implication computer

What is nanaotechnology and whats its implications on computers ?


In Defense of Material Implication

Indeed. Something is deeply wrong here, but it has mostly to do with failures to understand material implication and very little to do with anything wrong with material implication itself.


There are three points to keep in mind. The first is that material implication – as you and many others have noted elsewhere – isn’t the same as what people are talking about in ordinary speech when they say that one thing is implied by another. It should be completely unsurprising that one of two statements is materially implied by the other when we wouldn’t ordinarily say it is implied by the other. All that’s required is that we keep clearly in mind which we’re talking about.

If it’s not the same notion, though, it might be wondered why it should be called “implication.” The short answer is that it captures features that are present in any inference that deserves to be called implication. Specifically,

1. it requires that Q be true whenever P and P  Q are. That’s necessary to support Modus Ponens inferences.
2. it requires that P  Q can be true while both P and Q are false. That’s necessary to support Modus Tollens inferences.
3. it requires that P  Q is false when P is true but Q is false.
   

No sensible account of implication denies any of those. Material implication doesn’t give us the whole story about what we normally call implication, but it gives the common core that has to be present in any more developed account.