But the hybrid contingens ad impossibile construction that Rigg discerns here is very odd – and I flatter myself that both of my suggestions are more amusing. I know nothing about mediaeval poetry, so for all I know this second suggestion may be metrically untenable. Or rather impossible, all things implied. If instead he were metaphorically ascribing these modal properties directly to the flatterer, we would expect impossibilis instead of impossibile, in which case (understanding quod as ‘because’) we could translate:įor he is contingent towards either side. Here I have construed Wimborne as metaphorically identifying the flatterer with things that have certain modal properties. Ex Falso Quod Libet definition: The principle or axiom of logic stating that if a contradiction or a false proposition is proven to be true, then it proves that everything is true. Or else the impossible all things implying. If the text is correct, then, we may translate:įor he's the contingent towards either side, And the proposed emendation would break the allusion in the last line to the logical principle often termed ex falso quodlibet. The contingens line has nothing to do with dependence, but imputes to the flatterer an indeterminate attitude towards pairs of contradictory propositions. AB agree on quidlibet, but quilibet would be better.’Īs I suspect anyone reading this will have noticed, this interpretation is faulty. He pleases whoever 'cause he's a chameleon įor the second couplet, George Rigg suggests in his 1978 edition: ‘“He is contingent on (depends on) either side, or on whatever impossible inference is made.” That is, the flatterer is like a conclusion in logic, dependent on the preceding premise, however impossible it may be. The first couplet is straightforward enough: which should seem quite plausible.Īs Graham Kemp points out in his answer, the convention of using 'efq' to discharge an assumption is a little bit non-standard and usually this is called RAA or framed as double negation elimination.The mid-C13th satire De palpone by the Franciscan schoolmaster Walter of Wimborne includes this stanza (§64, spelling modified): (And this was certainly not an unconditional proof of an absurdity, it was under specific assumptions that were framed up in the larger structure of the proof.) Perhaps a better way to think about it is that what we wanted to prove was $P\to Q$ under the assumption that $P$ is false. So we did assume $\lnot P$ and assume $P$ and get nonsense, but the assumptions had an orderly motivation and nonsense was exactly what we needed to prove $Q,$ which was a goal we had at that moment in the proof. There is a contradiction between our assumption of $\lnot P$ and our assumption of $P.$.We will prove $Q$ by proving a contradiction, from which we can prove anything (ex falso.).We will prove $P\to Q$ by assuming $P$ and then proving $Q.$.We will derive a contradiction by proving $P\to Q,$ which contradicts with our assumption of $\lnot(P\to Q).$.We will prove $P$ by assuming $\lnot P$ and deriving a contradiction.We want to prove $\lnot(P\to Q)\to P,$ so we assume $\lnot(P\to Q)$ and our goal is to prove $P$.Here's how we can organize things (informally) to make a bit more sense. Here we see that a contradiction can be derived on raising the third assumption, and so we may validly derive $Q$ within that context (because whatever $Q$ may be, it is at least as true as an absurdity).Įx falso Quodlibet: If we can say "false is true", then we may say anything is true. In this notation we keep track of the order in which assumptions are raised and discharged by indentation. To show $P$, we will use proof by contradiction and we will assume $\neg P$. Assume $\neg (P \Rightarrow Q)$, show $P$.Suppose we want to prove that $\neg (P \Rightarrow Q) \Rightarrow P$. Some of these proof rules defies my intuition so I wanted to ask for some clarification. I am at the very beginning, Gentzen style natural deductions. I began studying some formal logic for possible future proof and type theory dives.
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