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Syllogism: Logic and Minor Conclusion

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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. Along with the major term it is one of the two end terms. Example:

Major premise: All men are mortal.
Minor premise: Socrates is a man.
Conclusion: Socrates is mortal.
The minor term is bolded above.middle term : (in bold) must distributed in at least one premises but not in the conclusion of a categorical syllogism. The major term and the minor terms, also called the end terms, do appear in the conclusion. Example:

Major premise: All men are mortal.
Minor premise: Socrates is a man.
Conclusion: Socrates is mortal.
The middle term is bolded above.What is major / minor conclusion ?To identify the Major Term, look at the conclusion and find the predicate term. To find the Minor Term, look at the conclusion and find the subject term. The remaining term of the three categorical terms is the Middle Term. (NOTE: The Middle term never appears in the conclusion)Example:All light bulbs are human.All Bostonians are light bulbs.Therefore, All Bostonians are human.(Major term = ‘human’, Minor term = ‘Bostonians’, Middle term = ‘light bulbs’) What is hypothetical syllogism? hypothetical syllogism : is a valid argument form which is a syllogism having a conditional statement for one or both of its premises. If I do not wake up, then I cannot go to work.

If I cannot go to work, then I will not get paid.
Therefore, if I do not wake up, then I will not get paid.
In propositional logic, hypothetical syllogism is the name of a valid rule of inference (often abbreviated HS and sometimes also called the chain argument, chain rule, or the principle of transitivity of implication). Hypothetical syllogism is one of the rules in classical logic that is not always accepted in certain systems of non-classical logic. The rule may be stated: \frac{P \to Q, Q \to R}{\therefore P \to R}

where the rule is that whenever instances of “P \to Q”, and “Q \to R” appear on lines of a proof, “P \to R” can be placed on a subsequent line. Hypothetical syllogism is closely related and similar to disjunctive syllogism, in that it is also type of syllogism, and also the name of a rule of inference. What are different kinds of hypothetical syllogism ?It is also possible to mix up these two forms: the disjunctive and the hypothetical. There are two valid and two invalid forms of a mixed hypothetical syllogism. The first valid form is called modus ponens (From the Latin “ponere”, “to affirm”), or “affirming the antecedent”: Modus Ponens

If P is true, then Q is true
P is true
Therefore, Q is true
The next form, Affirming the consequent, is invalid:
Affirming the consequent

If P then Q
Therefore, P is true
Why is this form invalid? This argument differs from modus ponens in that its categorical premises affirms the consequent, not the antecedant . As we will see when we discuss Truth tables , there is no inconsistency in holding that P is false and Q is true: we can hold that the propositon “IF p, then Q” to be true, even if “P” is false, which would mean that we could have all true premises and a false conclusion: “If p, then Q” as a statement would be true, “q” would be true, and yet the conclusion, “P” all its own, would be false! – which, if we remember from earlier lessons, is not possible. Affirming the consequent can therefore be made valid, if the term “if” is replaced by the term “If and only If”, so that P and Q can only be true when both are true. The next valid form is called modus tollens (Latin: “To deny”), and it takes the following form: Modus Tollens

If P, then Q
Not Q
Therefore, not P
Here the syllogism denies the consequent of the conditional premise, and the conclusion denies the antecedant. Make sure not to confuse this form with the next form. The next form, Denying the antecedent, is invalid:

Denying the antecedent
If P, then Q
Not P
Therefore, not Q
This deductively invalid form differs from modus tollens in that it’s categorical premise denies the antecedent rather than the consequent. This
makes this form invalid because, while there is no case of all true premises and a false conclusion, the argument leads to a non sequitur. This can be made more clear with an example: If it is raining, I will carry an umbrella

I am not carrying an umbrella
Therefore, it can’t be raining
Such an argument confuses a correlative fact for a causal fact, where not causality has been established. For this reason, it can also be referred to as a vacuous implication. Denying the antecedent is valid if the first premise asserts that there is some necessary connection between the antecedent and the consequent, but using the term: “if and only if” rather than “if”.

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