## Can you prove anything in philosophy?

73

46

I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly until you get to the question of "why/how/are we here?"

Can you prove, absolutely, and 100% that something is true, in the field of philosophy?

4Furthermore, if we're throwing out deductive proof, then there goes all proof in one fell swoop. Because surely you can't accept inductive logic as a way of obtaining proof, yet discard deductive logic. – boehj – 2011-06-15T00:59:40.517

We can prove many things and proving things would be the entire point of the discipline. Examples are easy. Take Kant's antinomies. They exist because we can prove that their extreme solutions fail in logic. If we could not prove anything then they would not exist. – None – 2019-04-16T11:18:29.550

– Muhd – 2014-04-28T23:34:55.397

From here: "As we know today, Frege's principles of proof are complete for classical predicate logic." What's subjective about this? The proposition P is '8 is an even number'. P ∧ ¬P is false.

– boehj – 2011-06-14T10:08:52.480

## Answers

44

There are two categories of things that can be proved in philosophy:

• That a thinking thing exists;
• The trivial truths of logic.

I'll cover these in order. In fact, there are philosophical arguments you'll find against them both. The basic idea that 'a thinking thing exists' comes to us via the Ancient Greeks but became widely known and was made popular by Descartes in his Meditations.

In this work he doubted everything he possibly could until he reached a base, the truth of which he could be absolutely certain. He thought it important to have a solid foundation to build his philosophical system on.

Archimedes used to demand just one firm and immovable point in order to shift the entire earth; so I too can hope for great things if I manage to find just one thing, however slight, that is certain and unshakable.

(Unfortunately he very quickly lost his way and went from this solid foundation to a very questionable argument for the existence of God.)

Cogito ergo sum ("I think therefore I am") is the famous phrase from Descartes' Meditations. "I think therefore I am" is a stronger statement than "A thinking thing exists" so I have put the second forward for this answer.

It is in the class of truths that are self-evident. Thinking about it proves its truth. In philosophy we can't do physical experiments to disprove our theories so we need to rely on thought experiments instead. This is an example of a thought experiment. I can't conceive of any logically possible way of this being self-contradictory, i.e. false. By simply doing that thinking I have proved the proposition's truth.

The second class of provable things are the trivial truths of deductive logic. I'll divide this into two parts:

• The Laws of Thought - axiomatic laws that we should agree on before we can start discussing philosophy.
• The truths of propositional logic - these follow after we set up an axiomatic system.

I'll cover these in turn, very briefly. I'll leave others to tear them down.

The Laws of Thought as a collection are attributed, like so much in philosophy, to Aristotle. They are:

• The Law of Identity - an object is the same as itself - (A ≡ A).
• The Law of (Non)-Contradiction - "the same attribute cannot at the same time belong and not belong to the same subject and in the same respect"1 - ¬(P ∧ ¬P).
• The Law of the Excluded Middle - "it will not be possible to be and not to be the same thing... there cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate."2 - (P ∨ ¬P).

There are arguments against each of these.

Propositional logic is a simple formal system. We define what is and isn't true via truth tables before we enter into discourse about it.

A simple truth, by definition, in propositional logic is found in logical conjunction. Here's the truth table (from wikipedia):

If both of its operands (p, q) are true the conjunction of them (p ∧ q) is also true.

1Aristotle, Metaphysics. Aristotle claimed this as the most secure and unshakable of all principles.

2Ibid.

I agree with @labreuer, "A thinking thing exists" assumes that thoughts have to come from a thing. The only certainty is that "thoughts exist", and tha't's accepting that existing is necessary in order for something to be... Which I think is a tautology, but that's besides the point.Great answer nonetheless. – LordHieros – 2018-03-27T09:35:11.080

3Just a note (I realize this thread is more or less stale): why are we even discussing consensus? Consensus has no bearing on truth or the aim of philosophy. It's completely irrelevant and an arbiter of nothing. – danielm – 2013-01-20T10:32:15.950

@LordHieros - It's actually even more difficult. if 'exists' means exists fundamentally then even thought may be reducible, Those who claim Mind is reducible do not reify thoughts or their objects. At any rate, it cannot be proved in logic that thinking things exist. if they did then this would prove that time exists and logic cannot do this. – None – 2019-04-16T14:56:36.450

1

The question Could 'cogito ergo sum' possibly be false? puts the certainty of "That a thinking thing exists" into doubt. Would you comment? The accepted answer possible cedes the statement "there are thoughts", but that wasn't the statement under question.

