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I am reading the book An Introduction to Formal Logic by Peter Smith. I was checking the following argument (Exercise-1 Question no-15) :

Miracles cannot happen. Why? Because, by definition, a miracle is an event incompatible with the laws of nature. And everything that happens is always consistent with the laws of nature.

Now, the author has written the following in the answer sheet:

Invalid. The premisses tell us that in fact no miracle ever happens. But they don’t tell us that miracles cannot happen. Compare:

Crimes cannot happen. Since, by definition, a crime is an act incompatible with the criminal law. And everything that happens is always consistent with the criminal law.

In a law-abiding community the premisses may be true: it doesn’t follow that criminal activity is impossible!

The author and some people seem to stress that 'And everything that happens is always consistent with laws of nature' means everything that has happened or is happening is consistent with laws of nature. It doesn't eliminate the possibility that anything can happen in future which is incompatible with the laws of Nature.

Similarly, they want to stress that 'No miracle ever happens' doesn't eliminate the possibility that it can happen in future. However, 'Miracle cannot happen' is the statement that eliminates that possibility. The same thing can be said about the second argument.

Now, Is the author making the right point? I mean we have other such simple present sentences:

  1. Two plus two equals four.
  2. Sun rises in the East.
  3. Forces occur in pair.

Now, are these sentences claiming only about past and present but not about future? How should we interpret these simple present sentences?

P.S- I have also posted this question on Mathematics Stack exchange for those of you interested.

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    You seem to have said exactly what the difference is: general truths, vs what is not possible. The fact that miracles generally don't happen is not the same as whether miracles can ever happen. – Daniel Roseman Mar 9 at 11:01
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In direct answer to your question, "cannot happen" usually means that something is not possible, although it is also sometimes used to mean that something is not permitted, for example:

  • Pigs cannot fly (not possible)
  • You cannot walk on the grass (not permitted)

Saying that something "does not happen" is a reference to currently available historic data. It means that something has not happened to date but doesn't exclude the possibility of it happening in the future, for example:

  • Crime does not happen in this town (suggesting a historic zero, or low-rate of crime, but this does not exclude the possibility it could happen in the future)

I don't see that the author of your text is examining the difference between these two phrases you asked about - firstly because I can't see the term "does not happen" in the source text, and secondly because someone arguing for the possibility of miracles is unlikely to exclude that any miracles have ever happened in the past, which "miracles do not happen" could suggest. Rather, I understand the author is challenging the logic of the reasoning behind someone else claiming that "miracles cannot happen", namely that they are "incompatible with the laws of nature". What they are trying to suggest is that the laws of nature are not immutable, but enforced principles like man-made laws. They attempt to do this by comparing them to such laws which can be broken. The question raised is over the definition of "law", and if the two contexts (natural law, and legally established standards of conduct) are comparable.

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  • Might be that they are so emotionally wedded to their belief that miracles could happen that they refuse to accept "cannot happen" (because of the laws of physics etc.) and instead adopt the position that they "do not happen, but could if the circumstances so demanded". – Prime Mover Mar 9 at 11:44
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    @PrimeMover I think that makes an assumption and also strays into an off-topic area. I don't think anyone who argued for miracles in the future would exclude them happening in the past, and the language in question could do that. I feel I've covered the language question, I don't really want to get into the belief aspects in any more detail. – Astralbee Mar 9 at 14:13
  • Well okay, if you say so, but in this sort of case the belief aspect is essential for a complete understanding of what is being discussed here. It's the ultimate motivation of why such a specious argument can be made in the first place. – Prime Mover Mar 9 at 14:18

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