Syllogism: Logic and Minor Conclusion

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  • Topic: Logic, Traditional logic, Modus ponens
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1. Read the chapter syllogism.2. what are kind of syllogism?Types of syllogismAlthough there are infinitely many possible syllogisms, there are only a finite number of logically distinct types. We shall classify and enumerate them below. Note that the syllogisms above share the same abstract form:Major premise: All M are P.Minor premise: All S are M.Conclusion: All S are P.The premises and conclusion of a syllogism can be any of four types, which are labelled by letters[1] as follows. The meaning of the letters is given by the table:code quantifier subject copula predicate type exampleA All S are P universal affirmatives All humans are mortal.E No S are P universal negatives No humans are perfect.I Some S are P particular affirmatives Some humans are healthy.O Some S are not P particular negatives Some humans are not clever.(See Square of opposition for a discussion of the logical relationships between these types of propositions.)In Analytics, Aristotle mostly uses the letters A, B and C as term place holders, rather than giving concrete examples, an innovation at the time. It is traditional to use is rather than are as the copula, hence All A is B rather than All As are Bs It is traditional and convenient practice to use a,e,i,o as infix operators to enable the categorical statements to be written succinctly thus:Form ShorthandAll A is B AaBNo A is B AeBSome A is B AiBSome A is not B AoB 3. What are 3 part of a syllogism?A categorical syllogism consists of three parts: the major premise, the minor premise and the conclusion. Each part is a categorical proposition, and each categorical proposition contains two categorical terms. In Aristotle, each of the premises is in the form "All A are B," "Some A are B", "No A are B" or "Some A are not B", where "A" is one term and "B" is another. "All A are B," and "No A are B" are termeduniversal propositions; "Some A are B" and "Some A are not B" are termed particular propositions. More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, it is the minor term (the subject) of the conclusion. For example: Major premise: All men are mortal.

Minor premise: All Greeks are men.
Conclusion: All Greeks are mortal.
Each of the three distinct terms represents a category. In the above example, "men", "mortal", and "Greeks". "Mortal" is the major term, "Greeks" the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, "men". Both of the premises are universal, as is the conclusion. Major premise: All mortals die.

Minor premise: Some men are mortals.
Conclusion: Some men die.
Here, the major term is "die", the minor term is "men", and the middle term is "mortals". The major premise is universal; the minor premise and the conclusion are particular. A sorites is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, if one argues that a given number of grains of sand does not make a heap and that an additional grain does not either, then to conclude that no additional amount of sand will make a heap is to construct a sorites argument. 4. What is major / minor / middle term ?major term : is the predicate term of the conclusion of a categorical syllogism. It appears in the major premise along with the middle term and not the minor term. It is an end term (meaning not the middle term). Example:

Major premise: All men are mortal.
Minor premise: Socrates is a man.
Conclusion: Therefore Socrates is mortal.
The major term is bolded above.
minor term : is the subject term of the conclusion of a categorical syllogism. It also appears in the minor premise together with the middle term....
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