Saturday, September 9, 2023

Logical and causal possibility (think of mind experiments)

Logical Impossibility:

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

Law of non-contradiction: 

Nothing can both have and lack a property at the same time. 

Conceivability: 

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

2. The first step in the evidence that p is possible is to conceive it. Just that. 

we say p is imaginable when its details can be filled and its implication drawn without it being contradictory, i.e., 

ø That the Big Bang has a cause is conceivable. Therefore, it's causally possible.

Analysis: 

Does ø violate a law of nature? Well, according to Big Bang Theory, it does, but there's a conflict here. The Big Bang Theory can be contradicted with another cosmological theory in the future. If so, then ø is causally possible. LQQD.

Clearly, not everything that is conceivable is possible, e.g. Superman, dragons, gremlins, and succubi are all conceivable but not possible (they violate laws of nature).

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. As such, the applicability of a law 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).

No comments: