fixtures
formal logic is so called because it is concerned with form. that is to say, it is concerned with symbols. we render arguments in symbols, and then we work syntactically, applying inference rules derived from foundational axioms to evaluate them.
in a proof-theoretic context, we determine the formal validity of an argument. it is a brutal kind of abstraction; when we work syntactically, we are not interested in the truth of an argument, but in its validity. would the truth of an antecedent necessitate the truth of a consequent? we aren't concerned with whether sappho is a woman, or whether all women are mortal, but with whether, in a world in which those two statements are true, it would follow that sappho is mortal.
similarly but differently, when we work in a model theoretic context, we consider the question of overall consistency given a set of premises. is it possible to create a model of this world you have proposed without contradictions? this is another way of approaching an argument formally, questioning soundness rather than validity. and it is a bit like dreaming, building, we are asking: is there a possible world where all of this is true? show me this world in which sappho is mortal.
it is not an exaggeration to say that these systems hinge on maintaining tautology. ignoring many-valued and paraconsistent logics for now, the rules of inference in classical logics are derived from foundational axioms constructed to save the phenomenon of our belief that an argument must be true or false. these axioms are derived from a class of tautologies, including (particular formulations of) the classical 'laws of thought,' which include identity (a equals a), non-contradiction (a does not equal not a), and excluded middle (either a or not a must be true).
deductive methods for evaluation of validity, for instance, perform tautological transformations of an initial set of symbols based on these rules, working back to a set of simple atomic formulae that can then be checked for contradictions with foundational tautologies. as with anything we might label 'laws of thought,' it is easy to confuse them with universal truths.
i like to compare poetry to formal logic because they rhyme like sevenths. they are both concerned with meaning, abstraction, truth, and exploring worlds that could be true. i can see them both as kinds of dreaming, building, as archetypal exemplars of our often bipolar modes of approaching all of this. they both employ symbols, drawing from that mystical property of language: discrete infinity. perhaps symbols are all we really have.
and yet they are so fundamentally, intentionally, and categorically unalike. poetry and her friends use the discrete to reach out and touch that spicy kind of infinity. the kind of infinity that logic inherently cannot work with - it is not asking the right questions, and it did not bring the right tools. poetry is a kind of magic, cast so often by flying in the face of tautology, reveling in contradiction, playing the forms.
artists are not so much interested in whether we can determine that sappho is mortal, but with everything up to, including, and beyond the ineffable parts of what it means to be mortal, what it means to be a woman. from form to content to nature to immanence. what does sappho know of woman, in that quiet part of her heart? and you? how does it feel? and isn't it true that there is some mortal part of her, of all of us, after all? how can either one be true? why does it matter to ask the questions? where do the questions come from? where do they go?
these kinds of questions and their answers are steeped in contradiction. i find myself pre-occupied with the sense that everything true is also not true, that everything is like everything else, and that everything is completely unlike everything else, too. how can this be? and how can i express it?
anyway, i think this is part of what drives me to write.
other things said
hear me out!set it down say something clearanother apparition intercessionsomething a little different great husking lights descend from the trees when the cars have gone