Task 8 - Categorical syllogisms - Chapter 5 Flashcards
Syllogism
a deductive argument consisting of two premises and one conclusion
Categorical syllogism
a syllogism consisting of three categorical propositions and containing a total of three different terms, each of which appears twice in distinct propositions
Major term
one of three terms in a categorical syllogism which has it’s own name depending on its position in the argument
the predicate of the conclusion
Minor term
one of three terms in a categorical syllogism which has it’s own name depending on its position in the argument
the subject of the conclusion
Middle term
one of three terms in a categorical syllogism which has it’s own name depending on its position in the argument
it provides the middle ground between the two premises – it is the one that occurs once in each premise and does not occur in the conclusion
- used for holding hands rule
Major premise
Premises of a categorical syllogism
the one that contains the major term
Minor premise
Premises of a categorical syllogism
the one that contains the minor term
Standard-form categorical syllogism
Premises of a categorical syllogism
the one that meets the following four conditions:
1) All three statements are standard-form categorical propositions.
2) The two occurrences of each term are identical.
3) Each term is used in the same sense throughout the argument.
4) The major premise is listed first, the minor premise second, and the conclusion last.
Now that we have a definition of standard-form categorical syllogism, we can give a more
Categorical syllogism
a deductive argument consisting of three categorical propositions that is capable of being translated into standard form
Mood (of a categorical syllogism)
consists of the letter names of the propositions that make it up
Figure (of a categorical syllogism)
it is determined by the location of the two occurrences of the middle term in the premises
(four different arrangements are possible)
Venn diagrams – pointers for making Venn diagrams of categorical syllogisms
1) Marks (shading or placing an X) are entered only for the premises. No marks are made for the conclusion.
2) If the argument contains one universal premise, this premise should be entered first in the diagram. If there are two universal premises, either one can be done first.
3) When entering information contained in a premise, one should concentrate on the circles corresponding to the two terms in the statement. While the third circle cannot be ignored altogether, it should be given only minimal attention.
4) When inspecting a completed diagram to see whether it supports a particular conclusion, one should remember that particular statements asserts two things. “Some S are P” means “At least one S exists and that S is a P”; “Some S are not P” means “At least one S exists and that S is not a P”.
5) When shading an area, one must be careful to shade all of the area in question.
6) The area where an X goes is always initially divided into two parts. If one of these parts has already been shaded, the X goes in the unshaded part. If one of the two parts is not shaded, the X goes on the line separating the two. This means that the X may be in either (or both) of the two areas – but it is not known which one.
7) An X should never be placed in such a way that it dangles outside of the diagram, and it should never be placed on the intersection of two lines
To test a syllogism from the Aristotelian standpoint
1) Reduce the syllogism to its form and test it from the Boolean standpoint. If the form is valid, proceed no further. The syllogism is valid from both standpoints.
2) If the syllogistic form is invalid from the Boolean standpoint and has universal premises and a particular conclusion, then adopt the Aristotelian standpoint and look to see if there is a Venn circle that is completely shaded except for one area. If there is, enter a circled X in that area and retest the form.
3) If the syllogistic form is conditionally valid, determine if the circled X represents something that exists. If it does, the condition is fulfilled, and the syllogism is valid from the Aristotelian standpoint
To test a syllogism from the Boolean standpoint
1) The middle term must be distributed at least once → fallacy of undistributed middle.
2) If a term is distributed in the conclusion, then it must be distributed in a premise → fallacy of illicit major or illicit minor.
3) Two negative premises are not allowed → fallacy of exclusive premises.
4) A negative premise requires a negative conclusion and a negative conclusion requires a negative premise → fallacy of drawing an affirmative conclusion from a negative premise or drawing a negative conclusion from affirmative premises.
5) If both premises are universal, the conclusion cannot be particular → existential fallacy
The middle term must be distributed at least once
fallacy of undistributed middle
