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1 I, 20| 20~Now, it is clear that if
2 I, 21| 21~Further, if in affirmative
3 I, 22| 22~In the case of predicates
4 I, 23| 23~It is an evident corollary
5 I, 24| 24~Since demonstrations may
6 I, 25| 25~The preceding arguments
7 I, 26| 26~Since affirmative demonstration
8 I, 27| 27~The science which is knowledge
9 I, 28| 28~A single science is one
10 I, 29| 29~One can have several demonstrations
11 I, 30| 30~There is no knowledge by
12 I, 31| 31~Scientific knowledge is
13 I, 32| 32~All syllogisms cannot have
14 I, 33| 33~Scientific knowledge and
15 I, 34| 34~Quick wit is a faculty of
16 I, 22| B cannot be a quality of A-a quality of a quality. Therefore
17 II, 14| character B inheres in D-namely A-and that it inheres in C and
18 I, 13| is an attribute of C, and A-not twinkling-of B. Consequently
19 I, 22| genus or differentia of A-the predicate now become subject.
20 I, 20| some terms of the series AB...F are contiguous so as
21 II, 17| otherwise how shall we be able to say that A is predicable
22 I, 7 | the genus must be either absolutely or to some extent the same.
23 I, 18| the so-called mathematical abstractions only through induction-i.
24 II, 5 | another way. Nor is there any absurdity in this: induction, perhaps,
25 II, 13| differentiae are a useful accessory to this method. What force
26 II, 2 | essential attribute or some accident-are both alike the middle".
27 II, 17| virtue of a symptom or an accident-because the middle is then the definition
28 II, 3 | anything-essential attribute or accident-did we get knowledge of it.
29 II, 11| two kinds. It may work in accordance with a thing’s natural tendency,
30 II, 19| such as to rank higher in accuracy than these developed states.
31 I, 15| If no term in the series ACD...is predicable of any term
32 I, 13| astronomy, mathematical and acoustical harmonics.) Here it is the
33 I, 24| essential relatedness, or action. If such a supposition is
34 I, 22| quantified, essentially related, active, passive, placed, or dated.~(
35 II, 13| figures; the definition of acuteness, but only of sound-and so
36 I, 10| fortiori demonstration, is addressed not to the spoken word,
37 I, 18| sense-perception alone which is adequate for grasping the particulars:
38 II, 13| totality, this totality admits of no division into species.
39 II, 13| discuss the method to be adopted in tracing the elements
40 I, 12| anything which can be validly advanced as an "objection" must be
41 I, 3 | unqualified sense of the term.~The advocates of circular demonstration
42 I, 11| that the conclusion is not affected even if the middle is extended
43 I, 9 | in kind. They therefore afford knowledge of an attribute
44 II, 8 | 8~We must now start afresh and consider which of these
45 II, 19| experience. From experience again-i.e. from the universal now
46 II, 11| men make war on the unjust aggressor. So A, having war waged
47 I, 3 | are true. The other party agree with them as regards knowing,
48 I, 19| syllogism. If, however, one is aiming at truth, one must be guided
49 I, 19| inheres in C. If our reasoning aims at gaining credence and
50 I, 23| simple but not identical in all-in a system of weight it is
51 II, 13| subjects not numbers at all-odd on the other hand is an
52 II, 19| single identity within them all-originate the skill of the craftsman
53 II, 5 | appropriate middles, the alleged necessity by which the inference
54 | almost
55 I, 5 | proportionals alternate. Alternation used to be demonstrated
56 I, 29| property, and that which alters a property changes. Again,
57 | although
58 I, 6 | truth-whether we think it altogether devoid of necessity, or
59 I, 2 | and "better known" are ambiguous terms, for there is a difference
60 II, 13| element have equanimity amid the vicissitudes of life
61 II, 8 | that this method could not amount to demonstration of essential
62 I, 13| cause too remote, as in Anacharsis’ account of why the Scythians
63 II, 14| prove we have to select our analyses and divisions. The method
64 I, 32| sciences, nor is it possible in analysis, since it is the immediate
65 [Title] | Posterior Analytics~
66 I, 33| e. cannot be other than animal-and (2) that man is not essentially
67 II, 6 | question why man should be animal-biped-terrestrial and not merely animal and
68 II, 4 | true that every man is an animal-but not as identical with being
69 I, 33| that man is essentially animal-i.e. cannot be other than
70 II, 13| consists of two elements and "animal-tame" forms a unity, and again
