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I have witnessed a lot of debates and arguments of different beliefs, and noticed that each side uses logic to prove its point. So, can any belief be proven by logic regardless of its nature (religious\irreligious) and regardless of its differences (Islam\Christianity\Judaism etc.)?

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    Your use of any is ambiguous. Do you mean 'are there any beliefs that can be proved by logic' or do you mean 'for any given belief, it is true that it can be proven by logic'? -- Logic preserves or combines beliefs. So it can never prove the simplest and most basic of beliefs. But it can obviously construct more complex beliefs out of simpler ones that are proven if you accept the underlying simple ones. – jobermark Jul 28 '16 at 22:57
  • I feel reminded of en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems – bers Jul 28 '16 at 23:02
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    Logic cannot be used to validate one's belief in logic. – Jerry Guern Jul 29 '16 at 0:09
  • There's a famous example that's maybe relevant to what you're asking: ceadserv1.nku.edu/longa//classes/mat385_resources/docs/… – John Forkosh Jul 29 '16 at 9:43
  • I feel that logic relies on propositions which are a) assumptions or axiomatic or b) based in empirical data or models that may be overturned in light of new observations. Logic can make connections between these ideas but since neither of them are absolute it would seem to me that logic is only as good as the underlying propositions. Maybe logic can be used to support many beliefs given the propositions used but this is not the same as proving they are true. – syntonicC Jul 30 '16 at 5:55
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According to the Duhem-Quine thesis and the underdetermination of theories in philosophy of science, no theory can ever be completely dismissed by empirical data (See Quine's "Two dogmas of empiricism" 1951).

I will give you two examples, one historical and one hypothetical, to illustrate my point:

  • In 1845, Newton's theory of motion was contradicted by the measurements of the motion of the planet Uranus. Did this data mean that Newton was wrong and we should reject it? Or did it mean that we were missing information? As it turns out, in this case we were missing information. There was an unknown planet, later called Neptune, which was causing the orbit of Uranus to deviate from the orbit predicted by Newton's laws. Imagine in 1845, two scientists, one anti-Newton, the other pro-Newton: the first argues that the orbit of Uranus is definitive proof against Newton's laws of motion. The other one argues "Ahhh, but how do you know that there isn't another planet disturbing Uranus' orbit?"
  • A secular person and a Christian fundamentalist (who believes in a literal interpretation of the Bible) are arguing over the story of creation in the Bible: The secular person argues that the fossil record and geology disprove once and for all the Biblical account of creation. The religious person responds "Ahh, but how do you know that those fossils weren't put there by Satan to turn people away from God? How do you know Satan didn't plant evidence to make the world look like it was 5 billion years old, when in fact it was only 6000 years old?"

The point here is that any set of true facts about the world can always be reconciled with a given theory, as long as you are willing to include additional hypotheses and assumptions to bridge the theory with the fact. So to answer your question: Yes, logic can be used to prove any belief, as long as a person is willing to add additional assumptions to support their belief.

So then, how can one settle such arguments?

  • You can try to show that a set of assumptions are contradictory, but then you run the risk of having the opposing party simply adding new assumptions which make the original contradiction disappear.
  • More importantly, and this was Quine's answer to the dilemma, you can resort to pragmatism: We can never decide between different belief systems using logic, but of the competing belief systems, which one has proven the most useful? Which one has lead to the most good, improvement, etc....
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The basic laws of logic are used in any reasoning. Implicitly, we are always using deduction strategies. Therefore, a proof of anything will use logic. However, that does not mean that a religious belief can be proven using logic alone.

In Christian theology, a distinction is made between general and special revelation. General revelation is 'the disclosure of a natural knowledge of God via the structures of creation'; special revelation 'the disclosure of a special knowledge of God via divine redemptive acts and words.' (Plantinga 2010)

There are some medieval philosophers like Anselm of Canterbury and Thomas Aquinas who have developed proof-like arguments for God's existence. They were already debatable at that time and especially Thomas' five ways aren't considered valuable as a proof any more. It does show that people have thought about proving things about the God-concept in a general revelation-manner. Also the God proof of Descartes can be seen from this perspective.

The 'general revelation proofs' for God's existence lead, even if they are correct, to a very restrained image of God. For example, Aquinas could only prove the existence of a first cause and Anselm only that of a perfect thing. Descartes only arrived at an entity that guarded his senses to not be fooled by an evil genius.

To actually arrive at the God of a religion from this takes some effort. That is why Thomas Aquinas cannot really be seen as a purely general revelationist. That is why:

According to Aquinas faith is a conviction as unshakeable as knowledge, but unlike knowledge it is not based on rational vision; it depends instead on the acceptance of something that presents itself as a revelation from God. The conclusions of faith cannot contradict those of philosophy, but they are neither derived from philosophical reasoning nor are they the necessary basis of philosophical argument. — (Kenny 2006, p. 153, emphasis mine)

There are also philosophers who argue for an approach strictly based on special revelation, most notably Karl Barth, who thinks the theologian should be focused on God talking (special revelation) rather than human chattering (general revelation) (Barth 1963, 280-97). This position is however difficult to uphold in Christianity considering many scripture passages pointing to general revelation (e.g. Ps. 8, Job 38:1-39:33).