– labreuer – 2013-10-25T01:08:05.340

3

You described classical logic, but philosophy is hardly defined by classical logic, given that many non-classical logics exist and their existence is inherently the result of philosophical pursuit.

– Joseph Spiros – 2011-06-08T00:31:12.173

I'm not defining philosophy by classical logic. I'm answering the question, "Can anything be proved in philosophy?" In your answer you say: "Note: This answer assumes you're asking whether it is possible to prove any SINGLE thing in philosophy. If you are instead asking if it's possible to prove ANYTHING, well, that's a different question. I'm sure SOME people would say you can." That's exactly what I've done. – boehj – 2011-06-08T00:34:38.493

@boehj Well, then wouldn't the answer be "yes, ANYTHING can be proven in philosophy, but not conclusively or with any consensus" ? And what's the use in that? :) – Joseph Spiros – 2011-06-08T00:36:08.520

I divided my answer into two parts. Do you deny that a thinking thing exists? – boehj – 2011-06-08T00:38:14.377

3@boehj Personally, no, but I also don't doubt that someone could deny it and come up with a decent argument for it. :) – Joseph Spiros – 2011-06-08T00:39:33.557

Well, then the onus is on you to put that argument forward for us to inspect. I've done my bit. – boehj – 2011-06-08T00:46:17.637

@boehj I have put forward my argument above. But, don't get me wrong, I appreciate your thorough response. :) – Joseph Spiros – 2011-06-08T00:52:09.307

The first two paragraphs in your answer seem to admit both of the things I claim. In particular, you say "Proof is a concept in mathematics...". Proof is also a concept in logic. Are you claiming that logic is not part of philosophy? – boehj – 2011-06-08T00:58:03.767

@boehj There is no consensus on what constitutes valid "logic" in philosophy. You're relying too strongly on classical logic for your point. What about non-classical logics?

– Joseph Spiros – 2011-06-08T01:00:45.870

The question is: "Can you prove anything in philosophy?" If we accept classical logic as a part of philosophy, and if we accept the axioms of the predicate calculus, then yes, we can prove things in philosophy. You seem to not accept classical logic as a part of philosophy on the basis that there are other logics. That's akin to saying "I don't accept Lions as a part of the animal kingdom because there are other Great Cats." – boehj – 2011-06-08T01:05:49.460

@boehj I was responding to the style of the question. The question actually was "Can you prove, absolutely, and 100% that something is true, in the field of philosophy?". 100% of philosophy is not classical logic. Classical logic is not the arbiter of absolute truth within philosophy. – Joseph Spiros – 2011-06-08T01:08:01.017

1You're quite correct that it's not. But again I'll say: If we accept classical logic as a part of philosophy, and if we accept the axioms of the predicate calculus, then yes, we can prove things in philosophy. – boehj – 2011-06-08T01:11:00.300

@boehj So since I can philosophize on any formal logic I like, anything that's consequential from that logic is proven in philosophy? If so, then ANYTHING, and not just any ONE thing, can be proven "in" philosophy. At which point the question about "proof" becomes meaningless. I tried to come up with an answer that actually IS an answer, rather than something that descends into insanity. Of course, it's just my opinion... :) – Joseph Spiros – 2011-06-08T01:13:47.707

All I can say is that one can prove things using classical logic, if you first accept some axioms. This conversation can go no further I'm afraid. – boehj – 2011-06-08T01:18:11.610

@boehj Well, it can go a little further: I appreciate the discussion and the time you put into it. Thank you :) – Joseph Spiros – 2011-06-08T01:19:55.130

I answered a related question that corresponds to your first point: http://philosophy.stackexchange.com/questions/206/is-skepticism-the-most-rational-stand-point/209#209

– Jon Ericson – 2011-06-08T19:04:39.277

21

Philosophy is generally predicated on, and perhaps more about, asking questions rather than finding answers. It's a search for wisdom, not truth. The only thing that all philosophers would all agree exists, besides themselves perhaps, would be questions. And sometimes, philosophers will pretend that even those don't exist. So, philosophy doesn't, as a whole, assume that any fundamental rules exist upon which to build "proven" answers.

