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| Aristotle Posterior Analytics IntraText - Concordances (Hapax - words occurring once) |
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501 I, 24| knowledge (for this is the ideal of demonstration), and we
502 II, 13| similar-i.e. specifically identical-individuals, and consider what element
503 I, 2 | appropriate" basic truths, for I identify primary premiss and basic
504 I, 2 | proof by the teacher, yet ignorance of it does not constitute
505 I, 16| 16~Ignorance-defined not as the negation of knowledge
506 I, 12| hand, arguments formally illogical do sometimes occur through
507 I, 24| reasoning after a fashion well illustrated by the argument that the
508 II, 4 | investigate, because it best illustrates the point under discussion.~
509 II, 4 | premisses are primary and immediate-which we ought to investigate,
510 II, 10| other hand the definition of immediates is an indemonstrable positing
511 II, 5 | all animal is mortal or immortal: but such a formula taken
512 I, 1 | use of old knowledge to impart new, the syllogism assuming
513 II, 13| vicissitudes of life and impatience of dishonour. If they have
514 I, 31| universal and universals imperceptible, we clearly cannot obtain
515 I, 24| universals which comprise the imperishable, particulars that tend to
516 II, 19| which even sense-perception implants the universal is inductive.
517 I, 1 | exhibiting the universal as implicit in the clearly known particular.
518 I, 22| assume first that predication implies a single subject and a single
519 II, 19| knowledge of objects of which no impression persists; animals in which
520 II, 5 | definer asks "Is man animal or inanimate?" and then assumes-he has
521 I, 17| before.~(b) The middle may be inappropriate. Then (i) if D is subordinate
522 I, 3 | demonstration" be extended to include that other method of argument
523 II, 13| the differentiae are all included, because there is now no
524 I, 10| and cube, geometry that of incommensurable, or of deflection or verging
525 II, 17| involving a given determinate increment. In all proportionals this
526 I, 12| B of C, C of D, and so indefinitely. Or the expansion may be
527 I, 3 | the immediate premisses is independent of demonstration. (The necessity
528 I, 12| number-a number or number taken indeterminately; B determinate odd number;
529 I, 6 | necessary premisses is also indicated by the fact that the objection
530 II, 13| if these have in common indifference alike to good and ill fortune,
531 II, 19| of a number of logically indiscriminable particulars has made a stand,
532 I, 18| abstractions only through induction-i.e. only because each subject
533 II, 2 | e.g. eclipse, equality or inequality, interposition or non-interposition.
534 I, 12| conclusion would in that case inevitably reciprocate. I might then
535 I, 16| the error resulting from inference-which here concerns us-takes many
536 II, 13| in definitions, just as inferential movement is the minimum
537 II, 5 | then assumes-he has not inferred-that man is animal. Next, when
538 I, 17| the true-conclusion is inferrible. Thus, let A be attributable
539 I, 6 | ignorant, whether he actually infers the mere fact through middle
540 I, 20| predicated of another ad infinitum, since you have an infinity
541 II, 13| definition, i.e. the simple infirma species, and the attributes
542 I, 32| coexist, e.g. "justice is injustice", and "justice is cowardice"; "
543 I, 1 | came to know "this figure inscribed in the semicircle" to be
544 I, 13| as we have often a clear insight into a universal, but through
545 II, 13| belongs-quantity or quality, for instance-he should examine the properties "
546 I, 12| special science-geometry for instance-what kind of error is it that
547 I, 4 | truly predicable of all instances-not of one to the exclusion
548 I, 34| hitting upon the middle term instantaneously. It would be exemplified
549 II, 19| given already, though with insufficient clearness. When one of a
550 II, 13| that it was intolerance of insult; it was this which drove
551 I, 12| these middle terms with an intellectual vision, while in dialectic
552 II, 11| Of the products of man’s intelligence some are never due to chance
553 II, 17| explanation in formal terms of the inter-relation of cause and effect is demanded,
554 I, 20| predicated of F, and that the intermediates-call them BB’B"...-are infinite,
555 I, 25| must be interposed. Let us interpose D between A and B, and E
556 I, 25| expanded, a middle must be interposed. Let us interpose D between
557 II, 12| eclipsed because the earth intervened, is becoming eclipsed because
558 II, 3 | to say with a point most intimately connected with our immediately
