# Posterior Analytics (Bouchier)/Book I/Chapter XXII
### Chapter XXII: In Affirmations some final and ultimate point is reached where the series must cease

    In the case of essential attributes, the attributions may easily be seen to be limited in number, so that the demonstrations of them are limited also. The mind cannot traverse an infinity, and as Substance, for instance, is definable, its attributes must be limited. In other words demonstration is applicable only to Essentials (καθ’ ατά) which cannot be unlimited, for that would render definition impossible. As it is possible, the attributes are limited. Hence demonstration possesses certain principles which are not themselves capable of any demonstration.
That affirmative demonstration terminates at a certain point may be proved dialectically as follows. It clearly terminates in the case of predications concerning the essence of a thing, for if the essential attributes can be defined and are knowable, and if one cannot reach to the end of the infinite, predications of essential attributes must needs have some limit. To give a general turn to the statement we may express ourselves thus. It is equally possible to say with truth that ‘this white thing is walking’ and ‘that great thing is a stick,’ or again ‘the stick is great’ and ‘the man is walking,’ but there is a difference between the two pairs of expressions. In saying ‘the white thing is a stick,’ I mean ‘that which has the accidental quality of whiteness is a stick,’ not that ‘the white thing’ is the subject of which ‘stick’ is the predicate. It is in fact a stick not because it is white nor from being essentially white, so that ‘this white thing’ is only accidentally a stick. But when I say ‘the stick is white,’ I do not mean that another thing distinct from stick is white, and that stick is an accidental quality of it; (as e.g. when I say ‘the musician is white;’ for in that case I mean that the man, who has the accidental quality of being a musician, is white) but the stick is the subject which is white without being, as a result of that, anything else than the genus or a species of ‘stick.’ Thus if we are to provide separate designations for the two methods, the latter form of expression may be called the ‘predication of attributes,’ the former either not predication at all or accidental, not absolute, predication. In the first case ‘white’ is the attribute,’ ‘stick’ that of which the attribute is predicated.
We may now lay down the rule that the attribute is always predicated of its subject absolutely, not accidentally, for that is how demonstrations are able to effect proof. Hence when one thing is predicated as an attribute of another it concerns Substance, Quality, Quantity, Relation, Action, Passion, Place or Time. Moreover that which denotes a substance denotes either the Genus or the Species of the thing of which the attributes are predicated, but that which does not denote a substance, but is predicated of another subject without being either the Genus or the Species of that subject, is an accident: e.g. White as predicated of Man; for ‘man’ neither belongs to the genus ‘white,’ nor is he a species of it. He should rather be called ‘animal,’ for man is a species of animal.
Everything which does not denote substance must be affirmed of some subject as an attribute, and nothing can be (e.g.) white, in the sense that it is simply white, without being at the same time something else besides. We may at once dismiss Ideas; they are mere empty names, and if they do exist cannot concern our argument, for demonstrations deal only with subjects such as we have already mentioned.
Further if one thing be not an attribute of another nor yet the latter an attribute of the former, and if no attribute of an attribute can exist, the two terms in question cannot be reciprocally predicable as attributes. One of them may be correctly predicable of the other, but each cannot really be predicable of the other, for one would have to be predicated as a substance, as if it were a genus or differentia of the attribute. It has however been proved that these attributions cannot be continued to infinity, either in the direction of the universal or of the particular. Take the proposition ‘Man is a biped, this again an animal, while animal belongs to some other genus.’ Nor can the process be infinite when ‘animal’ is predicated of ‘man,’ ‘man’ of ‘Callias,’ and ‘Callias’ of an individual definite man who is Callias. It is indeed possible to define every substance of this sort, but one cannot even in thought complete the infinite. Hence one cannot arrive at the infinite, either in the direction of the universal or of the particular, for one cannot define that substance of which infinites are predicated.
Two terms, of which one is an accident, cannot be reciprocally predicable as genera are; otherwise each would be a species of itself. Neither can qualities or any other of the categories be so predicated, unless the predication be accidental, for all these categories are accidents and are predicated of substances.
