Subvert the argument – a fallacy

‘If it rains, the picnic will be cancelled.’

This argument is often interpreted as: If it does not rain, the picnic will go on.

What assumption is made?
The reasoning behind it is, that if the first part of the argument is negated (or denied), then the consequence will be denied as well. So, if it does not rain, it automatically means the picnic will go on.

Why is this deduction wrong?
Let’s start with what this argument exactly means.
‘If’ is the condition,
‘it rains’ is the antecedent (the cause);
‘the picnic will be cancelled’ is the consequent (the effect).

Expressing the assumption in capital letters:
If A then not B  (if the condition is it rains, then there’s no picnic)
Not A                (the situation is it does not rain)
Thus: not B       (then there is not no picnic = double negation = positive; so there is picnic)

The implication has 4 possible outcomes, because the antecedent as well as the consequent can be affirmed or negated. The condition (if) calculates the possible result from these affirmations and negations.

If A then not B  (if the condition is it rains, then there’s no picnic)
1. A                   (rain)
Thus: not B       (no picnic) This conclusion is valid; the implication says: if it rains, then no picnic.

2. A                    (rain)
Thus: B              (a picnic) This conclusion is impossible; the implication says: if it rains, then no picnic.

3. not A              (no rain)
Thus: B              (a picnic) This conclusion is valid. It is possible that there is a picnic if it doesn’t rain.

4. not A              (no rain)
Thus: not B        (not no picnic) This conclusion is valid too; both parts of the argument are negated. It is also possible that there is another reason than no rain why there is a picnic.

What is wrong about denying the antecedent is: it assigns only 1 cause (rain) to the effect (no picnic) and thus other possibilities (for no picnic) are dismissed.

The fallacy of subverting the argument – or denying the antecedent, as it’s also called – is that it undermines or disrupts logic (deliberately or accidentally). It thereby shrinks reality’s possibilities.

I know, we all want to reduce the information, but if that’s done by not taking something into account that we should, then that might have unanticipated or unwanted consequences. To reduce the information effectively we apply logic, so we can truly anticipate.

(24) What is the simplest logical proof?

The idea is to weave a whole of referrals from which we can conclude something irrefutable. We call this deductive reasoning. How do we do that?

Two assumptions, called premises, lead to a conclusion. The premises are simple sentences or statements that consist a subject and a predicate.
The two premises have a common term: the 2nd (minor) premise’s predicate refers back to the 1st (major) premise’s subject.
Also, each of the premises has one term in common with the conclusion. The major premise (1) has the same major term (predicate), the conclusion’s predicate; and the minor premise (2) has the minor term (subject), the conclusion’s subject in common. With shared terms, we have constructed a new fact: a conclusion (3).

Example of reasoning at work:

(1) All men are mortal.
(2) Socrates is a man.
(3) ∴  Socrates is mortal.

This is the classic example of a syllogism, a logical argument in which the conclusion is deduced from two (or more) premises. Although I’ve seen it many times, I still love the symmetry of this simple proof.