We have laid out each of at least six different propositions which one might have in mind when one says, "It's impossible to prove that God exists." What remains is to perform an analysis of each of the propositions to discover which proposition one means when one makes the aforementioned assertion. Let's look at them one at a time.
First, we shall analyze the proposition that "no sound argument with the conclusion that God exists is logically possible." In general, a sound argument for a given proposition is logically possible when when the given proposition is true and there are other true propositions (premises) which together necessitate the truth of the given proposition. In a similar for example, to inquire in geometry whether a proof for squaring the circle is logically possible is to ask whether or not there are true mathematical propositions which together necessitate the true conclusion that in a given instance the area of a square is equal to the area of a circle. Thus, in order for a sound argument for God's existence to be logically possible, the proposition that God exists must be true and there must be other true propositions which together necessitate the conclusion that God exists. It follows that for the proposition "no sound argument with the conclusion that God exists is logically possible" to be true, that is, in order for no sound argument for God's existence to be logically possible, the proposition that "God exists" must be false, or there cannot be true propositions which together necessitate the proposition that God exists.
This raises a number of issues which center on the relationship between the logical possibility or impossibility of a proof of God's existence and the ability or inability of any human being to prove that God exists. With respect to the latter, it is first necessary to distinguish between the ability of a human being to formulate a proof, and his ability to know that the argument he formulates is a proof.
First, we shall analyze the proposition that "no sound argument with the conclusion that God exists is logically possible." In general, a sound argument for a given proposition is logically possible when when the given proposition is true and there are other true propositions (premises) which together necessitate the truth of the given proposition. In a similar for example, to inquire in geometry whether a proof for squaring the circle is logically possible is to ask whether or not there are true mathematical propositions which together necessitate the true conclusion that in a given instance the area of a square is equal to the area of a circle. Thus, in order for a sound argument for God's existence to be logically possible, the proposition that God exists must be true and there must be other true propositions which together necessitate the conclusion that God exists. It follows that for the proposition "no sound argument with the conclusion that God exists is logically possible" to be true, that is, in order for no sound argument for God's existence to be logically possible, the proposition that "God exists" must be false, or there cannot be true propositions which together necessitate the proposition that God exists.
This raises a number of issues which center on the relationship between the logical possibility or impossibility of a proof of God's existence and the ability or inability of any human being to prove that God exists. With respect to the latter, it is first necessary to distinguish between the ability of a human being to formulate a proof, and his ability to know that the argument he formulates is a proof.
When a person formulates a proof, he thinks two or more propositions according to some logical form. Thus, an argument is formulated regardless of whether it is sound or unsound. Note: in order for an argument to be sound, it is not required that a person know it is sound. More precisely, it is not a condition for an argument being valid or the proposition being true that a person know that the argument is valid or the propositions are true. This explains why it is possible for a person to formulate what is in fact a proof for God's existence without knowing it is a proof. In other words, the argument he formulates is sound, but he does not know it is sound. Unless this is possible it is difficult to understand how a person can err in formulating an argument he believes is sound when in fact it is not, or believing an argument he formulates is not sound when in fact it is.
Thus, two different interpretations are possible regarding the ability or inability of a human being to prove that God exists. On the one hand, whether or not a human being can prove that God exists might refer to the ability or inability of a human being merely to formulate a proof for God's existence. On the other hand, it might refer to the ability or inability of a human being to know that an argument is sound. Of course, in order for him to know it is sound, he must have the ability to formulate it, but his ability to formulate it is no guarantee that he is able to know it is sound.
We will assume the first interpretation since this accords with the fact that an argument can be sound without any human being knowing it is sound. Therefore, whether or not a human being can prove that God exists is equivalent to whether or not a human being can formulate a sound argument with the conclusion that God exists.
Note: to assume the the second interpretation wouldn't move us far, since if one attempts to show that no sound argument for God's existence can be known since no sound argument can be formulated, then one has the same burden of proof as the person who simply claims that no sound argument can be formulated. If one instead argues that a sound argument for God's existence can be formulated, but its soundness cannot be known, one assumes the burden of proving that a sound argument for God's existence can be formulated, but then also proving that no human being can know that the argument is sound - which is absurd.
No, it strengthens our adversary's position to use the first interpretation: whether or not a human being can prove that God exists will refer to the ability or inability of a human being merely to formulate a proof for God's existence.
Thus, two different interpretations are possible regarding the ability or inability of a human being to prove that God exists. On the one hand, whether or not a human being can prove that God exists might refer to the ability or inability of a human being merely to formulate a proof for God's existence. On the other hand, it might refer to the ability or inability of a human being to know that an argument is sound. Of course, in order for him to know it is sound, he must have the ability to formulate it, but his ability to formulate it is no guarantee that he is able to know it is sound.
We will assume the first interpretation since this accords with the fact that an argument can be sound without any human being knowing it is sound. Therefore, whether or not a human being can prove that God exists is equivalent to whether or not a human being can formulate a sound argument with the conclusion that God exists.
Note: to assume the the second interpretation wouldn't move us far, since if one attempts to show that no sound argument for God's existence can be known since no sound argument can be formulated, then one has the same burden of proof as the person who simply claims that no sound argument can be formulated. If one instead argues that a sound argument for God's existence can be formulated, but its soundness cannot be known, one assumes the burden of proving that a sound argument for God's existence can be formulated, but then also proving that no human being can know that the argument is sound - which is absurd.
No, it strengthens our adversary's position to use the first interpretation: whether or not a human being can prove that God exists will refer to the ability or inability of a human being merely to formulate a proof for God's existence.
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