559 II, 13| had in common, that it was intolerance of insult; it was this which
560 I, 31| it in each instance and intuit that it must be so in all
561 I, 33| any concern of rational intuition-by rational intuition I mean
562 I, 6 | accidental premisses are invariable but not essential, as in
563 I, 22| then, that the predicate is invariably predicated strictly and
564 I, 13| and that is when they are investigated respectively by different
565 I, 10| essential attributes of which it investigates, e.g. in arithmetic units,
566 I, 29| subject.~A further point worth investigating is how many ways of proving
567 II, 14| genus of all our subjects of investigation-if e.g. they are animals, we
568 II, 5 | definitions reached by division invite the same question.~Thus
569 II, 17| not numbers, identical as involving a given determinate increment.
570 I, 10| the spoken word, to the inward discourse we cannot always
571 II, 2 | but without qualification is-and the cause through which
572 II, 2 | a fact or that the thing is-i.e. ascertained either the
573 I, 18| though they do not exist in isolation-it is consequently impossible
574 I, 24| particular demonstration issues in sense-perception.~
575 I, 6 | he will not even believe it-in which case he will be equally
576 II, 8 | actually a dialectical proof of it-so let us begin again and explain
577 II, 16| will be at once implied by it-the eclipse by the earth’s interposition,
578 I, 5 | that "all" triangles have it-unless "all" means "each taken
579 I, 33| man is the subject in both judgements, but the mode of inherence
580 II, 17| coagulation of sap at the junction of leaf-stalk and stem which
581 I, 21| If this assumption is justified, the series will also terminate
582 II, 13| definition by division one should keep three objects in view: (
583 I, 12| based on premisses of this kind-"of" the science but false-that
584 I, 31| through, the reason of the kindling would be clear to us because
585 II, 10| which we do not genuinely know-the cause of this difficulty
586 I, 24| prior, we have a kind of knowledge-a potential grasp-of the posterior
587 I, 24| this point we have full knowledge-but at this point our knowledge
588 I, 33| originative source of scientific knowledge-nor of indemonstrable knowledge,
589 I, 2 | is non-existent cannot be known-we cannot know, e.g. that the
590 II, 13| definable form; and nothing lacking, since any omission would
591 II, 11| light shines through a lantern (1) because that which consists
592 I, 6 | himself or in the fact and no lapse of memory on his part; then
593 II, 5 | here urge that though these lapses do occur, yet we can solve
594 I, 32| middle terms is finite; and lastly some of the basic truths
595 I, 12| Or the expansion may be lateral: e.g. one major A, may be
596 I, 32| the former are common, the latter-number, for instance, and magnitude-are
597 I, 33| can have the same object leads them to embrace many strange
598 II, 17| of sap at the junction of leaf-stalk and stem which defines deciduous.~
599 II, 16| eclipse or of the fall of the leaves-the possession of broad leaves,
600 I, 5 | denote that in which numbers, lengths, durations, and solids are
601 I, 4 | While he was walking it lightened": the lightning was not
602 I, 4 | walking it lightened": the lightning was not due to his walking;
603 II, 5 | division demonstrates as little as does induction. For in
604 I, 22| happens to be white is a log-not that white is the substratum
605 II, 5 | as was said in my formal logic, is the method of division
606 II, 17| For instance, the cause of longevity in quadrupeds is lack of
607 II, 17| cause? This cause we must look for. Let us call it C.~We
608 I, 2 | us than the object of our love. So since the primary premisses
609 I, 2 | attribute; e.g. the cause of our loving anything is dearer to us
610 II, 13| next examine other cases, Lysander, for example, or Socrates,
611 I, 10| while as regards unity and magnitude we assume also the fact
612 I, 32| latter-number, for instance, and magnitude-are peculiar.~
613 I, 11| it is true to predicate man-even if it be also true to predicate
614 II, 4 | is predicated of being a man-since it is true that in all instances
615 II, 15| subjects or in their mode of manifestation. This latter class may be
616 I, 13| existence though they are manifestations of forms. For the mathematical
617 II, 18| severally in which it is manifested, for that is the cause of
618 I, 5 | or qua numbers, but qua manifesting this generic character which
619 I, 13| thus predicable that the mathematician demonstrates properties
620 I, 13| to know the fact, of the mathematicians to know the reasoned fact;
