The Frege-Geach argument
The Frege-Geach argument is a problem started by the late Peter Geach as a response to emotivism, a position in moral epistemology, which claims that morality comes from emotional responses as opposed to reason and is subjective. Geach argues that morality comes from reason, and is objective, according to his moral epistemic position, moral rationalism. How he does this we shall see below:
Now figure 1 demonstrates a standard well-formed formulae as the sentence are able to go through a logical deconstruction. Ergo, the rationalist approach is logically consistent and conforms to natural deductive logic. How this is done is by taking the letter of a character from the words “torture” and “execution” from the two premises and conclusion to form a conditional proof.
Figure 1: Cognivist proposition:
Premise 1: If torture is bad then execution is bad,
Premise 2: Torture is bad,
Conclusion: Therefore execution is bad.
T -> E, T |- E
1 (1) T-> E A (CP)
2 (2) T A (CP)
1, 2 (3) E 1,2, MPP
For figure 2, it demonstrates the inability to form a well-formed formulae. Specifically since premise two does not form a sentence and only an emotional reaction, then there is a gap in the conditional proof. Ergo, the emotivist approach fails to conform to natural deductive logic.
Figure 2: Non-cognivist proposition:
Premise 1 If torture is bad then execution is bad, Premise 2: Boo! Torture! Conclusion: Therefore execution is bad.
T ->E, ? |- E
1 (1) T -> E A (CP)
2 (2) ? ? (??)
1 (3) E 1, MPP