A little bit of logic.

From a simple “if… then…” statement one can formulate four arguments, two are logically invalid. Let’s look at an example.

We will start with the premise: “If something is perfect, then it must exist.” This premise is contentious (is existence a property of perfection?), but just for our examples, we’ll assume that lacking anything, including existence would render something imperfect.

In a statement like this, the if part (if something is perfect) is called the antecedent. The then part (then it must exist) is called the consequent.

Affirming the antecedent – Modus Ponens

If something is perfect, then it must exist.
God is perfect, therefore God exists.

This is called affirming the antecedent, or modus ponens (a statement where the antecedent is in agreement with the original statement). It is logically valid as long as peoples’ definition of God assumes a perfect being. Obviously the nature of God is not empirically testable, & thus this statement tells us little about the existence of God, but it is logically valid. This is an ontological argument for the existence of God from Descarte.

Denying the consequent – Modus Tollens

If something is perfect, then it must exist.
Unicorns do not exist, therefore they are not perfect.

This is called denying the consequent or modus tollens (a statement where the consequent is contrary to the original statement). It is logically valid as long as unicorns don’t exist, if they did, then we’d be compelled to examine whether they where perfect before making that judgment.

Denying the antecedent

If something is perfect, then it must exist.
Humans are not perfect, therefore they don’t exist.

This is called denying the antecedent (a statement where the antecedent is contrary to the original statement). This is illogical, because there could be other reasons for our imperfection rather than non existence, like war; rape; environmental destruction, et cetera.

Affirming the consequent

If something is perfect, then it must exist.
Serial killers exist, therefore they are perfect.

This is called affirming the consequent (a statement where the consequent is in agreement with the original statement). This is illogical, because the assumption would be that existence is the measure of perfection, & that there are no other reasons for existence.

The only thing that can make 3 & 4 valid would be “& only if” thus the original statement would read:

If, & only if, something is perfect, then it will exist.

This “& only if” can only be assumed in light of a logical or empirical argument for the specific argument under discussion, but cannot simply be assumed.

Logic isn’t infallible, as can be seen in the first example, but it does prove whether or not something can be used as a reason for what we are saying. Perhaps serial killers are perfect (perfect serial killers, at least), but if they are, it is despite the fourth example, not because of it, & more evidence would be needed to make that statement, or an alternative argument must be formulated.

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