621 II, 13| does make a difference—it matters whether we say animal-tame-biped,
622 II, 10| 2) what are the various meanings of the term definition,
623 I, 13| subordinated to geometry, mechanical problems to stereometry,
624 I, 9 | demonstrations to theorems in mechanics or optics, or of arithmetical
625 I, 12| the notion that parallels meet is in one sense geometrical,
626 I, 6 | are necessary because one member or the other necessarily
627 I, 1 | with the dilemma in the Meno: either a man will learn
628 I, 9 | such exceptions as we have mentioned of the application of geometrical
629 II, 13| metaphors, clearly metaphors and metaphorical expressions are precluded
630 I, 33| art, practical wisdom, and metaphysical thinking, belongs rather
631 I, 32| as the law of excluded middle-serve as premisses for the proof
632 II, 17| subject, and after that a middle-the coagulation of sap or something
633 I, 23| system of weight it is the mina, in music the quarter-tone,
634 I, 16| but as a positive state of mind-is error produced by inference.~(
635 I, 24| considerations might lead some minds to prefer particular demonstration.~(
636 II, 13| inferential movement is the minimum required in demonstrations;
637 II, 11| premiss is assumed-two is the minimum-still when there are two it holds
638 I, 12| A, may be proved of two minors, C and E. Thus let A represent
639 I, 24| touches the real and will not mislead is superior to that which
640 I, 22| truths are demonstrable is mistaken. For if there are basic
641 I, 8 | that a fact is true at the moment-not commensurately and universally.
642 I, 34| divined that he was borrowing money, or that the friendship
643 I, 24| did he come?" "To get the money-wherewith to pay a debt-that he might
644 I, 8 | eclipse as happening to the moon-are, as such, clearly eternal:
645 I, 33| natural science, partly to moral philosophy.~
646 I, 12| attributable to fire in its motion. Sometimes, no doubt, it
647 II, 7 | call it the definition of mountain copper. For definitions
648 II, 13| definitions, just as inferential movement is the minimum required
649 I, 24| is superior to that which moves among unrealities and is
650 I, 22| definition of odd; of the former, multiplicity or the indivisible, which
651 I, 13| sciences not standing in this mutual relation enter into it at
652 II, 13| triad as a genus named or nameless. It will then be of wider
653 II, 8 | demonstration of essential nature-it is actually a dialectical
654 II, 3 | and assume the essential nature-mathematical demonstrations, for example,
655 I, 13| name; e.g. mathematical and nautical astronomy, mathematical
656 I, 31| by the act of perception: nay, it is obvious that even
657 I, 6 | them affirm facts which necessitate facts affirmed by the conclusion,
658 II, 11| exist for an end and be necessitated as well. For example, light
659 II, 2 | ask whether the moon or night exists, the question concerns
660 II, 15| For example: Why does the Nile rise towards the end of
661 II, 10| name, or of an equivalent nominal formula. A definition in
662 I, 25| because it is a sine qua non of negative demonstration.~
663 I, 16| other hand, an error of non-attribution may occur either in the
664 I, 2 | either the existence or the non-existence of a subject, it is a hypothesis;
665 I, 2 | true: for that which is non-existent cannot be known-we cannot
666 II, 7 | be definable, since even non-existents can be signified by a name: (
667 II, 2 | inequality, interposition or non-interposition. For in all these examples
668 I, 6 | Thus: let A be predicated non-necessarily of C but necessarily of
669 I, 21| of which A is primarily non-predicable. In the second figure the
670 I, 21| series of more universal non-predicables will terminate also. Even
671 I, 6 | But when the conclusion is nonnecessary the middle cannot be necessary
672 I, 10| statements that anything is or is not-are not hypotheses: but it is
673 I, 11| be also true to say that not-Callias—is animal and not not-animal.
674 I, 11| be also true to predicate not-man of it—still grant simply
675 I, 4 | necessary consequent of not-odd. So, since any given predicate
676 II, 1 | the sun suffers eclipse or not-then we are asking as to the
677 II, 19| demonstration and fail to notice them. If on the other hand
678 I, 12| ungeometrical, whereas the notion that parallels meet is in
679 I, 12| E. Thus let A represent number-a number or number taken indeterminately;
680 I, 22| is odd as an attribute of number-though it is number’s attribute,
681 I, 4 | and compound, square and oblong, to number; and also the
682 I, 13| business of the empirical observers to know the fact, of the
683 II, 13| investigation: We must start by observing a set of similar-i.e. specifically
