Logical and causal possibility (think of mind experiments)

Logical Possiblity:

Something is logically possible if and only if it violates a law of logic. 

Here is one logical possibility: "President J. F. Kennedy was not killed by Larry Oswald in Texas on November 22, 1963." 

He was indeed killed that day. So, why is it still logically possible? There's no contradiction in assuming Larry Oswald missed his shot or that Kennedy was hurt but survived. 

Causal Possibility:

Something is causally possible if it does not violate law of nature.

Law of non-contradiction: 

Nothing can have and lack property at the same time. 

Examples: "A triangle of four sides," "2 + 2 = 5", "A married bachelor," etc.

Conceivability: 

1. If p is conceivable, it is imaginable (imagination is a mental faculty linked to rationality). An example of that is mind experiments in physics and math. 

Is Superman logically possible? The first step in the evidence that p is possible is to be able to conceive it. Just that. 

We say p is conceivable if its implication can be drawn without it being contradictory, i.e., 

Can Superman be conceived? 

Yes, that's why we talk about him and can even watch him in a movie. 

Now, Clearly, not everything that is conceivable is possible. For example, Superman, dragons, gremlins, and succubi are all conceivable but not possible. 

Why not?  They violate laws of nature.

Remember: If p is conceivable, then from 2. It's logically possible. 

finally,

3. p is causally possible if it doesn't violate a law of nature.  

Now, let's talk a little bit about LAWS OF NATURE: 

Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena; they are merely distillations of the results of repeated observation. 

A law's applicability is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated. 

How do logical possibility (LP) and causal possibility (CP) relate?

If something is logically impossible, it is causally impossible.

If something is causally possible, it is logically possible. 

LI → CI
CP → LP

Clearly, LI is sufficient for CI. Is it necessary? It would be if CI cannot exist without LI. Let's pursue this point further.

Something cannot be and not be at the same time. 

But time is a causal variable, not a logical one. If time is outside us, then "same time" is sort of cheating for a logical category. 

Logic is aprioristic. And yet, Kant has argued that time is not outside. Of course, being a physicist, you will swear that time is outside since you can work with it mathematically. But that doesn't contradict Kant's point (though we don't have time to pursue that here).