71 II, 13| it matters whether we say animal-tame-biped, or biped-animal-tame. For
72 I, 9 | the subject may share with another-and consequently they apply
73 I, 13| wall breathe?" might be answered, "Because it is not an animal";
74 I, 6 | propositions which if the answerer affirm, he must affirm the
75 I, 2 | in order to be causes; antecedently known, this antecedent knowledge
76 I, 26| conclusion, nor are its antecedents proper premisses. On the
77 II, 3 | for never yet by defining anything-essential attribute or accident-did
78 I, 9 | belong. Thus, even these apparent exceptions show that no
79 II, 7 | prove essential nature by an appeal to sense perception or by
80 II, 7 | name has this meaning. It appears then from these considerations
81 I, 12| premisses, he is clearly to be applauded; if he goes outside these
82 II, 19| it means that we possess apprehensions more accurate than demonstration
83 I, 24| universal as its middle term approaches nearer to the basic truth,
84 II, 5 | animal into terrestrial and aquatic, he assumes that man is
85 I, 32| If, however, it is not argued that from the mass of all
86 I, 19| questions then cannot be asked-unless, indeed, the terms can reciprocate
87 II, 5 | respondent deny it. The definer asks "Is man animal or inanimate?"
88 I, 13| and conversely, if the assertion of x causes the inherence
89 II, 11| hold if only one premiss is assumed-two is the minimum-still when
90 II, 5 | or inanimate?" and then assumes-he has not inferred-that man
91 II, 13| demonstrations; and we shall attain perspicuity if we can collect
92 I, 24| causes also full knowledge is attained when an attribute no longer
93 I, 11| any science which might attempt a universal proof of axioms
94 I, 24| something else is x—e.g. in attempting to prove that isosceles
95 I, 19| prior to B to which a is not attributable-G, let us say, which is attributable
96 I, 9 | truths appropriate to each attribute-the differentia of true knowledge.
97 II, 12| failure of heat. Then B is attributed to C, and A, solidification,
98 I, 19| or that both subjects and attributes-and we raised the question in
99 II, 14| character they possess these attributes-namely their horned character-the
100 I, 1 | the syllogism assuming an audience that accepts its premisses,
101 II, 4 | nature—two-footed animal, or aught else it may be. Then, if
102 II, 13| being of the subject.~The author of a hand-book on a subject
103 II, 13| universal with a careful avoidance of equivocation. We may
104 II, 13| only possible method of avoiding the omission of any element
105 II, 8 | negative state as regards awareness of its essential nature;
106 I, 32| Nor can any of the common axioms-such, I mean, as the law of excluded
107 I, 19| which is attributable to all B-and there may still be another
108 I, 15| if C is not the genus of B-for A may well have a genus
109 I, 15| which is not the genus of B-there will be a syllogism proving
110 I, 12| geometry at all, in the other bad geometry? It is this error,
111 I, 2 | does not constitute a total bar to progress on the part
112 II, 16| through the cause is of the bare fact, one who knows it through
113 I, 11| interrogative method is barred to the demonstrator, who
114 II, 19| apprehend and learn without a basis of pre-existent knowledge?
115 II, 19| sense-perception. It is like a rout in battle stopped by first one man
116 I, 20| intermediates-call them BB’B"...-are infinite, then
117 I, 3 | saying that if A is, A must be-a simple way of proving anything.
118 I, 24| coming-or being or coming to be-and we regard ourselves as then
119 I, 13| Some of these sciences bear almost the same name; e.g.
120 II, 12| not every man can grow a beard, but it is the general rule.
121 I, 4 | is essential; e.g. if a beast dies when its throat is
122 I, 7 | straight line is the most beautiful of lines or the contrary
123 I, 15| of any term in the series BEF...,and if G-a term in the
124 I, 16| true, positive error may befall one in alternative ways;
125 II, 4 | through reciprocating terms beg the question. It would be
126 II, 4 | the question. It would be begging the question, for example,
127 | beginning
128 II, 6 | hypothetical proof also begs the question. If evil is
129 | behind
130 I, 9 | the science to which they belonged would possess universal
131 II, 13| which the subaltern genus belongs-quantity or quality, for instance-he
132 | below
133 I, 2 | follows that we know them better-that is, are more convinced of