684 I, 31| imperceptible, we clearly cannot obtain scientific knowledge by
685 I, 4 | instance in which, or an occasion on which, it is not true.
686 II, 12| that again the first.~Some occurrences are universal (for they
687 I, 8 | science of merely frequent occurrences-e.g. of eclipse as happening
688 I, 4 | curvature, in number either oddness or evenness. For within
689 I, 1 | these latter make use of old knowledge to impart new,
690 I, 16| causes and in this form only-for we found that no syllogism
691 I, 32| premisses, yet this occurs once only-I mean if A for instance,
692 I, 25| something else is not, and thus operating through more kinds of premiss
693 I, 27| which is a science of pr,operties inhering in a substratum;
694 I, 33| concerned is the same, the two opinions have objects so far the
695 I, 6 | at any rate so far as our opponent’s previous argument goes.
696 II, 11| food from rising to the orifice of the stomach, and let
697 II, 12| actually have their source of origin in previous events—a fact
698 II, 11| the production does not originate in chance, and the end is
699 II, 14| as if there were a single osseous nature.~
700 II, 7 | knows what human-or any other-nature is, must know also that
701 I, 4 | one to the exclusion of others-and at all times, not at this
702 I, 33| capable and incapable of being otherwise-an impossibility. Knowledge
703 I, 33| animal" as capable of being otherwise-e.g. the apprehension that
704 II, 4 | primary and immediate-which we ought to investigate, because
705 I, 22| some-referred to at the outset-that all truths are demonstrable
706 I, 12| though the possibility is overlooked. If false premisses could
707 I, 3 | 3~Some hold that, owing to the necessity of knowing
708 I, 32| man is horse", and "man is ox"; "the equal is greater",
709 I, 21| no B is A, all C is B. In packing the interval B-C we must
710 I, 6 | own essential nature. (The pairs of opposites which the latter
711 I, 2 | them the name of axioms par excellence. If a thesis
712 I, 2 | But we are faced with this paradox if a student whose belief
713 I, 5 | But it is not so, for the parallelism depends not on these angles
714 I, 12| whereas the notion that parallels meet is in one sense geometrical,
715 II, 11| consists of relatively small particles necessarily passes through
716 II, 11| pores larger than those particles-assuming that light does issue by
717 I, 33| many strange doctrines, particularly the doctrine that what a
718 I, 24| substance apart from its particulars-any more than we need make a
719 I, 28| entities of the genus-i.e. the parts of this total subject-and
720 I, 3 | premisses are true. The other party agree with them as regards
721 II, 11| small particles necessarily passes through pores larger than
722 I, 31| the glass and the light passing through, the reason of the
723 I, 22| essentially related, active, passive, placed, or dated.~(2) Predicates
724 II, 12| subsequently to A but still in the past-and the same holds good if the
725 I, 24| get the money-wherewith to pay a debt-that he might thereby
726 II, 11| that light does issue by penetrationand (2) for an end, namely to
727 II, 2 | inquire, because we have not perceived it, whether there is or
728 I, 5 | supposed that lines thus perpendicular were the proper subject
729 I, 5 | a proof were given that perpendiculars to the same line are parallel,
730 II, 13| possess any identity, and persevere until we reach a single
731 II, 11| Athenians become involved in the Persian war?" means "What cause
732 II, 19| sense-impression comes to persist, in others it does not.
733 II, 19| objects of which no impression persists; animals in which it does
734 I, 33| simultaneously in the same person. That would involve a man’
735 I, 1 | known particular. Again, the persuasion exerted by rhetorical arguments
736 II, 16| cause is not present, these phenomena will have some other cause:
737 I, 13| province of the natural philosopher, knowledge of the reasoned
738 I, 33| science, partly to moral philosophy.~
739 I, 22| related, active, passive, placed, or dated.~(2) Predicates
740 II, 3 | animal, nor yet figure of plane-plane not being figure nor figure
741 I, 29| and A of D, for he who is pleased suffers alteration of a
742 I, 6 | possess knowledge. For (1) popular acceptance or rejection
743 I, 6 | proposition which is (1) popularly accepted and (2) true, such
744 I, 18| loss of a corresponding portion of knowledge, and that,
745 I, 10| elements: (1) that which it posits, the subject genus whose
746 I, 6 | middle term; otherwise its possessor will know neither the cause
747 I, 10| science and from illegitimate postulate-I say "must believe", because
