Quote:
Originally Posted by Mondo
Could you explain some of the key differences between LFJ and LHJ?
I'm not familiar with either of those terms.
I'm sorry for stating the obvious but it seems like that Hilbert is kind of Fitch's bitch here.
Unlike most of the humanities, you need to be well-versed in the rules of formal logic to excel in philosophy.
This is no surprise to me. My brother who was a Math major in college is actually on his way to getting a P.H.D in Philosophy right now.
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Well LHJ has only one inference rule which is modus ponens. LFJ has rules hyp, conditional proof, modus ponens, and reiteration. What I've been given are inductive definitions of each system (which amount to linear representations of the inference rules for each system as the induction step), and from those I'm supposed to use induction to prove that if A is an immediate consequence of the set of sentences Gamma in LFJ, then A is also an immediate consequence of the set of sentences Gamma in LHJ, and vise versa. My problem is that I don't know how I would go about setting up the proof.