Trying to understand this conditional statement

[Sayleeee]

Summary: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The conditional is defined to be true unless a true hypothesis leads to a false conclusion.

So if the condition occurs within a statement but the conclusion doesn't follow, does that mean that the conditional statement is false? For example:



"If they just manage to perform fusion successfully, than I think that they'll definitely defeat Majin Buu within 30 minutes."


The condition is that 'if they just manage to perform fusion successfully' while the conclusion is 'they'll definitely defeat Majin Buu.'

The only problem about this statement is that they did perform fusion successfully but they weren't shown to defeat Majin Buu and weren't stated to be capable of doing so. Implicit statements are not synonymous with explicit statements. Summarily, doesn't this lead to a false conditional statement because the conclusion did not follow: they did not defeat Majin Buu.

[YesNo]

I would think the conditional is false because the hypothesis (antecedent) and conclusion (consequent) are unrelated and there is a situation where the hypothesis is true, but the antecedent is false.

One thing about conditionals I am trying to think through is whether conditionals are truth "functions" of their antecedents, p, and their consequents, q. This seems to be what you are claiming. That is, knowing the truth values of p and q can one derive the truth value of p implies q? Within a restricted domain, like an area of mathematics, I assume this would be the case because the p and q statements are explicitly related.

For example, is the following a true conditional: If 1 equals 1, then the Earth today has a Moon. Both the antecedent, "1 equals 1" and the consequent, "the Earth today has a Moon" are true, but they aren't related.

I am trying to make sense of Graham Priest's "Logic A Very Short Introduction".