1. Let’s try to apply the language of Logic and Propositions that we learned in
ID: 3197280 • Letter: 1
Question
1. Let’s try to apply the language of Logic and Propositions that we learned in class to the rag “Everybody loves my baby, but my baby don’t love nobody but me” (by Jack Palmer, ca. the 1920s). Suppose that our universe has one relationship, LOVES, and two distinguished individuals, ME and MYBABY. For example, LOVES (ME, MYBABY) means --”I love my baby” and x¬ LOVES(x, ME) means --”not everybody loves me.”
a) Write a proposition, using this vocabulary and the Boolean connectives , V, ¬, -> as well as quantifiers and
b) Look now at what you wrote, and argue that this proposition implies ME = MYBABY !
Explanation / Answer
a).
We have to convert this sentence into symbolic logic --> “Everybody loves my baby, but my baby don’t love nobody but me"
Then the symbolic logic by using Boolean connectives , V, ¬, -> as well as quantifiers and for this sentence is
(x LOVES(x,MYBABY) )(x LOVES(MYBABY,x) x=ME) or
x LOVES(x,MYBABY) and x LOVES(MYBABY,x) x =ME
b).
We can substitute MYBABY for x to obtain
LOVES(MYBABY, MYBABY)(LOVES(MYBABY,MYBABY) MYBABY=ME)
The truth of the first proposition LOVES(MYBABY,MYBABY) together with the left to right implication LOVES(MYBABY,MYBABY)MYBABY=ME , implies that MYBABY=ME.
We conclude that “ME” and “My Baby” are one and the same person.
Therefore proposition implies ME = MYBABY
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