My question is following: can we estimate how many validities (formulas that are always true) are there among all formulas of propositional logic? Is there a method of doing it?

Are all paradoxes false? That is, when philosophers talk about paradoxes, is it always assumed that there's actually a solution out there which will resolve the problem?

Are there as many true propositions as false ones? More of one than the other?

I never loved my wife, but I married her. We have a child. I’ve been in Love with another woman for the past year, but now I’m moving soon and will lose her. Would it be wrong to have an affair? Doesn’t Love, by nature irrational, transcend my duty to my wife? What is right: to be true to my promise of fidelity, or to be true to myself, my heart, to love? I want to be an authentic person. Recently I read Soren Kierkegaard’s telling of Abraham sacrificing Isaac in his _Fear and Trembling_. He demonstrates that confrontation with the religious can, and often does, go beyond the ethical, the rational. All I know is that it feels right with this other woman, and time is short. It's not just about sex, I love her soul. I don’t know where it will lead. Is adultery always wrong?

Can sentences refer to themselves? Take the "Liar" paradox: (1) This sentence is false. Does "This" really refer to the sentence I've labeled as (1)? Can sentences predicate properties to themselves in this way?

Do these statements mean exactly the same thing: (a) You should not not buy that book. (b) You should buy that book.

Logically what is the difference between conceivable and probable or possible?

Dialetheist: "Some contradictions are true." My question: "Who claims (if any), that some tautologies are false?"

Alex George wrote [http://www.amherst.edu/askphilosophers/question/1663] that we can't ask "why should we be convinced by logic" or some similar question without thereby already submitting to logical priority; i.e., because the question itself has logic embedded in it. I'm not sure I understand this claim fully. Logic studies entailment relationships; if p, then q, therefore if not q, not p. On the other hand, logic doesn't tell us how to love another person. Insight from experience might tell us that. So there are other ways of knowing things, and different sorts of things, than logic. So if someone asks why choose to listen to logic at all, when I can learn plenty of important things from other roads to knowledge, why isn't this a fair question that doesn't already involve logic?

Can anyone recommend a good logic/critical thinking book? I majored in Philosophy in college and have kept sharp by getting into computer programming, however, there is a lot of stuff I forgot from those college days. I remember how quick my reasoning had become and I want to get there again. I was hoping for a textbook/book that comes with a workbook or exercises. Can you recommend some good readings? Recommendations from a beginner to advanced level are welcome. Thanks.