Introduction to Philosophy/Logic/Modes

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Introduction to Philosophy > Logic > Modes

There can be no smoke without fire.

—old proverb

You will need to know about at least two 'modes' before skipping to propositional calculus.

modus ponens[edit]

First premise: If you drive too fast, you will have an accident.
Second premise: You drive too fast.
___________________________________________
Conclusion: you will have an accident.


Well, that was pretty obvious. Here is another example:

smoke implies fire
smoke
__________________

fire


Generally: 'From the premises "p implies q" and "p", we can infer "q".'

modus tollens[edit]

Sometimes we want to reason backwards:

First premise: If you drive too fast, you will have an accident.
Second premise: You will not have an accident.
________________________________________________________________
Conclusion: You do not drive too fast.

The second premise is in the future tense. Only a clairvoyant would assert such a thing in real life. The argument is valid, though it is not possible to know in advance the truth of the second premise.

Here is another example:

smoke implies fire
no fire
__________________
no smoke

Generally: 'From the premises "p implies q" and "not q", we can infer "not p".

some bad reasoning[edit]

smoke implies fire
no smoke
__________________
no fire

Someone who reasons like this could end up being burned alive in an accident involving smokeless fuel. Whereas modus ponens and modus tollens are examples of deduction, our last example is an example of abduction. It works some of the time, it can suggest what might be the case, but it is unreliable. This logical fallacy is known as denying the antecedent.

We used to have a safety officer who would come from head office and say 'if it is tidy, it is safe'. He concluded things were safe if they were tidy. This did not impress the computer programmers in the department since to be a programmer you need to have a bit of sensitivity to logic. To conclude things were safe if they were tidy, he would have more correctly said 'if it is untidy, it is unsafe', or 'if it is safe, it is tidy'.

The Wikipedia has a long list of different kinds of logical fallacy. I suggest you have a look at it, and read some of the entries. Not only will you find it amusing, it could stop you from being duped by bad arguments.


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