Yazata
Valued Senior Member
Several currently active threads seem to revolve around the concept of 'proof'.
We have dueling threads that purport to 'prove' God's impossibility in one case and God's necessary existence in the other. And there's yet another thread that proclaims that 'belief systems' are foolishness and anounces that intelligent people have 'proof systems' instead.
So I figured that maybe we need a thread about what the word 'proof' actually means. The quotes that follow come from the 'Oxford Dictionary of Philosophy', page 306. The comments that accompany the quotes are my own.
This is the weakest usage of the word 'proof', but it's the one that's most often used in everyday life. When somebody says 'prove it', they usually mean 'convince me'. What satisfies that demand typically isn't going to be a logical proof at all. In some cases it might be some sort of informal fallacy such as an emotional appeal or an appeal to self-interest.
I don't see any difficulty in both proving and disproving the existence of God if this is the standard of 'proof' that we are using. It's kind of trivial.
This more specifically logical definition, on the other hand, is awfully strong. It requires that our premises all be true and that we argue from those premises using only deductively valid reasoning.
Specifying what that latter actually is leads us to...
And the intermediate steps are termed 'lemmas'. In this most technical sense, the demand that axioms be true has been dropped and all attention is being directed at the inferential relationships that exist among the lemmas and conclusion. It's entirely possible to create proofs that proceed from false axioms so as to explore their logical implications.
In Sciforums philosophy and religion discourse, the meaning of 'proof' seems to veer crazily back and forth between a purely intuitive (and often trivial) 'convince me' and a stronger desire for the kind of deductive rigor that yields up its conclusions with logical necessity and force.
Unfortunately, those latter kind of stronger logical proofs don't seem to be forthcoming in religion, whether pro or con. People have been trying to demonstrate the logical necessity of their religious conclusions for thousands of years, without any notable success. Their chains of reasoning either aren't deductively valid or they assume the truth of premises that are just as doubtful as the theorem that they seek to prove.
We have dueling threads that purport to 'prove' God's impossibility in one case and God's necessary existence in the other. And there's yet another thread that proclaims that 'belief systems' are foolishness and anounces that intelligent people have 'proof systems' instead.
So I figured that maybe we need a thread about what the word 'proof' actually means. The quotes that follow come from the 'Oxford Dictionary of Philosophy', page 306. The comments that accompany the quotes are my own.
Informally, a procedure that brings conviction
This is the weakest usage of the word 'proof', but it's the one that's most often used in everyday life. When somebody says 'prove it', they usually mean 'convince me'. What satisfies that demand typically isn't going to be a logical proof at all. In some cases it might be some sort of informal fallacy such as an emotional appeal or an appeal to self-interest.
I don't see any difficulty in both proving and disproving the existence of God if this is the standard of 'proof' that we are using. It's kind of trivial.
More formally, a deductively valid argument starting from true preises, that yields the conclusion.
This more specifically logical definition, on the other hand, is awfully strong. It requires that our premises all be true and that we argue from those premises using only deductively valid reasoning.
Specifying what that latter actually is leads us to...
Most formally, in proof theory, a proof is sequence of fomulae of which each member is either an axiom or is derived from a set of preceding members by application of a rule of inference, and which terminates in the proposition proved. The final member of such a sequence is a theorem.
And the intermediate steps are termed 'lemmas'. In this most technical sense, the demand that axioms be true has been dropped and all attention is being directed at the inferential relationships that exist among the lemmas and conclusion. It's entirely possible to create proofs that proceed from false axioms so as to explore their logical implications.
In Sciforums philosophy and religion discourse, the meaning of 'proof' seems to veer crazily back and forth between a purely intuitive (and often trivial) 'convince me' and a stronger desire for the kind of deductive rigor that yields up its conclusions with logical necessity and force.
Unfortunately, those latter kind of stronger logical proofs don't seem to be forthcoming in religion, whether pro or con. People have been trying to demonstrate the logical necessity of their religious conclusions for thousands of years, without any notable success. Their chains of reasoning either aren't deductively valid or they assume the truth of premises that are just as doubtful as the theorem that they seek to prove.