134 II, 17| in quadrupeds is lack of bile, in birds a dry constitution-or
135 II, 13| say animal-tame-biped, or biped-animal-tame. For if every definable
136 II, 14| essential properties of every bird-and so on, always characterizing
137 II, 17| quadrupeds is lack of bile, in birds a dry constitution-or certainly
138 I, 24| supposition is entertained, the blame rests not with the demonstration
139 II, 14| s spine, and an animal’s bone, although these too possess
140 II, 11| by necessity a stone is borne both upwards and downwards,
141 I, 34| and divined that he was borrowing money, or that the friendship
142 I, 34| of this, namely that she borrows her light from him; or observed
143 I, 22| analytic process will show more briefly that neither the ascent
144 I, 12| premiss, one should not bring an "objection" against it.
145 I, 9 | knowledge. Such proofs are like Bryson’s method of squaring the
146 II, 4 | peculiar" to B and B to C-in fact all three terms are "
147 I, 23| essential predicate-suppose it C-of the subject B, and then
148 I, 12| An instance of this is Caeneus’ proof that fire increases
149 II, 19| discriminative capacity which is called sense-perception. But though
150 II, 13| common universal with a careful avoidance of equivocation.
151 I, 19| raised the question in both cases-are infinite in number. These
152 I, 22| of the other adjectival categories, or else is an element in
153 I, 24| the particular which is causative (as may be shown thus: that
154 II, 12| the middle which is the cause-except that if the effect actually
155 II, 11| aggressors. Hence here too the cause-in this case the efficient
156 II, 11| this case the efficient cause-is the middle term. (d) This
157 II, 11| it come to be through two causes-as for instance if thunder
158 II, 2 | is or is not a "middle" causing, e.g. an eclipse. On the
159 II, 19| and the process does not cease until the indivisible concepts,
160 II, 1 | whether there is or is not a centaur or a God. (By "is or is
161 II, 7 | which is equidistant from a centre, yet why should the thing
162 II, 17| birds a dry constitution-or certainly something different.~
163 I, 22| subject of the whole infinite chain of attributes, and be an
164 II, 5 | the substantial being?~The champion of division might here urge
165 I, 29| which alters a property changes. Again, we can predicate
166 II, 12| been proved in our early chapters, and the circular process
167 I, 9 | as their middle a common character-a character, therefore, which
168 II, 14| attributes-namely their horned character-the next question is, to what
169 I, 24| Since, then, such a proof is characteristically commensurate and universal,
170 II, 5 | since at no point does the characterization of the subject follow necessarily
171 I, 33| knowledge? And if any one chooses to maintain that all that
172 I, 6 | one’s basic truths rightly chosen if one starts with a proposition
173 I, 12| minor premiss "Are epics circles?" is shown by the diagram
174 I, 3 | not convertible cannot be circularly demonstrated at all, and
175 II, 14| examples from the traditional class-names, but we must not confine
176 II, 14| the first of the remaining classes-e.g. if this first subgenus
177 I, 4 | case may be.~Extending this classification to all other attributes,
178 I, 24| forms, and when we have cleared up this problem proceed
179 II, 11| then the detail will become clearer. Incidentally, here the
180 I, 24| however, are dialectical. The clearest indication of the precedence
181 II, 19| though with insufficient clearness. When one of a number of
182 I, 10| truths of every genus those clements in it the existence of which
183 I, 14| and have their intervals closepacked until immediate premisses
184 I, 24| is characterized by this closer dependence, and is therefore
185 I, 33| opinion of the same thing can co-exist in two different people
186 I, 32| of one another and cannot coexist, e.g. "justice is injustice",
187 I, 29| other than the immediately cohering term e.g. by taking C, D,
188 I, 4 | it was, we should say, a coincidence. If, on the other hand,
189 I, 19| essentially or naturally and not coincidentally-not, that is, in the sense in
190 I, 22| constitutive elements with their coincidents-both of which are finite. We
191 I, 19| man because "being white" coincides with "humanity" within one
192 II, 13| but that merely towards collecting the essential nature they
193 I, 21| and if finite things are combined in a finite number of ways,
194 II, 12| universal (for they are, or come-to-be what they are, always and
