OP strikes me as thoroughly INTP.
NOBODY but NOBODY, I would wager, goes through mental arguments using formal logical systems, if only because the Fregean logic system we've been given, with &, or, ~/not, ->, <--> etc. operators are inadequate to describe many of the statements that we ordinarily use. If you consider the nature of the material conditional and all the issues we have with 'if' statements, Bayesian and Frequentist debates, you'll realize that... for instance, the inability to make universal statements even using universal evidence... that's a poor way of explaining something of the quandary one faces with a situation like... there have NEVER been any recorded instances of a man living past 180 years of age... hence, it is impossible for men to live to 181 years of age. That clearly goes against what a reasonable person would think... if a guy lives to 180, then other people could possibly also live to 181 or more.
Logic needn't be cut and dried, as a lot of people assume (I'm not saying you are, but much of the debate on Thinking types seems to rely on these sorts of assumptions).
Also, the issue with using what Owl said about value judgments... it raises some questions... a "thinker" ultimately needs to have some sort of a value system... what is 'right'? What sort of thinking is correct? What axioms does one use? Thinkers have to deal with masses of unproven statements to base their arguments off of. Thinkers have to make gut-feel decisions, if only at the beginning, in order to continue... everyone needs a value system... even physicists must accept large numbers of empty concepts or circular arguments off of which to build more elaborate and fleshed-out systems (what exactly are mass and force? gravity?)