Aristotle's On Interpretation Ch. 7. segment 11b2-11b16: To assert universally or non-universally, that is the question
(11b2-11b16) of Ch. 7: To assert universally or non-universally, that is the question
We may make an assertion about a particular or a universal. That is, we may assert something of a particular as subject (e.g. Socrates has two feet) or of a universal (e.g. a man has two feet). In turn, when we assert something of a universal as subject, we may do so in two ways. Namely, we may assert it (i) universally or (ii) non-universally
(i) to assert something universally of a universal means to either affirm or deny something of the sum of things (πράγματα) which instantiate that universal, i.e. all the particulars and universals which happen to accept the subject of our assertion as a predicate. For this reason, when we affirm something of a universal universally we add “every” (πᾶς) before the subject to signify the inclusion of all things the universal encompases and when we deny it we add “no” (οὐδεὶς) to signify the exclusion of all those things.
By way of illustration, in the assertion “every bird is winged” we affirm “is winged” of a universal “bird” universally by placing “every” before the subject. Conversely, in “no bird is three-footed” we deny “is three-footed” of “bird” universally with a “no” before the subject. Thus, in the former assertion we affirm “is winged” of all things (πράγματα) which take “bird”, i.e. the subject of our two assertions, as predicate and in the latter we deny “is three-footed” of them.
As such, given that, for example, “every ostrich is a bird”, it is also the case that “every ostrich is winged” and that “no ostrich is three-footed”. In turn, since Camus, the individual ostrich, is a bird, we may also by extension assert that “Camus is winged” and “Camus is not three footed”.
What we therefore learn is that where we conceive of each particular as single in number and individual, we see a universal subject as something we may quantify in terms of proportion. When we affirm something universally, we assert it of the whole. When we deny it, we assert it of none of it. When we affirm or deny something non-universally, we assert it only of a part of it.
(ii) to assert something non-universally of a universal means to affirm or deny something of a part of the things which instantiate that universal. Put differently, as long as we do not assert something of strictly all or none of the things which accept that universal as predicate, we assert it non-universally. To this effect, we may quantify the subject universal with “a(n)”, “few”, ”some”, “several”, “most” among many other choices.
To demonstrate, in the assertion “some bird is flight-capable” we affirm “is flight-capable” of a universal “bird” non-universally by placing “some” before the subject. Further, when we state that “not every bird is flight-capable” we use “not” to deny the “every”, yet still affirm “is flight- capable” of “bird”. Thus, in the one assertion we affirm and in the other deny “is flight-capable” of at the very least one of all the things which take the subject “bird” as predicate.
All in all, when we assert “is flight-capable” non-universally of the universal “bird” as a subject, we communicate that of the sum of things which instantiate “bird” we are to find (a) those that are flight-capable (e.g. every hawk is flight-capable), (b) those which are not (e.g. no penguin is flight-capable), as well as (c) mixed cases (some chickens are flight-capable).
(segm. - 11b12-11b16) On affirming a universal applied universally of a universal applied universally
Having acknowledged that universals are quantifiable, we have so far only quantified universals when they occupied the position of subject in an assertion. In this part of ch. 7 Aristotle considers assertions in which we quantify a universal which forms part of the predicate.
A few such assertions we may come up with are “a hawk is no plant”, “some hawk is some animal”, “every hawk is not every bird” and so forth. As we may observe, assertions formulated as shown are coherent and carry the capacity to be true or false.
Be that as it may, the philosopher makes the point that when we affirm one universal of another universal and both universals are applied universally (e.g. “every bird is every hawk”, or “every hawk is every bird”), we will always end up with an assertion that is false.
Key points: (i) We may affirm or deny something of a particular as subject, i.e. a single thing, or of a universal as subject, i.e. a grouping of things. In turn, when we assert something of a universal we may do so universally, i.e. on the whole or non-universally, i.e. in part. (ii) Our assertion will alway be false when we affirm one universal of another universal and both of them are applied universally.