748 I, 5 | character which they are postulated as possessing universally.
749 II, 5 | definable form, and if, postulating the genus, we produce by
750 I, 24| commensurate universal either potentially or actually. Moreover, commensurately
751 II, 14| name to give to a squid’s pounce, a fish’s spine, and an
752 II, 19| sense-impressions develop a power of systematizing them and
753 I, 27| harmonics, which is a science of pr,operties inhering in a substratum;
754 I, 33| intuition, science, art, practical wisdom, and metaphysical
755 I, 24| clearest indication of the precedence of commensurately universal
756 I, 1 | were to know it in that precise sense and manner in which
757 II, 13| metaphorical expressions are precluded in definition: otherwise
758 II, 13| fallacy: not every differentia precludes identity, since many differentiae
759 I, 23| take a primary essential predicate-suppose it C-of the subject B, and
760 II, 4 | subjects of which it is predicated-A will not necessarily be
761 I, 22| generally we have the following prefatory remarks to make. (1) We
762 I, 24| might lead some minds to prefer particular demonstration.~(
763 I, 24| which teaches two things is preferable to demonstration which teaches
764 I, 24| an additional reason for preferring commensurately universal
765 I, 12| of course never has the prefix "all"); and in mathematics
766 I, 16| some B is C, then if it is premised that all A is C and no B
767 I, 3 | thing-be it one term or one premiss-never involves a necessary consequent:
768 II, 12| convertibility of conclusions and premisses-has been proved in our early
769 I, 2 | not only know the primary premisses-some if not all of them-beforehand,
770 II, 13| the physician does not prescribe what is healthy for a single
771 II, 16| present, and if coagulation is present-not in any subject but in a
772 II, 5 | man is animal. Next, when presented with an exhaustive division
773 II, 7 | attribute. Therefore, since presumably one cannot prove essential
774 II, 11| possess the property of preventing food from rising to the
775 I, 4 | random instance of itself and primarily-that is the first subject to
776 I, 1 | rhetorical arguments is in principle the same, since they use
777 I, 4 | attribute is either its privative or its contradictory; e.g.
778 II, 2 | being of the thing-and are proceeding to ask the reason of the
779 II, 2 | or is there not a cause producing eclipse of the moon?", and
780 I, 7 | science, nor even that the product of two cubes is a cube.
781 II, 11| indeterminate (though only where the production does not originate in chance,
782 I, 6 | objection we raise against a professed demonstration is that a
783 I, 3 | Since then-by the circular proof-if A is, B must be, and if
784 I, 3 | scientific knowledge nor properly knowing at all, but rests
785 I, 6 | determinate premisses should be proposed in order to deal with such
786 I, 23| seeing that the immediate propositions-or at least such immediate
787 I, 21| will be proved by a similar prosyllogism. But since it is assumed
788 I, 25| premiss, A-D. In the further prosyllogisms too it is the same, because
789 II, 7 | being of everything must be proved-unless indeed to be were its essence;
790 I, 32| each subject-genus will provide one basic truth. If, however,
791 I, 14| figure which enables us to pursue knowledge of the essence
792 II, 11| and also designed, as the Pythagoreans say, for a threat to terrify
793 II, 17| the cause of longevity in quadrupeds is lack of bile, in birds
794 I, 32| attach to quanta and some to qualia only; and proof is achieved
795 I, 9 | arithmetical properties, but with a qualification-the fact falls under a separate
796 II, 1 | thing is thus or otherwise qualified-whether, e.g. the sun suffers eclipse
797 I, 7 | of the circle; for these qualities do not belong to lines in
798 I, 32| some attributes attach to quanta and some to qualia only;
799 I, 2 | that to be a unit is to be quantitatively indivisible; but it is not
800 II, 12| then blocks must have been quarried and shaped. The reason is
801 I, 23| is the mina, in music the quarter-tone, and so on—so in syllogism
802 II, 10| latter will clearly be a quasi-demonstration of essential nature, differing
803 I, 26| inherence of B in C is not questioned, A’s inherence in B is impossible.~
804 I, 1 | says he does know it. The questioner then produces a particular
805 I, 34| 34~Quick wit is a faculty of hitting
806 I, 34| turned towards the sun, and quickly grasped the cause of this,
807 II, 11| answer is, "Because they raided Sardis with the Eretrians",
808 II, 19| of them is made clear by raising some preliminary problems.~
809 I, 4 | does one take a figure at random-a square is a figure but its
