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.


(15) On logic

Sun. 24-2-2013
What logic aims at
We want to understand arguments – sentence for sentence. An excellent tool to check that is 2-valued logic.
Why? Our brains work with 2 values as well, so logic is a representation of how our brains work and thus how understanding works.
What do we do to understand something? (Understand literally means “put together,” or “separate,” or “take, grasp”) We check: can the information be verified, or falsified? We do this, because we want to build further on the information that is presented to us. Therefore, if we can’t depend on the information – we don’t know that it will work as predicted – then we can’t build on this knowledge.

What are the advantages of logic?
What the method of logic does is make us understand on the deepest possible level what is said or stated. Through analyzing the information with the logical methodology, we fully understand all the implications of the stated, and we can’t misinterpret. So we don’t have problems in communication.

How – the steps
1. translate the linguistic sentence into a logical form
2. analyze the logical implications
3. add the statement’s data to the logical form
4. deduce what to exclude
5. from the combined logic -> data -> context further eliminate on possible interpretations
6. when still more than one interpretation is possible, ask or search till only one possibility remains.

Update on my goals
I do my early morning writing and jumping skipping rope daily. I like doing those and it gives me some structure. I haven’t written new stuff, but cleaned up what I had already. It takes some more time and thinking about how to practically implement these new habits of monitoring time and sticking to my goals. Today I noted just with pen and paper the times I spent and on what. This way it seems quicker than starting the computer, have it run all day and for every new task walk towards it to type it in.

Another thing: I thought it’d be a change for the reader as well as the writer, to talk about logic.