Leibniz's numerical characteristics
Can someone explain to me what Leibniz means in his philosophical essay on numerical characteristics for his universal language when he says:
"We must also consider the fact that all negative terms have the property that
when positive terms are related as genus and species, their negations, on the
other hand, are inversely related, as species and genus."
And to help you explain, Leibniz gives an example of what he is trying to say:
"For example, "body"
is genus, and "animal" is species, for "body" is broader than "animal" since
"body" contains animals, plants, and other things. But, on the other hand,
"nonanimal" is broader than "nonbody." For all nonbodies are also nonanimals,
but not conversely, for there are nonanimals which, however, are not
nonbodies, for example, plants. Thus, just as there are more bodies than
animals, so, on the other hand, there are more nonanimals than nonbodies."
"We must also consider the fact that all negative terms have the property that
when positive terms are related as genus and species, their negations, on the
other hand, are inversely related, as species and genus."
And to help you explain, Leibniz gives an example of what he is trying to say:
"For example, "body"
is genus, and "animal" is species, for "body" is broader than "animal" since
"body" contains animals, plants, and other things. But, on the other hand,
"nonanimal" is broader than "nonbody." For all nonbodies are also nonanimals,
but not conversely, for there are nonanimals which, however, are not
nonbodies, for example, plants. Thus, just as there are more bodies than
animals, so, on the other hand, there are more nonanimals than nonbodies."
Comments (1)
A non-food must not be a cake, since if a non-food was cake it would indeed be food. This is because cakes are foods. Another way of saying that cakes are foods is that cakes are a genus of the species foods.
A non-cake could still be food, for example a sandwich. This is because some non-cakes are still foods.
So there are more things which are 'non-cakes' than there are things which are 'non-foods'.