810 II, 19| sort, but not such as to rank higher in accuracy than
811 I, 3 | convertible terms occur rarely in actual demonstrations,
812 II, 17| latter case equality of the ratios of the sides and equality
813 II, 13| when by this process one reaches subjects incapable of further
814 II, 13| that equivocation is less readily detected in genera than
815 I, 24| universal, and less touches reality than does particular demonstration,
816 II, 12| questions, however, must receive a more explicit treatment
817 I, 1 | ALL instruction given or received by way of argument proceeds
818 | recent
819 II, 17| And the middle likewise reciprocates, for the middle is a definition
820 I, 12| reciprocate, infer A from B.~Reciprocation of premisses and conclusion
821 II, 12| conversion is conditioned by reciprocity in the terms of the proof.
822 I, 1 | simultaneously with that recognition-knowledge, this latter, of the particulars
823 I, 31| by watching the frequent recurrence of this event we might,
824 II, 3 | and in what way it can be reduced to demonstration; what definition
825 I, 3 | in addition their theory reduces to the mere statement that
826 I, 31| connexions to be proved which are referred for their explanation to
827 II, 15| respectively of echo, of reflection, and of the rainbow: the
828 I, 12| and obviously cannot even refute the geometer except accidentally.
829 II, 17| conjunctions would not be regarded as connexions demanding
830 I, 6 | 1) popular acceptance or rejection is no criterion of a basic
831 I, 24| substance but quality, essential relatedness, or action. If such a supposition
832 I, 24| demonstrable: but since relative and correlative increase
833 I, 29| feeling pleasure, and G relaxation. We can then without falsehood
834 I, 11| from equals leaves equal remainders, or other axioms of the
835 I, 13| in making the cause too remote, as in Anacharsis’ account
836 I, 24| being the higher term would render the demonstration which
837 II, 15| because all three are forms of repercussion; but specifically they are
838 II, 15| proved through "reciprocal replacement"-and of these one class
839 I, 27| prior to geometry, which requires additional elements. What
840 II, 17| sort. Again, connexions requiring proof which are identical
841 I, 1 | number or triangle without reservation. For no premiss is ever
842 I, 12| never give true conclusions "resolution" would be easy, for premisses
843 II, 5 | its premisses, even if the respondent deny it. The definer asks "
844 I, 6 | Demonstrative knowledge must rest on necessary basic truths;
845 II, 19| this process.~Let us now restate the account given already,
846 I, 3 | the original conclusion rested, by circular demonstration
847 II, 19| original formation has been restored. The soul is so constituted
848 II, 13| similarity not unqualified but restricted to colours and to figures;
849 II, 12| of cloud rain necessarily resulted and by the fall of rain
850 II, 13| said, is not the case.~To resume our account of the right
851 I, 6 | knowledge now, though he still retains the steps of the argument,
852 I, 24| particular demonstration.~We may retort thus. (1) The first argument
853 II, 7 | meaning of a name, also reveal that the name has this meaning.
854 II, 7 | definitions, in addition to revealing the meaning of a name, also
855 II, 11| order of coming to be is the reverse of what it is in proof through
856 I, 1 | the persuasion exerted by rhetorical arguments is in principle
857 I, 6 | suppose one’s basic truths rightly chosen if one starts with
858 II, 12| and when an exhalation had risen cloud was bound to form,
859 II, 11| of preventing food from rising to the orifice of the stomach,
860 II, 11| thunder be a hiss and a roar necessarily produced by
861 II, 8 | a screen, or the moon’s rotation or her extinction? But B
862 II, 19| sense-perception. It is like a rout in battle stopped by first
863 II, 14| third stomach and only one row of teeth. Then since it
864 II, 19| stand is made among these rudimentary universals, and the process
865 II, 12| connexions which embody a general rule-i.e. which exist or come to
866 II, 12| come to be as a general rule-will also derive from immediate
867 II, 11| others, such as health or safety, may result from chance
868 II, 11| walk after supper? For the sake of one’s health. Why does
869 II, 11| is, "Because they raided Sardis with the Eretrians", since
870 I, 2 | Unless these conditions are satisfied, the basic truths will not
871 I, 5 | attribute remains. "But"-you may say- "eliminate figure or limit,
872 I, 3 | if on the other hand-they say-the series terminates and there
873 I, 1 | every pair is even?" He says he does know it. The questioner
