Problems with the use of deduction in discussing the existence of reality

If someone asks you to prove that reality exists, they are probably have in mind a deductive proof involving some sort of syllogism or other combination of premises and propositions, that lead to an inescapable conclusion. They are implicitly asking for a valid and sound analytical, logical proof. In propositional logic using deduction, if the premises lead to the conclusion, if the terms are clear and unambiguous, if all premises are true, and the rules of logic are followed, then the conclusion reached is necessarily true - we say that the conclusion entails the premises. In my past discussions with "reality-skeptics", no vague expressions of likelihood or probability were enough for them - they wanted a rock solid proof which only deductive processes can supply.

In other words, they are challenging you to come up with an "All men are mortal / Socrates is a man / Therefore Socrates is mortal" style of proof. If they are looking for something of this form (e.g., Premise A, Premise B, Premise C, Therefore reality exists), that's just not going to happen. Why? Because each of the premises will be taken from Reality, but Reality is the conclusion we are trying to prove, so this would result in circular reasoning, or "begging the question". If the argument is a variant of "I see the table, you see the table, therefore the table exists", both premises already assume that there is something to see and something to do the seeing, which is what the conclusion asserts - thus, circular reasoning. The only deductive argument in which "Reality exists" can play a role is as one of the premises, one of the unproven assertions that has to be taken as a given, not the conclusion. As to whether this would form a valid argument, it would depend on its logical structure (does the conclusion follow from the premises?). As to whether it is a sound argument, this would require that the premises be true, in the case of reality - can we assume or use inference to convince ourselves that reality exists? So, deduction is just not going to work if someone is asking for a proof. Its existence would be one of the premises.

Deduction is not the appropriate form of logic to use for questions involving existence in the real world. As David Hume wrote in Dialogues Concerning Natural Religion, nothing can be proven to exist using only a priori (purely logical) reasoning. You could only prove this type of existence if its opposite (non-existence) generated a contradiction (i.e., contradicted its premises, which it doesn't). It is not contradictory to assert we are all inside a giant simulation or dream. To assert that nothing is real is just as viable as its opposite. For example, you can't prove that there is a person standing behind you by showing that it is inconceivable that there is not a person standing behind you. We obviously can imagine that there is no person standing behind you right now (their non existence does not cause a logical contradiction). The only way to prove that a person is standing behind you is through evidence. And the only way to prove this is to turn around and look - to collect the evidence.

Solid proofs and deductive reasoning are applicable primarily in highly controlled scenarios such as in deriving and proving mathematical theorems, formal and symbolic logic, and in applied areas of technology such as software and circuit design - all areas where the conclusion is completely contained in the premises, and the premises are totally clear, unambiguous, and universally agreed to. In other words, it works best in extremely constrained and "clean" scenarios. Math and logic, though they lend themselves to the deductive proof, don't reveal truths about the actual world. Instead, they reveal consequences of axioms and premises. They start with an axiomatic structure and set of rules, and from those building blocks, theorems can be derived. They don't tell us which of the axioms are actually true. For that you need to go into the real world and look around.

Requiring deductive proofs, and expecting formal/propositional/deductive logic to always be applicable, puts an undue burden on deductive logic, asking it to do something for which it was not designed. For example, you can't prove deductively that chocolate is your favorite food, or that you are still employed at your job, or that a dropped ball will fall to the ground, or that the sun will rise tomorrow, or that an action you performed was generous and kind, or that a piece of art is good. Those issues, which are really very important (you don't want a dropped ball hitting you under the chin) are not settled by deductive proofs anyway. Humans do not use deduction in their everyday lives all that much. We infer things based on past experience, perceived likelihood of outcomes, elimination of unlikely scenarios (inference to the best explanation), and a learned set of habits about how to move through the world we find ourselves in.

Even more intriguing, you can't prove the deductive method actually works without enlisting the use of deduction. If someone rejects deductive logic, you can't insist that they believe it because it would be illogical for them not to. The logic that you are employing in your argument is the very thing they doubt in the first place. So, to insist that the legitimacy of our use of inference come along with a solid proof which does not involve inference is something that the other primary form of logical inference cannot even provide.

Although I can't come up with a deductive proof that reality exists, I can use the well known modus tollens argument (also known as denying the consequent or contrapositve) showing that deduction cannot be used! This logical form is:

• If P, then Q.
• Not Q.
• Therefore not P.

as in:

• If (P) it is raining, then (Q) the sidewalks are wet.
• The sidewalks are not wet (not Q).
• Therefore (not P) it is not raining.

