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I'm reading Meaning and Argument and in one exercise of symbolization, there is a sentence which reads "That Jack ever slept here is unlikely."

The symbolization provided is: "Negation: ~J (J: It is likely that Jack ever slept here)".

Such that the symbolized sentence would read: "It is not the case that it is likely that Jack ever slept here."

But if it's not the case that an event is likely, does it necessarily have to be unlikely? What if the probability of that event happening is 50%?

I understand that if you say that an event is "not likely", then it is unlikely, but I'm not sure it has the same meaning as "it is not the case that it is likely."

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I think you're right about the meaning of 'unlikely' as the opposite meaning of 'likely'. See an example from Merriam-Webster Dictionary: Definition of unlikely  : not likely  : IMPROBABLE an unlikely outcome

  • Downvoted. This shouldn't be an answer. It should be, at the very best, a comment. It does not even begin to answer the question. – ixjf Dec 11 '18 at 12:07

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