i am under the belief...

that philosophy, as a whole, permeates everything we do. and the greatest tool that we use for this is logic; the laws of reasoning if you will. the Form of language. the Form of relationships. the study of relationships. what kind of effect has logic had? well, we are still using the works of aristotle some two thousand years ago. we still use his original studies in class today. he was the first to write on and about logic. the laws of logic.

throughout its time, logic was seen as more of a study of mathematics. throughout history, as some of the great mathematicians got on in years, they turned to philosophy. too many to begin to drop names, so i will not. well, durning the nineteenth century approached a mathematician by the name of boole; who came up with boolean algebra, and really since this logic was seen as an 'outgrowth' of mathematics. now in the early nineteen hundreds, two philosophers by the names of russell, and whitehead wrote a small book called; principia mathematica. and in this book they proceed to show that mathematics stems from logic, and not the other way around.

a small example...how are we able to have an understanding of the relationship between two and three, if we do not have understand of what it means for something to be 'greater than' something else? it is this relationship that has nothing to do with mathematics. this is more of a relationship of language. a Form of a given thing to another given thing.

so why this rant/background? well i'm reading my current issue of the bulletin of symbolic logic, and the writers use a lot of mathematics to try and prove given logic equations.

my question becomes...if, since russell and whitehead, mathematics owns, in a sense, its existence to logic, then are we able to use it to 'prove' logical theorems? how to use mathematics to 'solve' logic? or should i ask 'why'? what is mathematics without logic? however...isn't logic able to be without math? meaning logic covers much more than math does. mathematics is not used as a device in language in the sense that logic is.

just to prove my point...the journals are sent from the ams; rather than some philosophy society, or symbolic logic society.

kant once said (and i'm sorry that i can't find the exact quote but,) that no one takes the study of logic seriously, because no one deems themselves illogical.

[shalom..]