And then there are philosophers who claim faith cannot be rationally justified at all, for example Kierkegaard:

First of all, we can never achieve complete certainty about historical events. But a mere judgement of probability is insufficient for a religious faith which is to be the basis of eternal happiness. Secondly, historical research is never definitively concluded, so if we are to use it as the basis of our religious commitment, we must perpetually postpone that commitment. Thirdly, faith must be a passionate devotion of oneself; but objective inquiry involves an attitude of detachment. We must therefore give up the search for certainty, embrace the risk, and take the 'leap' of faith. — (Kenny 2006, p. 329, emphasis mine)


Summary

  • Logic is always used in arguments, but logic alone doesn't seem to be enough to arrive at a proof for a non-abstract god's existence.
  • There is a classical distinction between general and special revelation.
  • Medieval philosophers have attempted to prove God's existence from general revelation alone, but it takes some special revelation to arrive at the Christian god (or any other non-abstract god).
  • A strictly special revelation approach is difficult to uphold in Christianity.

References:
Barth 1963: K. Barth. Church Dogmatics I.2. T. & T. Clark 1963.
Kenny 2006: A. Kenny. An Illustrated Brief History of Western Philosophy. Blackwell Publishing 2006.
Plantinga 2010: R. J. Plantinga, T. R. Thompson and M. D. Lundberg. An Introduction to Christian Theology. Cambridge University Press 2010.

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    See also Fideism, the view that faith is independent of reason. – Dennis Jul 28 '16 at 20:11
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    @Dennis good point. While writing I wanted to add a passage about Kierkegaard, but forgot along the way. I added it in now. – Keelan Jul 28 '16 at 20:26
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Logic is about the connection between propositions. It is not about the truth or lack thereof of proposition. In consequence, logic is about whether arguments - ie, concatenations of propositions - are valid, not about whether they are true.

So, logic can prove that an argument is valid, or invalid. Not that it is true or false, nor that the propositions used in the argument are false or true.

Here is a valid argument:

  1. All the presidents of the United States are genocidal maniacs.
  2. Barack Obama is the current president of the United States.
  3. (from 1. and 2.) Ergo, Barack Obama is a genocidal maniac.

It is valid because, if its premises (1. and 2.) were true, then 3. logically follows. It's conclusion (3.) is false because one of its premises (1.) is false (or so we fervently hope).

Here is an invalid argument:

  1. Salvia flowers are blue.
  2. General Electrics' logo is blue.
  3. (from 1. and 2.) Ergo, the sky is blue.

Note that all propositions, both premises (1. and 2.) and conclusion (3.) are true. But the argument is invalid, because the conclusion does not follow from the premises.

Here is another valid argument:

  1. All burumbles are wentiful.
  2. This garpic is a burumble.
  3. (from 1. and 2.) Ergo, this garpic is wentiful.

Here, we don't even know whether any of these propositions is true. However, we know that if 1. is true, and if 2. is true, then 3. is necessarily true.

So, logic can only be used to demonstrate that an argument is internally consistent, ie, that its conclusion follows from its premises. It cannot prove wheter the argument is consistent with the observable universe, ie, that its conclusion is true, unless we are perfectly certain that all the premises are true (which usually is only the case for quite trivial arguments).

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Yes. Logic is only as reliable as it's starting point. Every logical proposition is based up one or more premises. Depending on the reliability of these premises, logical processes can be used to 'prove' just about anything.

For instance, let us pretend that I wish to prove that the universe is secretly controlled by bees.

This would be difficult to logically prove only upon observable data. However, when I present a book titled "Everything within these pages is 100% true," (which happens to include a chapter on "How the bees control everything!"), it becomes trivial to logically prove my position. Based on the premise that my book is correct (I mean come on, look at the title), then it logically follows that bees do indeed control everything. And, as you may well know, the universe is included in "everything" so obviously we are already subject to the iron-mandibled rule of our busily buzzing overlords. And we didn't even know!

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I suppose it depends on what you mean by logic. However, one thing you might be interested in knowing is that even in mathematics--perhaps one of the most pure applications of logic--there are some questions that cannot be decided by logic alone. Loosely speaking, Gödel's incompleteness theorems show that, for the natural numbers (positive integers), there are statements that are true but unprovable in any logical system that is internally consistent (none of the axioms violate each other) and also does not have so many axioms that no computer program could list them.

These incompleteness theorems would seem to be a counterexample to the proposition that all beliefs can be proven or disproven by logic, and thus answer your general question (no, all beliefs cannot be proven or disproven).

Regarding religious questions specifically: Gödel's theorems don't apply, but I would think that there likely exists some sort of analogous situation. Religious beliefs by their very nature are based on faith--and if we can't even prove or disprove all statements in mathematics, how should we expect to do so for religious statements?

  • Welcome to the site, thanks for your contribution. This is good, although your last paragraph about religious questions seems to be jumping to conclusions. – Keelan Jul 29 '16 at 6:10
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    Fair enough, I have changed my statement in the last para. I believe my counterexample answers the OP's question if religious and non-religious questions are to be considered together (since then one would only need to provide a counterexample for one), but it is not entirely clear whether the OP wants the religious angle considered separately, which is why I added that last, more speculative, paragraph. – Matt Jul 30 '16 at 13:02
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I think you may be confused between "rationality" and "logic"

If you are thinking that "logic" is the use of reasoning then Yes. Using our reason we can prove truth and also vice versa. Humans even lie to themselves, with a reason...

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    You seem to be suggesting that "reason" is complete: it can be used to prove any true claim. How do you reconcile this with undecidable problems? – commando Aug 3 '16 at 14:55
  • @commando Can you see a probable path to resolve your questions? If no then, why bang your head against the reality that ignorance burns? I feel it too, so hot indeed. Maybe in the future I will recall exactly who stated this way of time/energy administration. – userDepth Aug 21 '16 at 6:25
  • @commando building on the fact of all this being at that time. Does NULL ring any bells? – userDepth Aug 21 '16 at 7:08

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