What preliminary consideration can be given concerning what can be meant by "proof"?
To begin, by "proof" one might mean simply an argument which logicians call "valid." A valid argument is one in which the conclusion follows with logical necessity from the premises on account of the form of the argument. In order for an argument to be valid, it is not necessary, however, that all or even some of its premises be true. Consider the following valid argument:
To begin, by "proof" one might mean simply an argument which logicians call "valid." A valid argument is one in which the conclusion follows with logical necessity from the premises on account of the form of the argument. In order for an argument to be valid, it is not necessary, however, that all or even some of its premises be true. Consider the following valid argument:
- If the majority of people believe that God has a long white beard, then God has a long white beard;
- The majority of people believe that God has a long white beard;
- Therefore, God has a long white beard.
This argument is valid and follows the valid logical pattern of modus ponens; by its form the conclusion follows necessarily from the premises. Yet, each of the three propositions comprising the argument are obviously false. Hence, while the argument has a valid form, it is not what logicians call "sound." In order for an argument to be sound it must be valid, and all of the propositions comprising it must be true.
Why is this germane to the issue of whether God's existence can be proven? Well in short, it's because we must gather whether the proponent of the assertion that "It's impossible to prove that God exists" means by a "proof" merely a valid argument. Likely, they do not: we all should admit that God's existence is hardly proven if the proposition that God exists is the conclusion of an argument which is valid although one or more of its premises is false. If the proponents deny this, then they run into the problem that innumerable arguments can be offered for the existence of God as long as the arguments need only be valid but not sound.
No, it is probably the case - and here we are trying to help them strengthen their argument - that by "proof" they mean "sound argument."
Why is this germane to the issue of whether God's existence can be proven? Well in short, it's because we must gather whether the proponent of the assertion that "It's impossible to prove that God exists" means by a "proof" merely a valid argument. Likely, they do not: we all should admit that God's existence is hardly proven if the proposition that God exists is the conclusion of an argument which is valid although one or more of its premises is false. If the proponents deny this, then they run into the problem that innumerable arguments can be offered for the existence of God as long as the arguments need only be valid but not sound.
No, it is probably the case - and here we are trying to help them strengthen their argument - that by "proof" they mean "sound argument."
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