195 I, 24| of it as the end of the coming-or being or coming to be-and
196 I, 12| geometers, for in such a company an unsound argument will
197 II, 12| starting-point, so that a circle is completed; for posit any one of the
198 I, 16| direct belief is without complication; but the error resulting
199 I, 4 | of triangle and line is composed of these elements, which
200 I, 4 | odd and even, prime and compound, square and oblong, to number;
201 II, 13| attributes of the genera compounded of the infimae species will
202 I, 1 | must be assumed, in others comprehension of the meaning of the term
203 II, 5 | assumption whether the division comprises many differentiae or few. (
204 II, 19| cease until the indivisible concepts, the true universals, are
205 II, 15| difference consists in their concerning different subjects or in
206 II, 5 | question nor depend on a concession, but must follow necessarily
207 I, 7 | 1) what is proved, the conclusion-an attribute inhering essentially
208 I, 24| and correlative increase concomitantly, of the more demonstrable
209 II, 2 | Again, for "What is a concord? A commensurate numerical
210 I, 23| the interval is constantly condensed until subject and predicate
211 I, 24| last step of a search thus conducted is eo ipso the end and limit
212 II, 14| class-names, but we must not confine ourselves to considering
213 I, 12| qua geometer the disputant confines himself to geometry and
214 I, 32| argue the case as follows, confining-ourselves therefore to true conclusions.
215 II, 19| animals, for they possess a congenital discriminative capacity
216 I, 2 | of a contradiction which conjoins a predicate with a subject
217 II, 4 | definition, and the middle term connecting them must be reciprocally
218 II, 12| coming-to-be is a series of consecutive events: for in the terms
219 I, 2 | convinced of them-than their consequences, precisely because of our
220 I, 4 | the other hand, there is a consequential connexion, the predication
221 I, 33| other than animal.~Further consideration of modes of thinking and
222 II, 14| not confine ourselves to considering these. We must collect any
223 I, 13| explanations, which precisely consist in making the cause too
224 II, 12| must start from a premiss consisting of a middle and the present
225 I, 23| the proof: the interval is constantly condensed until subject
226 II, 13| that the synthesis of them constitutes the substance of triad is
227 II, 17| of bile, in birds a dry constitution-or certainly something different.~
228 II, 11| natural tendency, or by constraint and in opposition to it;
229 I, 12| erroneous conclusion one constructed from premisses opposite
230 II, 13| else is the unity under construction) is constituted, then the
231 I, 1 | the predicate is always construed as applicable to any and
232 II, 4 | question, for example, to contend that the soul is that which
233 II, 19| is of the particular, its content is universal-is man, for
234 I, 6 | the mediating link is a contingent fact. Or again, if a man
235 I, 2 | truths in their character as contradicting the fundamental premisses
236 I, 4 | either its privative or its contradictory; e.g. within number what
237 II, 6 | definition of a thing’s contrary-if it has one the contrary
238 I, 34| or observed somebody in conversation with a man of wealth and
239 II, 12| terms are reciprocal, since conversion is conditioned by reciprocity
240 I, 17| the quality of A-D must be converted, and the type of error is
241 II, 12| terms of the proof. This-the convertibility of conclusions and premisses-has
242 I, 2 | our knowledge-i.e. of our conviction-it follows that we know them
243 I, 2 | our knowledge-i.e. of our conviction-of a fact is the possession
244 II, 3 | Induction too will sufficiently convince us of this difference; for
245 I, 2 | better-that is, are more convinced of them-than their consequences,
246 I, 15| existence of mutually exclusive coordinate series of predication. If
247 II, 7 | the definition of mountain copper. For definitions do not
248 I, 23| 23~It is an evident corollary of these conclusions that
249 I, 2 | of scientific knowing is correct, the premisses of demonstrated
250 I, 24| but since relative and correlative increase concomitantly,
251 II, 17| as such, the middle will correspond to the extremes, and be
252 I, 12| pass unnoticed. This is correspondingly true in the other sciences.~
253 I, 1 | For no premiss is ever couched in the form "every number
