Reason and Argument Chapter 7 (2/2)

Existential Commitment Since existential commitment doesn’t make a difference to most syllogisms (arguments constructed out of A, E, I, and O claims) we don’t have to make a decision at all in most cases. Where a decision is required, assume that people DO make existential commitments. Otherwise, our Venn diagram system will be an incomplete system.

Syllogism A syllogism is made up entirely of categorical claims There are 2 and only 2 premises and one conclusion Major premise: contains the predicate term Minor premise: contains the subject term There are 3 and only 3 terms in a syllogism. Predicate term: predicate of the conclusion Subject term: subject of the conclusion Middle term: term that is not in the conclusion, but is in each premise

Validity for Syllogisms Validity means the same thing it always has. IF the premises are true, then the conclusion must be. To determine if a syllogism is valid, we make a Venn Diagram with three circles and then diagram the premises. If the information given by the conclusion is represented by diagramming the premises, then the premises guarantee the conclusion, and the argument is valid.

Venn Diagram Method: Draw three circles in the appropriate way Label each circle in the appropriate way Diagram the premises If any area is the only un-shaded area of its circle, put a * in it. (existential commitment) After this, put your pen/pencil down. Check if the information given by the conclusion is or is not represented on the diagram. If it is, the argument is valid, if not, the argument is not valid.

Note about the * When the * could go in one of two areas on a three-circle Venn Diagram, it must go on the line between them to indicate that the * is in one of the two areas, but that the premises do not specify which. The information that this conveys is NOT that there is a * in both areas, nor neither. See p.193-194

The Rules Method First, Vocab: (different context than Grice’s rules) Quality: as before, is the claim affirmative or negative? Quantity: Is the claim universal or particular? Distribution: Whether the whole of a term is being discussed. (more on this next slide)

Distribution (se p.214) Claim Subject Predicate A Distributed not E I

The Rules: Quality: Distribution: Quantity: 1. Nothing follows from two negative premises 2. If one premise is negative, then the conclusion must also be negative. (classical theory also maintained that if the conclusion is negative, one premise must be negative) Distribution: 3. The middle term must be distributed at least once. 4. The subject term may not be distributed in the conclusion if it is not distributed in the premises. 5. The predicate term may not be distributed in the conclusion if it is not distributed in the premises. Quantity: 6. Nothing follows from two particular premises.

Just for fun… Figure 1 Figure 2 Figure 3 Figure 4 Barbara Cesare Darapti Bramantip Celarent Camestres Disamis Camenes Darii Festino Datisi Dimaris Ferio Baroco Felapton Fesapo   Bocardo Fresison Ferison