Those who would read the following should really have first read the first part, posted here on March 28th. I'm going to dive into the middle of material today without reviewing that. Ready? Let's go. How have defenders of a middle choice (between true and false, EVEN for some well-formed propositions) defended that possibility against C.I. Lewis' critique? Well, to begin, they note that any effort to prove something involves premises. To the extent that the law itself (we will call it LEM for short) is supposed -- as it is supposed by many -- to be a foundational premise in logic, it of course cannot be proven. If Lewis has actually proven LEM, it must have been by discovering other deeper premises, and turning LEM into a lemma, so to speak, a steppingstone on the path from some important truths to others. In fact, the Lewis "explosion argument" takes it as a premise that every sentence entails the disjunction of itself and any other sentence. This is kno...
Mary Shepherd is 'having a moment' and I am out of sympathy. Yes, I agree that many women have been written out of the history of philosophy because the history is written by men. I agree that it is worth our while to reverse this trend and recover the contributions of neglected women where we can. But Mary Shepherd, an early 19th century British thinker best known for an essay on the relation between cause and effect, doesn't really fill the bill here. In response to Hume, Shepherd wrote thus: "We cannot imagine a beginning of existence to be wholly unconnected with any thing that went before it; and this is sufficient to refute the notion, that causes and effects are only conjunctions, or sequences observed by the experience of mankind." She thus infers the necessity of causal relations from our inability to imagine the contrary. This sort of thing reminds me of the scenes in The Princess Bride, where the bad guy Vizzini keeps assuring his confederates that ...