254 I, 11| the middle is extended to cover the original middle term
255 II, 3 | previous arguments which covers this too. Of a single thing
256 I, 32| injustice", and "justice is cowardice"; "man is horse", and "man
257 II, 19| all-originate the skill of the craftsman and the knowledge of the
258 I, 6 | acceptance or rejection is no criterion of a basic truth, which
259 I, 7 | that the product of two cubes is a cube. Nor can the theorem
260 I, 4 | be either straightness or curvature, in number either oddness
261 I, 4 | formula. Thus straight and curved belong to line, odd and
262 I, 4 | when its throat is being cut, then its death is also
263 II, 14| what character B inheres in D-namely A-and that it inheres in
264 I, 13| problems to arithmetic, the data of observation to astronomy. (
265 I, 22| active, passive, placed, or dated.~(2) Predicates which signify
266 II, 8 | the fact and the reason dawn on us simultaneously, yet
267 I, 6 | be proposed in order to deal with such and such determinate
268 I, 2 | of our loving anything is dearer to us than the object of
269 I, 24| money-wherewith to pay a debt-that he might thereby do what
270 I, 3 | either true or a necessary deduction from the premisses. The
271 I, 25| arguments constitute our defence of the superiority of commensurately
272 II, 5 | respondent deny it. The definer asks "Is man animal or inanimate?"
273 II, 17| leaf-stalk and stem which defines deciduous.~If an explanation
274 II, 13| two or more, evidently the definiendum cannot be one thing but
275 I, 10| without demonstration.~The definition-viz. those which are not expressed
276 I, 10| of incommensurable, or of deflection or verging of lines, whereas
277 I, 24| among unrealities and is delusory. Now commensurately universal
278 II, 17| inter-relation of cause and effect is demanded, we shall offer the following.
279 II, 17| be regarded as connexions demanding scientific proof. But if
280 I, 6 | necessary you will assuredly demonstrate-in such necessity you have
281 II, 4 | question whether syllogism-i.e. demonstration-of the definable nature is
282 I, 31| should still be looking for a demonstration-we should not (as some say)
283 II, 3 | things require different demonstrations-unless the one demonstration is
284 I, 5 | there was no single name to denote that in which numbers, lengths,
285 I, 2 | The term "enunciation" denotes either part of a contradiction
286 I, 24| characterized by this closer dependence, and is therefore superior.
287 II, 12| a general rule-will also derive from immediate basic premisses.~
288 II, 13| definitions by the method we have described-the definition, for example,
289 I, 4 | those that answer the above description as belonging essentially
290 I, 25| acquired, and that is a desideratum. The argument implied in
291 I, 22| anything which does not owe its designation to its being something other
292 II, 11| quenching of fire, and also designed, as the Pythagoreans say,
293 I, 5 | differentiae whose elimination destroys the attribute. "Then what
294 I, 26| of its premisses. For the destructive result of reductio ad impossibile
295 II, 11| transposed, and then the detail will become clearer. Incidentally,
296 II, 13| equivocation is less readily detected in genera than in infimae
297 I, 12| the ambiguity may escape detection. E.g. "Is every circle a
298 II, 5 | final or of an intermediate determinant of the substantial being?~
299 II, 8 | thing’s essential nature is determined by the sense in which we
300 II, 19| of such sense-impressions develop a power of systematizing
301 I, 6 | the conclusion must be the development of necessary premisses is
302 I, 6 | truth-whether we think it altogether devoid of necessity, or at any
303 I, 10| speaks, but from what his diagrams symbolize. A further distinction
304 I, 22| which before was shown dialectically, analytic proof has now
305 I, 4 | essential; e.g. if a beast dies when its throat is being
306 I, 5 | identical, and because they differed specifically from one another,
307 II, 10| why it exists. But it is difficult thus to learn the definition
308 II, 3 | us first discuss certain difficulties which these questions raise,
309 I, 1 | drawn, we are faced with the dilemma in the Meno: either a man
310 I, 21| series terminates in both directions, clearly it will terminate
311 I, 16| for it may arise where one directly believes a connexion or
312 I, 1 | and all other speculative disciplines are acquired in this way,
313 I, 15| call "atomic" connexions or disconnexions which involve no intermediate
