicts what we are given. Therefore, you must be interpreting pair-antipair creation in a bogus manner.

KevinScharp wrote:

The standard interpretation is that 'F=ma' is a definition of force, not a causal relationship. Force just IS the product of mass and acceleration (look at the units). It's not that force causes mass to accelerate any more than acceleration causes mass to have force. Neither of these is right. Moreover, in the Kinsler paper, he assumes that unless a differential equation has some quantity that has a time differential in the denominator, it does not have a cause/effect interpretation at all.

First of all, F = ma is only true in classical, Newtonian physics. in special relativity, F != ma, but rather, F = dp/dt. In Newtonian mechanics, these are equivalent, but in special relativity, they are not. This doesn't take away from your point, but I feel that it's nonetheless important to point out.

But why stop at F = ma? None of the laws of physics make reference to concrete physical objects. In fact, all of the laws of physics can be formulated in terms of abstract mathematical objects. So we can conclude that the existence of physical objects is just an illusion created by our intuitions and that we live in a Pythagorean style universe where only abstract mathematical objects exist.

See how stupid that sounds?

KevinScharp wrote:

Right, but my point was that one might be pretty certain that causation is transitive even after thinking about it for a while by considering the matter apriori -- that is by reasoning with principles that seem to be constitutive of causation. That causation is transitive is a principle like this as are principles used in the cosmological arguments (note that Craig mentioned in his most recent Defenders podcast that his confidence level in the latter is 100%). I'm saying that even if some principle is constitutive of causation, it can turn out to be false. Ex: transitivity. The principle of causality is too.

That goes for everything you're writing too. Unless you have a paper showing your arguments in computer-verifiable proof form, you're relying on intuition. Even Euclid reasoned with intuition, and it took over 1,900 years for others to figure out that the Axiom of Pasch was needed to formalize Euclidean geometry (meaning that he made a leap of logic in his proofs).

Here's my proof: a positron is the same as an electron, except for charge and pairity, and an antiproton is the same as a proton, except for charge and parity. Two antihydrogen atoms and one antioxygen atoms form an antiwater molecule, which is exactly like water except that if it means a real water molecule it will explode violently. But if you don't have any real water nearby, anti-water is the exact same thing as water and completely indistinguishable.