But this disjunctive syllogism
rests on a false dilemma.
To demonstrate this he reunites the fields of relevance logic and diagram logic, arguing: if the premises of an argument contain its conclusion, it is relevantly valid; if in the very act of diagraming all the premises of an argument one also diagrams its conclusion, the premises contain the conclusion; modus ponens, disjunctive syllogism
, and many other arguments that violate Anderson-Belnap variable sharing can be and have been so diagrammed; therefore they are relevantly valid.
This requires giving up at least one of (i) disjunction introduction; (ii) disjunctive syllogism; (iii) the thesis that entailment is transitive (99-100).
Perfectionist logic accepts disjunction introduction and disjunctive syllogism, but employs a non-transitive notion of entailment (104): p [conjunction] [??]p perfectibly entails (p [disjunction] q) [conjunction] [??]p; (p [disjunction] q) [conjunction] [??]p perfectibly entails q; it is not the case that p [conjunction] [??]p perfectibly entails q.
(DS, [alpha]v[beta], [logical not][alpha][??][beta]) and modus ponens for the material conditional (MMP, [alpha][contains][beta], [alpha][??][beta]) also fail in the system, and that might initially seem to be a steep price to pay.
Lewis' disjunctive syllogism
proving the deity of Christ; Plato's hypothetical argument concerning the power of love; Christ's conjunctive syllogism: "You cannot serve both God and mammon"; David Hume's famous dilemma stating the problem of evil; the stoic Seneca's justification of the virtuous life; and St.
The banker opposes what is natural and true to social fictions and conventional lies through a disjunctive syllogism:
Most of the categorical alternatives the banker casts before his admiring acolyte are disjunctive syllogisms, a statement of alternatives of the type 'either p or q; not q therefore p'.
For to show that the [mu]-term satisfies the first disjunct of its definition, we need to employ the disjunctive syllogism
illicitly at a crucial point.(5)
All things considered, not much is said about why we ought to assent to Boyle's interpretation, which will be a disappointment to those who demand more than a disjunctive syllogism
to prop up an interpretation.
(5) (Disjunctive syllogism
) It follows that there must be a fully actualized state (identified by Aristotle as nous poietikos) that is "in the soul" (en tei psuchei) and causes the fully actualized, occurrent knowing of a human knower.
The third chapter, Ackermann's Strenge Implikation, deals with Ackermann's work on a classical two-valued calculus, and a system equivalent to the authors' system E with the [gamma] rule (disjunctive syllogism
) added as primitive.