Applied to the possibility of a deductive proof of reality's existance:

• If (P) there were a clear, ironclad deductive proof of reality, then (Q) we would not still be arguing about it.
• We are still arguing about it (not Q).
• Therefore (not P) there is not a clear, ironclad deductive proof of reality.

Again, using the argument form of “denying the consequent” we can offer a positive deductive proof that viewing the external world as really being there is correct. The argument that "We can rely on empirical and naturalistic evidence to learn about the external world" follows:

• If (P) "using naturalism and induction from sense experience to make inferences about the world is invalid and unjustifiable", then (Q) "science (which relies on inference and naturalism) has no hope of working".
• Science does work (not Q)! There are countless examples of the progress that it has introduced, discoveries that it has made, and new technologies it has spawned. There are no counter examples to its success during the centuries it has been practiced.
• Therefore, (not P) "using naturalism and induction from sense experience to make inferences about the world is invalid and unjustifiable" is FALSE. We CAN use naturalism and induction to make inferences about the world.

So, this argument would seem to prove that the external world really is there (using deduction to prove induction about the real world is a valid way of interacting with the world. But there are objections - no matter how far fetched. The hyper-religious could counter that this is all a deception by the Devil, or that it is a test by God to exercise our faith. Or the Solipsist might say we are dreaming the whole thing. The fact is - they are technically right - we can't prove they are wrong. But I would say, "so what?". Realists need not be concerned with it. Nature and the external world do not demand a proof - those are only requested by some people, and probably for reasons they would have a hard time justifying. And for those who consider themselves to be pragmatists - they don't care about "proofs" of the external world at all. The pragmatist employs what is useful, and discards the rest. Metaphysical proofs can be left to the others.

In any case, the type of reasoning called propositional logic (along with deduction and induction) was invented in Classical Greece and integrated into a system of thought by Aristotle. It uses deduction from premises to draw conclusions. He intended it as a tool for finding truth, but it didn't keep him from making many outrageous errors. His armchair deductions about the nature of the world were frequently wrong (the behavior of falling bodies, that flies had four legs, thought mucus was brains leaking out of our noses, he deduced five elements, that women have fewer teeth than men, and more). Although he contributed greatly to our understanding of the natural world (he invented the core of western logic and gave shape to several of the basic sciences we still practice today), he made a number of errors by misapplying the powerful tool of logic. Any tool can be misused, and in these pre-scientific days logic was misused repeatedly (and it continues to be misused today).

Aristotle understood that logic can be used to deduce true consequences from true premises. His technique has been much abused over the years. Many who have followed him failed to realize that we have usually have no absolutely true premises, except ones we define to be true (such as "2+2=4", or "no geese are felines"). There are no handy, obviously true premises about the existence of an external reality that we can bring to bear in formal deductive logic.

I have seen so many seemingly plausible attempts at the use of deductive proofs to prove the existence of god and other hypothetical entities that I have lost confidence in the entire endeavor (for a great example, see Anselm's ontological proof of god). The laws of logic do work, but it is not magic. You have to frame the premises correctly, and they have to be true. We say many things about the world that seem true on the surface, but may, in fact, lack meaning or be incorrect. Wittgenstein, in his Philosophical Investigations, wrote that conceptual confusions involving our use of language are the cause of many problems in philosophy. Clearing up the errors in language can make entire philosohical questions just disappear:

“Philosophy is a battle against the bewitchment of our intelligence by means of language”.

and:

"Most of the propositions and questions to be found in philosophical works are not false, but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical … it is not surprising that the deepest problems are in fact not problems at all”.

Put another way, much of what is debated in philosophical terms is nothing but impressive, but empty, verbal gymnastics. For example, when arguing about "existence" I am not convinced we have a coherent, single interpretation of that concept. Prior to Kant, many philosophers thought "existence" was a property that objects either had (i.e., they were concrete things) or lacked (i.e., they were abstract things). Anselm, in his ontological argument, made this error. Kant demonstrated that "existence" is not a property like color or weight, but is "prepossessed" by the object, making it capable of having any properties at all. So, I am not at all convinced that the discussions that we amateurs and dilettantes have about existence are really doing anything but creating a lot of noise and muddying up the water. Even the professionals are not of one mind concerning this question.