Is it ever possible to deduce the attributes of a thing by virtue of it being a member of a group, when those attributes are not actually part of the definition of the group?
Consider this conditional syllogism:
1. All horses are red.
2. Jenny is a horse.
Therefore, Jenny is red.
Can this ever be valid unless redness is part of the definition of ‘horse’? And if it is part of the definition, then the conclusion is merely a restatement of part of “Jenny is a horse.” If redness is not part of the definition, then the argument becomes either an inference or an equivocation. It seems to me that all groups exist only by definition, and its members can have no necessary attributes other than those we assign to them by definition. If we define a 'calcium atom' as an atom that has 20 protons, then we can’t “deduce” anything about any particular member of the group 'calcium atoms' other than that it has 20 protons. We can infer that it also has 20 electrons, but we can’t deduce it unless we also make the number of electrons part of the definition as well. But is a tautology really a deduction?
This is simply deductive logic
Logic does not care about truth, any statement afirming something has another which denys it.
So the the statement that all horses are red is just part of the starting point. All we care about is if the deduction is correct.
As a deduction it is correct. It is not a tautology.
If you have a set with property P, then a proper subset of this set also has property P. That is all a sylogism does.
I understand that it is a valid deduction, but not how it is not a tautology. Terms for groups of things, like "horses" are just shorthand for the definition of the group, so every place where the term "horse" occurs we could substitute the list of attributes a thing must have to be a member of that group. If "redness" is part of that definition, then the first premise becomes "'all things that are classified into a group that is defined, in part, by having the property of redness' are red." The second premise becomes "Jenny is a member of 'a group that is defined in part by being red'" We can now substitute "a member of a group that is defined in part by being red" for "Jenny," and conclude that "'a member of a group that is defined in part by being red' is red." If the person doing the reasoning is given incomplete information, so that all they know about the definition of horses is that they are red, then the whole thing becomes:
All things that are red are red
Jenny is a thing that is red
Therefore, Jenny is red.
If redness is not part of the definition of "horse" then her redness becomes an inference, not a deduction.
As far as I know an inference is a synonym of deduction (same thing)
A tautology is something more like
a horse is a horse
red is red
etc
It is true that a set can have elements with a list of properties, but maybe these elements with these properties are not sufficient to completely define the set. But if the full set has property p, the subset also has this property. That is where the deduction comes.
all men are mortal
socrates is a man
Thus socrates is mortal
The set is men
socrates is the subset
the property is mortal
Inference and deduction are fundamentally different. In deduction conclusions follow of necessity from premises. In induction (inference) the conclusion is only more or less likely.
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