@mark noble,
mark noble wrote:
kennethamy wrote:
Every apple is not a fruit is equivalent to not all apple are fruit, and that is equivalent to, some apples are not fruit.
Hi Ken!
Please consider this more carefully.
Every apple is not a fruit is conversed by 'Not any apple is a fruit', not 'Some apples are not fruit'. Note the key phrase here 'EVERY' apple is 'NOT', I repeat 'NOT' a fruit.
Do you see where you are mistaken?
Kind regards!
Mark...
"Not any apple is a fruit" just means, "No apples are fruit" But, that, of course, is false. What is true, as we all know, is that all apples are fruit.
Now, all apples are fruit, and no apples are fruit, are not
converses of each other. They are
contraries of each other. Two propositions are
contraries (of each other) if and only if, both propositions cannot be true together so that if one is true then the other is false; but they both can be false. So, by definition, all apples are fruit, and no apples are fruit, are contraries. But two propositions are converses of one another when their subject terms and predicate terms are reversed. Thus, all Xs are Ys, and all Ys are Xs are converses of one another. And so, of course, all apples are fruit and all fruit are apples, are converses of one another.
If you think that every apple is not a fruit, that is, that some apples are not fruit, I suggest that you need to learn some very basic horticulture (and commonsense) for most people over the age of about 4 know that all apples are fruit, so that it is false that not all apples are fruit. Now, the propositions: all apples are fruit, and not all apples are fruit (or some apples are not fruit) are i]contradictories[/i] of one another. Two propositions are
contradictories of one another if and only if they cannot both be true together, and cannot both be false together.
And so endeth my logic lesson for today. But I advise you not only to read up on horticulture if you really believe that every apple is not a fruit, that is that some apples are not fruit (do you really? Surely, even in Wales, apples are counted as fruit) and even make the effort to learn some logic.