874 I, 3 | the premisses. The first school, assuming that there is
875 I, 12| Further, in each special science-geometry for instance-what kind of
876 II, 2 | present fact of the earth’s screening the sun’s light, and from
877 I, 13| Anacharsis’ account of why the Scythians have no flute-players; namely
878 I, 4 | demonstration only in a secondary and unessential sense. Nor
879 II, 13| and that the subject one seeks to define is present in
880 | seems
881 II, 13| dyad-and then endeavour to seize their definitions by the
882 I, 10| which expresses necessary self-grounded fact, and which we must
883 I, 32| identical because they are self-identical is absurd, since everything
884 II, 19| the persistence of such sense-impressions develop a power of systematizing
885 I, 8 | i.e. in the unqualified sense-must also be eternal. Therefore
886 I, 31| knowledge is more precious than sense-perceptions and than intuition. (As
887 I, 24| right angles, one knows in a sense-potentially-that the isosceles’ angles also
888 II, 2 | in which the "middle" is sensible show that the object of
889 II, 7 | definitions, since any kind of sentence could be given a name; so
890 II, 7 | 2) all sets of words or sentences would be definitions, since
891 II, 5 | requisite uninterrupted sequence of terms, and omit nothing;
892 I, 22| of an infinite ascending series-every predication displays the
893 I, 15| if G-a term in the former series-is the genus of A, clearly
894 I, 29| different, i.e. not in the same series-yet not so that neither of these
895 I, 22| White" and "log" will thus serve as types respectively of
896 I, 19| terms. One kind of syllogism serves to prove that A inheres
897 I, 9 | therefore, which the subject may share with another-and consequently
898 I, 7 | through some property which it shares with other genera.~
899 II, 16| for instance, if a plant sheds its leaves or the moon is
900 II, 11| well. For example, light shines through a lantern (1) because
901 I, 25| postulates or hypotheses-in short from fewer premisses; for,
902 I, 19| prove that A inheres in C by showing that A inheres in B and
903 II, 7 | even non-existents can be signified by a name: (2) all sets
904 I, 6 | essential, as in proofs through signs; for though the conclusion
905 II, 13| start by observing a set of similar-i.e. specifically identical-individuals,
906 II, 13| established e.g. the definition of similarity not unqualified but restricted
907 II, 12| cases where they are not simultaneous? Can causes and effects
908 I, 25| of proof, because it is a sine qua non of negative demonstration.~
909 I, 24| becomes particular the more it sinks into an indeterminate manifold,
910 I, 6 | is liable to perish, this situation is possible and might occur.
911 I, 13| circular wounds heal more slowly, the geometer’s to know
912 II, 11| which consists of relatively small particles necessarily passes
913 I, 3 | constitute the first and smallest foundation for drawing a
914 II, 13| Lysander, for example, or Socrates, and then if these have
915 I, 24| is neither line, number, solid, nor plane, but a proportionate
916 II, 12| attributed to C, and A, solidification, to B: ice when B is occurring,
917 II, 5 | lapses do occur, yet we can solve that difficulty if all the
918 I, 22| and that the contention of some-referred to at the outset-that all
919 I, 34| light from him; or observed somebody in conversation with a man
920 II, 13| further divisible-i.e. that as soon as we have taken the last
921 II, 8 | apprehend the reason a moment sooner than the fact; and clearly
922 I, 2 | accidental way in which the sophist knows, when we think that
923 I, 5 | does not yet know, except sophistically, that triangle has its angles
924 I, 6 | and (2) true, such as the sophists’ assumption that to know
925 II, 17| sap or something of the sort-proving the connexion of the first
926 II, 13| of acuteness, but only of sound-and so proceed to the common
927 I, 9 | would possess universal sovereignty. This is so because he knows
928 I, 14| exclusively or generally speaking and in most cases in this
929 I, 10| particular line of which he speaks, but from what his diagrams
930 II, 16| commensurately to those species-i.e. either to all species
931 II, 13| genus into its first infimae species-number e.g. into triad and dyad-and
932 II, 5 | ultimately) incapable of fresh specific division. Nevertheless,
933 I, 1 | mathematical sciences and all other speculative disciplines are acquired
934 I, 25| fewer knowledge will be more speedily acquired, and that is a
935 I, 23| single". And as in other spheres the basic element is simple
936 II, 14| squid’s pounce, a fish’s spine, and an animal’s bone, although
937 II, 8 | failure to produce shadows in spite of the absence of an intervening