Proof is a concept in mathematics, and mathematics is in some ways a formalized version of philosophy that HAS acknowledged the existence of fundamental rules (axioms). It is also a concept in legal systems, where again, you have formal systems that have fundamental rules (laws).

For fun, read about Gödel's incompleteness theorems. Even formal systems with fundamental rules have problems.

Note: This answer assumes you're asking whether it is possible to prove any SINGLE thing in philosophy. If you are instead asking if it's possible to prove ANYTHING, well, that's a different question. I'm sure SOME people would say you can.

1Rubbish. Truth and wisdom are inseparable, questions and truth are inseparable. How could you even ask a meaningful question without beginning from some truth? What meaning does "wisdom" have without reference to some truth? Pseudo-philosophical claims like this (which ultimately degenerate into nihilism, which is the negation of philosophy) remind me of the postmodernist performative contradiction "there is no truth". You're free to believe it, but then you're no longer doing philosophy. And I repeat: consensus is meaningless. – danielm – 2013-01-20T10:39:32.457

3actually Goedel is a heck of a nightmare for those philosopher who thought they could reach the truth :) – Bob – 2011-06-07T22:48:07.510

@Bob : LOL, so what if there is no one ultimate truth, maybe even truth itself is not meant to be what to be aiming for but a step in reaching metatruth. – jimjim – 2011-06-08T01:24:07.987

1

My favorite critic of Gödel is: '"Deconstruction" is based on a specialization of the principle, in which a work is interpreted as a statement about itself, using a literary version of the same cheap trick that Kurt Gödel used to try to frighten mathematicians back in the thirties.' From: http://www.fudco.com/chip/deconstr.html. I think I'll ask a question about that.

– Jon Ericson – 2011-06-08T19:09:26.167

@JonEricson: The article that you quote contains one deragotary comment about Gödel, but no actual justification, no actual argument against him. Reading the surrounding sentences, I'd say Mr. Morningstar didn't have a clue what Gödel was about. – gnasher729 – 2015-04-06T16:37:04.757

4

Formal logic is a branch of philosophy, and yes, you can certainly prove that a given argument is valid. Other branches of philosophy, of course, have bigger issues with provability. Aesthetics, for example, doesn't lend itself to objective proof very well. Ontology and epistemology can at times shade into science, although of course many views of the philosophy of science reject that anything can be proven absolutely.

That said, your question itself is open to philosophical inquiry; certainly many philosophers have believed that they were proving things conclusively; you'd never convince Descartes that he did not in fact prove to himself that he existed, and many of Aristotle's ideas were held to be truths for many centuries.

3"Formal logic is a branch of philosophy, and yes, you can certainly prove that a given argument is valid." only valid within the rules of formal logic, but is there is no gaurantee that formal logic is consistent itself. – jimjim – 2011-06-07T22:41:15.443

3

It depends.

Consider the philosophers of science, their struggle is to define the nature of a fact or the "proven true" statement.

As there has been no final conclusion in the generational debate between Carnap, Popper, Kuhn, Lakatos, Feyerabend, and others, it would be difficult to apply their understandings to the domain of philosophy as a whole.

