Analytic, Synthetic, and Contingent

Analytic, Synthetic, and Contingent
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From Dictionary.com...

Analytic
4. Logic . (of a proposition) necessarily true because its denial involves a contradiction, as “All husbands are married.”

Synthetic
4. Also, syn·thet·i·cal. Logic . of or pertaining to a noncontradictory proposition in which the predicate is not included in, or entailed by, the subject.

Contingent
4. Logic . (of a proposition) neither logically necessary nor logically impossible.


p is Analytic, means, p is logically true or logically false.(tautologous or contradictory)

p is Synthetic, means, p is empirically true or empirically false.
..so that its truth or falsity can be established only by sensory observation.

p is Contingent, means, p is not analytic, i.e. p is possibly true and possibly false.

Analytic(p) =df (p is necessary or p is contradictory) []p v ~<>p.
Contingent(p) =df (p is possible and ~p is possible) <>P & <>(~P).
Synthetic(p) =df (p is factually true or factually false and neither necessary nor contradictory).

Analytic(p) <-> ~Contingent(p). ~Analytic(p) <-> Contingent(p).


There are two kinds of propositional truth and falsity:
analytic..those that do not require the world to show its truth or falsity,
and synthetic..those that do require the world to show its truth or falsity.

p is analytic and true, means, p is logically true...necessary.
p is analytic and false, means, p is logically false...impossible.

p is synthetic and true, means, p is empirically true...factually true and not necessary.
p is synthetic and false, means, p is empirically false...factually false and not contradictory.

If we let: T=logical truth, F=logical falsity, t=factual truth, f=factual falsity,
then we can establish the logical relations between these 4-truth values...

~T=F, ~F=T, ~t=f, ~f=t.

TvT=T, TvF=T, Tvt=T, Tvf=T, FvT=T, FvF=F, Fvt=t, Fvf=f,
tvT=T, tvF=t, tvt=t, tvf=T, fvT, fvF=f, fvt=T, fvf=f.

The other propositional operators are defined in the usual way.
p->q =df ~pvq, p&q =df ~(~pv~q), p<->q =df (p->q)&(q->p).

With this 4-valued logic we can demonstrate all of the 2-valued theorems and much more.

What do you think about this possibility?