Proof by logic
Logic is a fantastic tool for guiding one's investigations into reality, however, sometimes people don't understand it's application to the practicalities of reality, and its limitations.
One of the frequent theistic attempts at demonstrating their god, is a method known as proof by logic, or "logicing God into existence". The basic idea is that, devoid of any empirical evidence demonstrating the existence of the god, they will attempt to prove the existence using nothing but logical arguments. In philosophical jargon, a synthetic statement (a fact about the reality) cannot be proven by analytic statements (justified by pure reason) alone.
Hume's argument against proof by logic
- Premise: Nothing can be proved to exist a priori unless its non-existence would imply a contradiction.
- Premise: Nothing that is demonstrable or distinctly conceivable implies a contradiction.
- Premise: For everything that conceivably existing, we can also conceive its non-existence.
- From (2) and (3), there is no being whose non-existence implies a contradiction.
- From (1) and (4), there is no being who's existence is demonstrable a priori.
- "I propose this argument as entirely decisive, and am willing to rest the whole controversy upon it."
- God is love: God is love. Love exists. Therefore, God exists.
- Transcendental argument: Logic exists as a concept that requires a mind. Logic transcends human minds, so a transcendent mind must exist to hold that concept. That transcendent mind is God.
- Kalam: Everything that began to exist has a cause. The universe began to exist, therefore has to have a cause. Since we need a starting point, as opposed to an infinite regress, that cause is the "uncaused cause", which could only be God.
- Ontological argument: The greatest idea, God, must exist because it is greater to exist than to not exist.
None of these are confirmed true, and they rely on axioms that are dubious.
Sometimes, people believe that if an argument is logically sound (described as "logical"), it must therefore be true; for instance, that creationism is true because it's logical.
It's important to note that the concept of "proof" only really exists in math as an absolute claim. Once we start examining reality, the mathematical concept can only be used to approximate. For instance, one can define a perfect circle within mathematics, but we are incapable of creating a physically perfect circle in reality.
A perfect circle is defined as a set of points (in a 2D plane) that are equidistant to a center point.
If we're drawing on paper, and one of the atoms is off by a billionth of a billionth of a billionth of the diameter of an electron, the circle is no longer perfect, because one of the atoms is not exactly equidistant with the other atoms. Logical claims versus reality have similar issues.
There's a number of ways, overall, in which proofs by logic are dubious.
Validity of Premises
The primary reason why these arguments fail is because the premises of a logical argument are true and not simply assumed. Each premise must be demonstrably true to make the argument sound.
For instance, the Kalam cosmological argument makes the following undemonstrated assumptions:
- Everything has a cause - have they checked everything in existence to make sure it has a cause?
- The universe couldn't be eternal - voiding the "began to exist" clause.
- Even if the universe had a cause, that therefore it had to be intelligent, as opposed to another natural mechanism.
- That in reality, it's an endless cycle of universes, etc.
This argument cannot possibly work, because it relies on assumptions being plugged into the required logical premises. The fact is, we have little to no information about what happened "before" the big bang, or even have a complete understanding of causality beyond our simplified Earthly understanding of how things work. Just like we couldn't extend Newtonian mechanics into approaching-the-speed-of-light speeds, we aren't justified in extending our current laws of physics into the extremes, as discussed in this argument, where the laws break.
Arguably, the premises must be justified by additional arguments, and so on, causing an infinite regress called Münchhausen trilemma. The alternative sources of premise validity are axiomatic assumptions or based on perceptual experience (psychologism).
Limitations of Common Sense
Not only does "common sense" not work in all situations, but in advanced sciences, rarely ever works, because we're digging deeper into realms that aren't "common" to our understanding yet.
Limitations of Current Knowledge
Ultimately, the only way that logical proofs can work outside of mathematics is if one is omniscient. As it stands, we could discover and learn something new about reality tomorrow that demolishes one of the premises to a logical syllogism. As theists frequently point out, this happens in science. Thus, we cannot rely on the premises to be wholly accurate, but rather, a tentative assessment of what we currently know for the moment. The absolute logical arguments then fail because of that.
Logic, as applied to reality, works best as a guide to investigation, not as an end-all proof for claims.
Logic and the Scientific Method
- Observe a phenomenon and gather information.
- Using logic and analysis, propose a model that describes the phenomenon.
- Using logic, propose a series of testable hypotheses to validate the model, possibly falsify the model, and exclude other explanations.
- Test hypotheses, and return to #1 with results to revise model, until model converges on a stable answer.
- Theory is now well supported ("proved").
One example is the history of our knowledge about black holes. For a long time, all the evidence we had regarding gravity and light seemed to point to this idea that a star can be so massive that light couldn't escape. It wasn't until we had tested hypotheses, with empirical evidence, that the scientific community accepted that black holes were real. We didn't stop at making a logical argument for black holes, stop there, and assume we've proven they exist, even though the logical argument was very compelling.
A proof by logic follows the following basic pattern:
- Observe a phenomenon and gather information.
- Using logic, propose an explanation that describes the phenomenon, using bits of data that appear to fit the argument.
- Make no attempt to confirm the argument, or exclude it from other possibilities.
- Assertion is now "proved".
People making this error end up simply skipping the most important part of the scientific method - testing and revision. Even more importantly, they often make no attempt to find ways to falsify their claims, which is critical in science. In this way, proofs by logic are functionally very similar to conspiracy theories.