Why are these formulas not well-formed in syllogistic logic?


I'm studying formal logic, and I get stuck in the beginning.

I'm trying to do easier translations in syllogistic logic. I'm using Gensler book "Introduction to Logic".

They say that this examples are non-wffs (well-formed formulas). And i don't get why:

all A is not B

Why this are not wffs? All logicians are not charming. This is not valid?

A is B

Again: Logicians are charming.


Posted 2016-04-02T15:42:24.943

Reputation: 325



For "A is B" the explanation is simple.

Gensler's language has two types of "basic" formulae:

(i) formulae expressing relation between sets ("general categoris"): "All logicians are charming", translated as "all L is C"

(ii) formulae expressing the fact that an individual belongs to a set: "Gensler is a logician", translated as "g is L".

In this second case, g is the name of an individual; thus, we cannot quantify it with "all" or "some".

In the previous case, instead, L and C are names for sets and we have to quantify the first one in order to correctly express the relationship between them. If we say "Logicians are charming" (i.e. L is C) we have an ambiguous expression, because we do not know if we are asserting it of all or some Logicians.

I presume that he forbid the expression "all A is not B" as "ungrammatical" (non-wff) simply because it is already expressible as: "no A is B".


Posted 2016-04-02T15:42:24.943

Reputation: 33 575