It may also be shewn that this process of predication is not limitless in the direction of the universal, for that which is predicated of any subject must denote Quality, Quantity, or some such attribute of substance.
All these attributes are however limited, not less than the classes contained in the categories, namely Quality, Quantity, Relation, Action, Passion, Place or Time; and our hypothesis is that one thing should be predicated of one, and things should not be predicated of each other unless they denote substances, for all the categories, except substance, are accidents, some essential, others accidents in a different sense.
All these then are predicated of some substance. Accidents however are not subjects, for we hold none of those things to be subjects which are not called what they are called in virtue of their being already something else; one accident being predicated of one subject, another of another. Hence nothing indefinite will be predicated of any subject either in the direction of the universal or of the particular, for the terms of which accidents are predicated are those which constitute the substance of a thing, and such terms cannot be limitless. As we advance towards the universal we find that these substances and their accidents are neither of them limitless. There must then be some term of which an attribute is predicated as a primary attribute, while of this latter something further is predicated. The process must in time terminate, and there must be something which is not predicated of anything more primary, and of which nothing more primary is predicated.
This then is one method of demonstrating that the process of predication has limits. Another is as follows. The existence of antecedent predicates renders propositions demonstrable. One cannot grasp demonstrable things in any better way than by knowing them, nor can knowledge of them be obtained without demonstration. But if one thing can only be learned by means of others, and we are unacquainted with these latter, and do not know them by the help of any higher perception than knowledge, we shall have no real knowledge of these subjects which can only be learned mediately. If then it be possible to obtain absolute knowledge of anything by means of demonstration, not merely knowledge restricted by particular conditions or hypotheses, the intervening predications of attributes must necessarily terminate. Otherwise, if there were always some term higher than that actually employed, everything would be demonstrable.
Since however one cannot pass beyond the limitless, one cannot know by means of demonstration that which cannot be demonstrated. If then we have no higher perception of the demonstrable than knowledge, the result must be that we cannot know anything absolutely by means of demonstration, but only conditionally.
This proof may win a dialectic assent to our assertion, but the following argument, based on the real nature of things, will prove more shortly that predications of attributes in demonstrative sciences, such as we are now considering, cannot be limitless in either direction.
Demonstration deals with all the essential attributes of things; and Essential has two meanings, viz.: (1) Attributes forming part of the definition of the subject; (2) Things of the definition of which the subject forms part. For instance odd is essential to number, for odd is an attribute of number, while number itself forms part of the definition of odd. Again, multitude or discrete forms part of the definition of number. Neither of these processes can be unlimited. (1) The process by which e.g. odd is predicated of number, cannot be so, for if it were, there would be some other attribute included in odd, of which odd itself would be predicable as an attribute. If this were so number will be predicable as primary subject of all the attributes thus becoming predicable of it. (2) If, however, unlimited attributes cannot be predicated of a single term, predications in demonstration must reach a limit in the direction of the universal. Every attribute must be predicated of a primary subject, as in this example of number, while conversely number is an attribute of these others, so that both will be convertible and will not overlap. Neither are the attributes which form part of the definition unlimited, for in that case definition would be impossible. Hence if all the attributes are regarded as essential, and if that which is essential cannot be unlimited, a limit to predication must be reached in the direction of the universal, and consequently in that of the particular. If this be so, that which falls between the two limits of predication must always be limited, and this at once shews that demonstrations must necessarily have ultimate principles, and that not everything can be asserted, and that not everything is, as some have held, capable of demonstration. If ultimate principles do exist not everything can be demonstrable, nor can the process of demonstration continue to infinity. A necessary consequence of either of these conclusions would be that there can be no immediate and inseparable propositions, but that everything must be mediate and separable, for that which is demonstrated is demonstrated by the interposition of one term between two others, not by the addition of one from outside. Hence, if Deduction could go on to infinity, infinite means might exist between two terms. This, however, is impossible if attributes are limited in both directions; and that they are so has already been proved dialectically, and has now been demonstrated in accordance with the real nature of things.