London Ed writes:
Philosophers always refer to their arguments as 'arguments' and never as 'proofs'. This is because there is nothing in the entire, nearly three thousand year history of philosophy that would count as a proof of anything. Nothing.
This obiter dictum illustrates how, by exaggerating and saying something that is strictly false, one can still manage to convey a truth. The truth is that there is very little in the history of philosophy that could count as a proof of anything. But of course some philosophers do refer to their arguments as proofs. Think of those Thomists who speak of proofs of the existence of God. And though no Thomist accepts the ontological 'proof,' there are philosophers who refer to the ontological argument as a proof. The Germans also regularly speak of der ontologische Gottesbeweis rather than of das ontologische Argument. For example, Frege in a famous passage from the Philosophy of Arithmetic writes, Weil Existenz Eigenschaft des Begriffes ist, erreicht der ontologische Beweis von der Existenz Gottes sein Ziel nicht. (sec. 53)
These quibbles aside, an argument is not the same as a proof. 'Prove' is a verb of success. The same goes for 'disprove' and 'refute.' But 'argue' is not. I may argue that p without establishing that p. But if I prove that p, then I establish that p. Indeed, I establish it as true.
Why has almost nothing ever been proven in the history of philosophy?
It is because for an argument to count as a proof in philosophy -- I leave aside mathematics which may not be so exacting -- certain exceedingly demanding conditions must be met. First, a proof must be deductive: no inductive argument proves its conclusion. Second, a proof must be valid: it must be a deductive argument such that its corresponding conditional is a narrowly-logical truth, where an argument's corresponding conditional is a conditional proposition the protasis of which is the conjunction of the argument's premises, and the apodosis of which is the argument's conclusion.
Third, although a valid argument needn't have true premises, a proof must have all true premises. In other words, a proof must be a sound argument. Fourth, a proof cannot commit any infomal fallacy such as petitio principii. An argument from p to p is deductive, valid, and sound. But it is obviously no proof of anything.
Fifth, a proof must have premises that are not only true, but known to be true by the producers and the consumers of the argument. This is because a proof is not an argument considered in abstracto but a method for generating knoweldge for some cognizer. For example, if I do not know that I am thinking,then I cannot use that premise in a proof that I exist.
Sixth, a proof in philosophy must have premises all of which are known to be true in a sense of 'know' that entails absolute impossibilty of mistake. Why set the bar so high? Well, if you say that you have proven the nonexistence of God, say, or that the self is but a bundle of perceptions, or that freedom of the will is an illuison, or whatever, and one of your premises is such that I can easily conceive its being false, then you haven't proven anything. You haven't rationally compelled me to accept your conclusion. You may have given a 'good' argument in the sense of a 'reasonable' argument where that is one which satisfies my first four conditions; but you haven't given me a compelling argument, an argument which is such that, were I to reject it I would brand myself as irrational. (Of course the only compulsion here at issue is rational compulsion, not ad baculum (ab baculum?) compulsion.)
Given my exposition of the notion of proof in philosophy, I think it is clear that very little has ever been proven in philosophy. I am pretty sure that London Ed, as cantankerous and contrary as he is known to be, will agree. But he goes further: he says that nothing has ever been proven in philosophy.
But hasn't the sophomoric relativist been refuted? He maintains that it is absolutely true that every truth is relative. Clearly, the sophomoric relativist contradicts himself and refutes himself. One might object to this example by claiming that no philosopher has ever been a sophomoric relativist. But even if that is so, it is a possible philosophical position and one that is provably mistaken. Or so say I.
Or consider a sophist like Daniel Dennet who maintains (in effect) that consciousness is an illusion. That is easily refuted and I have done the job more than once in these pages. But it is such a stupid thesis that it is barely worth refuting. Its negation -- that consciousness is not an illusion -- is hardly a substantive thesis. A substantive thesis would be: Consciousness is not dependent for its existence on any material things or processes.
There is also the stupidity of that fellow Krauss who thinks that nothing is something. Refuting this nonsense hardly earns one a place in the pantheon of philosophers.
Nevertheless, I am in basic agreement with London Ed: Nothing of any real substance has ever been proven in philosophy. No one has ever proven that God exists, that God does not exist, that existence is a second-level property, that there is a self, that there is no self, that the will is free, that the will is not free, and so on.
Or perhaps you think you have a proof of some substantive thesis? Then I'd like to hear it. But it must be a proof in my exacting sense.
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