How Logic Works – Formal Logic

then a miracle occurs - logic

With a good deductive argument, the truth of the premises entails the truth of the conclusion.

In other words, if your premises are correct, your conclusion is unquestionable unless more premises are introduced. You will win any argument with such perfect logic.

Some classic examples of deductive arguments:

Formal logic

True and Valid:

All men are mortal.
Socrates is a man.
Therefore
Socrates is mortal.

It is simply not possible that both (1) and (2) are true and (3) is false, so this argument is deductively, or formally, valid.

False but Valid:

All men are green.
Socrates is a man.
Therefore
Socrates is green.

In this example, the first statement is false, but the form or structure of the argument is correct and valid. (If all men were green; then Socrates would also be.)

Humans also tend to use logical short-cuts, called heuristics. These are thought processes that are not strictly valid in their logic, but are true most of the time and therefore are a useful rule-of-thumb as to what is likely to be true. Where they get us into trouble is when we use these rules of thumb as a substitute for valid logic.

An example of heuristics is a stock going up on a profitable earnings report. When a more accurate indicator is if the earnings report meets analyst expectations or not, whether or not the company recorded a profit for that period. The rule of thumb, though better than chance, is hardly a logically valid conclusion.

False and Invalid:

Some men are green.
Socrates is a man.
Therefore
Socrates is green.

True but Invalid:

Some men are mortal.
Socrates is a man.
Therefore
Socrates is mortal.

Unlike the valid formal arguments, the first statement says something about some men, not about all men. One could correctly reason from this first statement that Socrates might possibly be green or mortal, but he could not correctly reason that Socrates necessarily is green or mortal, making this an invalid argument.

In short, formal fallacies are invalid arguments — arguments where the concluding statement does not necessarily follow from the statements preceding it.

While the conclusions may be true, their truth is not a result of the conditions presented.

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