314 II, 8 | how essential nature is discovered and becomes known, and we
315 II, 1 | inquiry ceases with the discovery that the sun does suffer
316 II, 19| they possess a congenital discriminative capacity which is called
317 II, 8 | contended in our preliminary discussions.~
318 II, 13| of life and impatience of dishonour. If they have none, there
319 I, 2 | an affirmation; the part disjoining them is a negation. I call
320 I, 22| white. The Forms we can dispense with, for they are mere
321 I, 21| and we will proceed to display the second, proof by which
322 I, 22| series-every predication displays the subject as somehow qualified
323 I, 13| inherence of y; e.g. if the disproportion of the hot and cold elements
324 I, 12| geometer qua geometer the disputant confines himself to geometry
325 II, 13| add that if dialectical disputation must not employ metaphors,
326 I, 12| reasoning from dialectical disputations.~A science expands not by
327 I, 6 | necessity you have at once a distinctive character of demonstration.
328 I, 4 | all other attributes, I distinguish those that answer the above
329 I, 33| modes of thinking and their distribution under the heads of discursive
330 II, 5 | conditions if what is to be divided falls whole into the division
331 II, 13| the lower divisions, the dividendum will not fall whole into
332 II, 5 | omitted; and that this-the dividendum-must without further question
333 II, 5 | essential nature of man?" the divider replies "Animal, mortal,
334 I, 34| with a man of wealth and divined that he was borrowing money,
335 II, 12| here too the same infinite divisibility might be urged, since future
336 II, 13| finally reach is not further divisible-i.e. that as soon as we have
337 II, 13| not only as possessing no divisors, but also as not being a
338 I, 33| to embrace many strange doctrines, particularly the doctrine
339 I, 28| single science is one whose domain is a single genus, viz.
340 I, 1 | unit" we have to make the double assumption of the meaning
341 II, 6 | It is only when some one doubts whether the conclusion proved
342 II, 11| is borne both upwards and downwards, but not by the same necessity.~
343 I, 10| stating that the line which he draws is a foot long or straight,
344 I, 1 | recognition or before he actually drew a conclusion, we should
345 II, 13| insult; it was this which drove Alcibiades to war, Achilles
346 II, 17| lack of bile, in birds a dry constitution-or certainly
347 II, 4 | take this relation as thus duplicated-if, that is, A is predicated
348 | during
349 II, 13| numbers, the last to the dyad also as well as to the triad,
350 II, 13| species-number e.g. into triad and dyad-and then endeavour to seize
351 II, 19| particulars has made a stand, the earliest universal is present in
352 II, 12| premisses-has been proved in our early chapters, and the circular
353 II, 13| species of eye. It is also easier by this method to define
354 II, 15| the causes respectively of echo, of reflection, and of the
355 I, 19| 19~Every syllogism is effected by means of three terms.
356 II, 12| simultaneous? Can causes and effects different from one another
357 I, 33| same object leads them to embrace many strange doctrines,
358 I, 13| it is the business of the empirical observers to know the fact,
359 I, 21| confined to one method, but employs them all and is now in the
360 II, 14| This will clearly at once enable us to say in virtue of what
361 II, 2 | of perception would have enabled us to know the universal
362 II, 13| triad and dyad-and then endeavour to seize their definitions
363 II, 3 | and the regress will be endless; or the primary truths will
364 I, 24| of the latter kind: if we engage in it we find ourselves
365 I, 34| people sprang from a common enmity. In all these instances
366 II, 6 | what they premise does not ensure that the predicates shall
367 II, 13| primary, and this will be ensured if the term selected is
368 I, 18| of any one of the senses entails the loss of a corresponding
369 I, 13| in this mutual relation enter into it at points; e.g.
370 I, 24| If such a supposition is entertained, the blame rests not with
371 I, 1 | a kind of induction, or enthymeme, a form of syllogism.~The
372 I, 17| both premisses cannot be entirely false; since if B is subordinate
373 I, 28| constituted out of the primary entities of the genus-i.e. the parts
374 I, 22| lay down a rule, let us entitle the latter kind of statement
375 I, 12| but the minor premiss "Are epics circles?" is shown by the