However, We can state that Carnap's refutation of validation:

The first thesis of physicalism may then be regarded as a new formulation of the principles of empiricism: (1) Statements are to be regarded as scientifically meaningful only if they are in principle intersubjectively confirmable or disconfirmable. If a statement, by the very interpretation imposed upon it, is in principle incapable even of the most indirect sort of intersubjective test, then though it may have meaning of a purely logical sort, or may be significant in that it carries pictorial, emotional or motivative appeals, or may even be testable in an exclusively subjective manner, it cannot be accepted as an answer to a scientific question. The phrase "in principle intersubjectively confirmable or disconfirmable" should be understood in the most liberal manner. The sort of indirect testing of assertions here allowed for includes of course the testing of only partially interpreted postulate systems. It countenances as scientifically meaningful, statements about the most remote, the most intricately concealed or difficult to disentangle states of affairs. It includes statements about unique and unrepeatable occurrences, if only they are of a type that places them within the spatio-temporal-nomological net which itself has an intersubjective confirmation base. (2) Statements are to be accepted as scientifically valid only if they are sufficiently highly confirmed by in principle intersubjectively available evidence. The precise meaning of "sufficiently highly confirmed," as well as the exact explication of "degree of confirmation," "inductive probability," or "evidential support" need not be discussed in the present context.

His use of "spatio-temporal-nomological net" restricts our knowing to confirmation as our perceptions-of-world are anchored temporally to the here-and-now. As we cannot perceive or predict the entire totality of the universe, we cannot declare that any statement is absolutely true or false, even in science, much less in the far harder to test reaches of philosophy.

1

Proving any statement is true or probably true is impossible, unnecessary and undesirable. This is true whether the statement is deemed to be philosophical or not. If you assess ideas using argument then the arguments have premises and rules of inference and the result of the argument may not be true (or probably true) if the premises and rules of inference are false. You might try to solve this by coming up with a new argument that proves the premises and rules of inference but then you have the same problem with those premises and rules of inference. You might say that some stuff is indubitably true (or probably true), and you can use that as a foundation. But that just means you have cut off a possible avenue of intellectual progress since the foundation can't be explained in terms of anything deeper. And in any case there is nothing that can fill that role. Sense experience won't work since you can misinterpret information from your sense organs, e.g. - optical illusions. Sense organs also fail to record lots of stuff that does exist, e.g. - neutrinos. Scientific instruments aren't infallible either since you can make mistakes in setting them up, in interpreting information from them and so on.

We don't create knowledge (useful or explanatory information) by showing stuff is true or probably true for reasons so how do we create knowledge? We can only create knowledge by finding mistakes in our current ideas and correcting them piecemeal. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. We shouldn't say that a theory is false because it hasn't been proven because this applies to all theories. Rather, we should look at what problems it aims to solve and ask whether it solves them. We should look at whether it is compatible with other current knowledge and if not try to figure out the best solution. Should the new idea be discarded or the old idea or can some variant of both solve the problem?

See See "Realism and the Aim of Science" by Karl Popper, especially chapter I and "The Retreat to Commitment" by W. W. Bartley III.

1

We would do well to keep in mind Dummett's notion of verification-transcendent truth, or what realists might commit themselves to with respect to either metaphysics/epistemology or logic (that some true things can't be known, or that some logical truths can't be proven).

1

Short answer: it all depends on your meta-theory

Long answer (from the Preface of D. Hofstadter's I am a strange loop):

It seems to me that many philosophers believe that, like mathematicians, they can actually prove the points they believe in, and to that end, they often try to use highly rigorous and technical language, and sometimes they attempt to anticipate and to counter all possible counter-arguments. I admire such self-confidence, but I am a bit less optimistic and a bit more fatalistic. I don’t think one can truly prove anything in philosophy; I think one can merely try to convince, and probably one will wind up convincing only those people who started out fairly close to the position one is advocating.

1

Can you name a field where anything is proved i.e finalised in every possible aspect? By their nature people seek simple things, like religion to promise them if they satisfy a criteria then they are gonna be ok. In philosophy an end result for anything is just an starting point for something else, it appeals to those who don't want just a yes or no answer but a 'why' as answer.

PS: as Joseph Spiros pointed out by refrencing Godel, the very nature of proofs are questioned in philosophy.