938 II, 13| is either whole-winged or split-winged but all winged animal, for
939 I, 34| friendship of these people sprang from a common enmity. In
940 I, 9 | like Bryson’s method of squaring the circle; for they operate
941 II, 14| identical name to give to a squid’s pounce, a fish’s spine,
942 II, 19| from the universal now stabilized in its entirety within the
943 I, 13| optician. Many sciences not standing in this mutual relation
944 I, 3 | that if behind the prior stands no primary, we could not
945 I, 10| which are not expressed as statements that anything is or is not-are
946 II, 11| for example a house or a statue; others, such as health
947 II, 17| junction of leaf-stalk and stem which defines deciduous.~
948 I, 13| mechanical problems to stereometry, harmonic problems to arithmetic,
949 II, 11| instance, by necessity a stone is borne both upwards and
950 | stop
951 II, 19| is like a rout in battle stopped by first one man making
952 I, 4 | e.g. in line must be either straightness or curvature, in number
953 II, 11| namely to save us from stumbling. If then, a thing can exist
954 II, 14| throughout the remaining subgenera always the same rule applies.~
955 II, 14| virtue of what character the subgenera-man, e.g. or horse-possess their
956 I, 28| the parts of this total subject-and their essential properties.~
957 I, 9 | and "appropriate" to the subject-unless we know, e.g. the property
958 II, 12| true to say that B, the subsequent event, occurred; for in
959 II, 12| an event B has occurred subsequently to A but still in the past-and
960 II, 2 | and a low note", we may substitute "What ratio makes a high
961 I, 3 | is, A must be, A may be substituted for C above. Then "if B
962 I, 22| a coincident is never a substratum-since we do not class as a coincident
963 I, 22| contrary, log is here the substratum-the substratum which actually
964 I, 19| with "humanity" within one substratum-therefore there are terms such as
965 I, 11| middle, the law that the subtraction of equals from equals leaves
966 I, 20| is of no moment, for the succeeding terms in any case are infinite
967 I, 22| essentially related, acting or suffering, or in some place or at
968 II, 12| change.~The following must suffice as an account of the manner
969 II, 3 | other.~Induction too will sufficiently convince us of this difference;
970 II, 13| Achilles wrath, and Ajax to suicide. We should next examine
971 I, 34| represent "bright side turned sunward", B "lighted from the sun",
972 II, 13| is clear that there is no superfluous addition, since all these
973 I, 5 | are parallel, it might be supposed that lines thus perpendicular
974 I, 1 | This becomes evident upon a survey of all the species of such
975 I, 2 | when, though it is not susceptible of proof by the teacher,
976 II, 8 | syllogism-i.e. no demonstrative syllogism-of essential nature, yet it
977 II, 4 | may be. Then, if we are to syllogize, A must be predicated of
978 II, 6 | too?~Further, just as in syllogizing we do not premise what syllogistic
979 I, 10| but from what his diagrams symbolize. A further distinction is
980 II, 17| inhering in virtue of a symptom or an accident-because the
981 I, 23| not identical in all-in a system of weight it is the mina,
982 II, 19| sense-impressions develop a power of systematizing them and those which do
983 II, 7 | so that we should all be talking in definitions, and even
984 II, 11| terrify those that lie in Tartarus? Indeed, there are very
985 II, 14| stomach and only one row of teeth. Then since it is clear
986 II, 11| be first, whereas in the teleological order the minor, C, must
987 II, 10| definition in this sense tells you, e.g. the meaning of
988 I, 8 | commensurately universal but temporary and special. If such a demonstration
989 I, 24| imperishable, particulars that tend to perish.~(3) Because the
990 II, 11| accordance with a thing’s natural tendency, or by constraint and in
991 I, 24| universal demonstration tends to the simple and determinate.
992 II, 17| definition of the major term-though possible if the demonstration
993 II, 5 | is the complete formula, terrestrial-animal, does not follow necessarily
994 II, 11| Pythagoreans say, for a threat to terrify those that lie in Tartarus?
995 I, 13| cause is not contained in them-a necessary condition of knowledge
996 I, 11| demonstrated as belonging to them-all the sciences have communion
997 I, 22| in number and number in them-as to be commensurate with
998 I, 2 | premisses-some if not all of them-beforehand, but know them better than
999 I, 2 | is, are more convinced of them-than their consequences, precisely
1000 I, 3 | if A is, C must be. Since then-by the circular proof-if A