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This last example is a syllogism. These were, from the time of Aristotle until the late nineteenth century, the favoured form of argument. Aristotle believed that, stripped down to fundamentals, all propositions were of one of four forms.

1. All S are P
2. No S are P
3. Some S are P
4. Some S are not P

(Note that ‘some’ as used by logicians, means ‘at least one’ – as in ‘There is someone at the door.) For Aristotle any two classes S and P whatsoever must be related to each other in at least one of those four ways. His syllogistic was an exhaustive account of deductive patterns involving two premises and a conclusion based on these four forms. It is now studied only for historical interest.

One obvious difference between deductive and inductive arguments is that inductive, but not deductive, are risk taking. Inductive arguments take a step, however small, beyond the premise(s). This is sometimes expressed by saying only deductive arguments are truth conserving. This makes deductive arguments sound ‘superior’ to inductive ones. One could be forgiven for thinking this if one relied on the interests of logicians who, for the most part, are only interested in deductive arguments. Yet it is via inductive arguments that knowledge of the world is advanced. That is why, while logicians (like pure mathematicians, with whom they have a lot in common – it was thought for many years that mathematics was simply a branch of logic) study deduction, epistemologists study induction.

Another way of putting this is to say that, in the case of deductive arguments, the conclusion is already wholly implicit in the premise set – the argument simply brings it out, and thus makes it explicit. But the conclusion of an inductive argument, while it may be ‘suggested’ by the premise set, is not wholly implicit in them.

TASK 1: Satisfy yourself that this is so by reviewing the examples of inductive and deductive arguments (Arguments 1,2,3, and 4) above.

A slightly more formal way of expressing all this is as follows:

An argument is a valid deductive argument if, and only if, it is logically impossible for all the members of the premise set to be true and the conclusion false.

To say something is ‘logically impossible’ is to say that it is, at least implicitly, self-contradictory.

Does all this mean that the conclusion of a valid deductive argument must be true? No – consider the following:

(Argument 5):

No socialists are politicians
All French people are socialists
So:
No French people are politicians.

This is a perfectly valid deductive argument. Yet – manifestly – the conclusion is false. However, a corollary of the definition of a valid deductive argument given above is that:

If the conclusion of a valid deductive argument is false, then at least one of the premises must be false also.

A valid deductive argument in which every member of the premise set is true is a sound argument.

In other words, if a valid deductive argument is sound, then its conclusion must be true.

Note that whether or not premises are true is generally not a question of logic, but something that can b本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。