2Gödel doesn't actually create any problems for the nature of proofs. What he demonstrated was that for some statements there is no proof that the statement is true, but neither is there a proof that the statement is false. Once you find a proof, you're fine, but you might never find one; not because you are not clever enough but because there is no proof. – gnasher729 – 2015-04-06T16:39:45.987

0

If you include the logical sciences as part of philosophy, then yes you can, but only with deductive logic. But like mathematics, for any proof you must begin with assumed truths (premises), and build from them.

If you mean whether can you prove something from nothing? Well I have no idea.

0

Believe in nothing, consider everything. I think philosophy's most valuable insight is the realization that nothing can be known with absolute certainty. Obviously we want to base our decisions on what seems most logical and practical but i think it's very important to always approach things with some level of caution and uncertainty in the back of your mind. You have to accept the fact that human beings are not capable of complete understanding. It's not always about what you see, but what you don't see. The only truth in our world is that those who claim to have found an infallible truth are not to be taken seriously.

0

To prove something true, you need to 1) know truth, 2) to agree about it and 3) to verify it on a system.

1. The only essential truth we know is causality.

Why 1+1 => 2? Because if you put an apple in an empty bag, then add another, and you count the apples, you will find two apples. The same happens if you-hit-your-head-against-the-wall => you-feel-pain. This mechanism of action and reaction is called causality. We learn the action-reaction mechanism before being born and along all our lives. When something breaks causality, we feel pain, anguish, fear. Imagine you bash your head against the wall, but you don't feel nothing. Imagine you lose a loving one. Imagine you see an UFO or a miracle. All this events break the causality rules in our head and we lose the sense of reality. The only reality we accept is the one we understand, and that is the one which follows the causality mechanism.

A proof is the application of the causal rule over a system.

1. Causality is an objective knowledge.

Therefore, we all know the mechanism, and we can share thoughts. You will probably agree that if you speak to a rock, it will not answer as a person would do. Therefore you and me can find the same proof. If we don't agree with causality, proof is impossible. Objectivity about causality is probably the base of all science. There is no deeper truth (for now).

1. Proof is finding that a consequence is related to a cause by a system.

As you and me 1) know the causality mechanism, and 2) agree about it, finding a proof is making a causal relationship between a cause and a consequence. Then, we can agree that sunlight makes plants grow (causal rule: sunlight-over-a-plant => plant-grows). Then, we can set a system plant, send the sunlight input (cause or action) and verify growth (reaction). Finding the system that relates action to reaction, or finding specific exceptional reactions can be difficult. But sometimes we find them and agree and reach a proof.

-1

Ultimately, nobody can prove anything with complete confidence, no matter the method used. See Underdetermination.

4If you disprove P, do you not prove ¬P? – None – 2015-04-06T16:02:10.413

1Saying that one thing is not false does not necessitate another thing is true. It appears you are using symbols to communicate. I do not understand your comment. Can you explain? Are you saying that if P then not -P? What does that mean? – Ronnie Royston – 2015-04-06T16:19:59.983

3The question is: "can we prove anything in philosophy?" - you say, that you cannot (which seems correct to me), because you can only disprove. My comment intends to show you that disproving some theory is equivalent to proving the negation of that theory (which is the meaning of that symbol). For example, if you disprove "All swans are white", you essentially prove "There exists at least one swan which is not white". The conclusion of your answer seems correct to me to some extent, the argumentation not. – None – 2015-04-06T16:21:55.357

You are assuming that reality is fact, are you not? – Ronnie Royston – 2015-04-06T16:30:32.553

3No, I'm explaining you a very basic definition from high school logic. – None – 2015-04-06T16:31:16.977

So you are saying that you have proved "¬P" because you disprove "P". – Ronnie Royston – 2015-04-06T16:33:33.140

1If you put your technicalities aside and actually focus on the content of what is being told to you you'd understand the very simple message: how do you go about disproving something if you cannot prove that it is disproven? – jony – 2016-12-22T01:06:19.360

Accepting that any idea is falsifiable is key to philosophy. – Ronnie Royston – 2016-12-22T02:23:34.447

I'm glad you were able to reconsider your position instead of insisting on hiding behind layers of sophistry. – jony – 2017-01-06T12:26:08.480