Logic and Philosophy

http://whitemyth.com/sites/default/files/downloads…

Thats the LINK to the Book we are using.

Exercise 51 … (For-Credit of 5 Points)

Come up with a series of the 3 items for each of the following
sentences:

(a) Predicate Logic symbolization of the original sentence

(b) result of applying QN to (a), i.e., with different
quantifier

(c) restatement of (b) back into a plain English sentence
which should be different from the original English
sentence in its utterance, but still the same in its
meaning

1. Anything that leads to violence is wrong.

2. Not every smile is genuine.

3. Terrorists are neither rational nor empathetic.

(NB: two predicates as one unit are ascribed to the
subject)

Compare the two different sentences in question 4 below
while doing the same tasks respectively as above:

4. (1) Humans are spiritual.
(2) Only humans are spiritual.

(NB: “only” makes the predicate a consequent of the
conditional)

3. on alternative symbols for quantifiers

You will get to use two kinds of what has been known as
“quantifier,” (1) Universal and (2) Existential, both of which
require unusual symbols that are difficult to write. As we
have adopted alternative notations which are easily put in
pure text format (ASCII characters) for the connectives, we
shall do the same thing for the two quantifiers in Predicate
Logic:

1. Universal Quantifier

(x) … the same from the textbook

but also you could use this:

(Ax) .. for it as well to make it
distinct from the other

2. Existential Quantifier

(Ex)