countless arguments of that form with true premises and a true conclusion.
That’s why I edited the post (before your comment) to change “P” to “Therefore, P”.
Subtle difference: if P is true, “P” (the statement that P is true) is true. But “Therefore, P” isn’t necessarily true, because it references a preceding argument that may (or may not) permit the valid derivation of the conclusion.
In that particular argument, the conclusion does NOT follow from the premises and is false regardless of the value of P.
That’s not really how “therefore” is usually used—it’s a marker to show where the conclusion is, like drawing a line or using ∴. The point of having the distinction of invalidity is to understand where something might be wrong with an argument even if it has true premises and conclusion; taking “therefore” to mean something in a formal argument doesn’t seem fruitful.
It just makes explicit what the other formulation implies: that the statement is said to follow from the premises.
The structure of the argument asserts that in the first version. The structure of the statement asserts it in the second. In terms of the totality of the argument, the two versions mean the same thing, but the shape of their presentation of truth is slightly different. Hopefully the second version reduces the tendency of people to confuse the truth of the statement with the truth of the conclusion.
That’s why I edited the post (before your comment) to change “P” to “Therefore, P”.
Subtle difference: if P is true, “P” (the statement that P is true) is true. But “Therefore, P” isn’t necessarily true, because it references a preceding argument that may (or may not) permit the valid derivation of the conclusion.
In that particular argument, the conclusion does NOT follow from the premises and is false regardless of the value of P.
That’s not really how “therefore” is usually used—it’s a marker to show where the conclusion is, like drawing a line or using ∴. The point of having the distinction of invalidity is to understand where something might be wrong with an argument even if it has true premises and conclusion; taking “therefore” to mean something in a formal argument doesn’t seem fruitful.
It just makes explicit what the other formulation implies: that the statement is said to follow from the premises.
The structure of the argument asserts that in the first version. The structure of the statement asserts it in the second. In terms of the totality of the argument, the two versions mean the same thing, but the shape of their presentation of truth is slightly different. Hopefully the second version reduces the tendency of people to confuse the truth of the statement with the truth of the conclusion.