376 II, 13| what common element have equanimity amid the vicissitudes of
377 I, 22| the other; for this would equate a genus with one of its
378 II, 7 | exist something which is equidistant from a centre, yet why should
379 I, 5 | equilateral, i.e. with each or all equilaterals, then clearly we have unqualified
380 I, 24| triangle-i.e. the term is not equivocal-and since equality to two right
381 II, 11| they raided Sardis with the Eretrians", since this originated
382 II, 19| unfailingly true, others admit of error-opinion, for instance, and calculation,
383 I, 12| dialectic the ambiguity may escape detection. E.g. "Is every
384 I, 24| demonstration is superior as more especially proving the cause, that
385 II, 4 | both premisses do predicate essence-i.e. definable form-C’s definable
386 II, 13| one of the two sides.~In establishing a definition by division
387 II, 5 | any more than is division, et it does make evident some
388 | everywhere
389 I, 2 | something of this sort is evident-witness both those who falsely claim
390 I, 17| have been true; but it is ex hypothesi false.~When the
391 I, 2 | sense, and they are thus exactly opposed to one another.
392 II, 8 | figure. So the method just examined of proving it through another
393 I, 10| essential attributes it examines; (2) the so-called axioms,
394 I, 32| be drawn. That would be exceedingly naive, for it is not the
395 I, 2 | them the name of axioms par excellence. If a thesis assumes one
396 I, 25| affirmative demonstration excels negative may be shown as
397 II, 7 | particulars which offer no exception, because induction proves
398 I, 2 | which of its own nature excludes a middle. The part of a
399 I, 1 | particular. Again, the persuasion exerted by rhetorical arguments
400 II, 13| assumed that the two sides exhaust the genus, and that the
401 II, 5 | when presented with an exhaustive division of animal into
402 II, 13| animal, e.g. is divisible exhaustively into A and B, and that the
403 II, 13| postulate that the division exhausts the genus is not illegitimate
404 I, 3 | thing exists, then it does exist-an easy way of proving anything.
405 II, 7 | nature of what does not exist-one can know the meaning of
406 II, 12| same as when it is actually existent-for it is the middle which is
407 I, 12| argue thus: let A be an existing fact; let the existence
408 I, 25| premisses are to be again expanded, a middle must be interposed.
409 I, 12| so indefinitely. Or the expansion may be lateral: e.g. one
410 I, 25| negative (since affirmation explains denial and is prior to denial,
411 I, 13| causes are like far-fetched explanations, which precisely consist
412 II, 12| however, must receive a more explicit treatment in our general
413 II, 6 | possible even without the express statement of what syllogism
414 I, 10| basic premisses.~That which expresses necessary self-grounded
415 II, 13| metaphors and metaphorical expressions are precluded in definition:
416 II, 13| pentad), but which does not extend beyond the genus of triad;
417 I, 4 | number as the case may be.~Extending this classification to all
418 II, 17| their totality), and it extends beyond each of them taken
419 I, 3 | knowledge. But if we accept this extension of its meaning, our definition
420 II, 8 | the moon’s rotation or her extinction? But B is the definition
421 II, 13| single eye, but for all eyes or for a determinate species
422 I, 1 | in some cases contain as factors both previous knowledge
423 II, 7 | premisses admitted to be facts-the method of demonstration:
424 I, 23| infinity of intermediates would fall-an impossibility. Thus it need
425 I, 16| indifferently. A-C may be true, C-B false-A-C true because A is not an
426 I, 17| A, A-D will be true, D-B false-A-D true because A was not subordinate
427 I, 12| kind-"of" the science but false-that is the contrary of science.
428 I, 26| denying A of C. When the falsity of the conclusion is the
429 I, 18| since it is possible to familiarize the pupil with even the
430 I, 13| breathe. Such causes are like far-fetched explanations, which precisely
431 I, 12| outside these he will be at fault, and obviously cannot even
432 I, 3 | unqualified knowledge will prove faulty; for there seem to be two
433 II, 13| such elements. The first is feasible because one can establish
434 I, 29| falsehood, and G of B; for to feel pleasure is to relax, and
435 I, 29| alteration of a property, B feeling pleasure, and G relaxation.
436 II, 3 | the doubt that might be felt as to whether or not it
437 I, 12| fall within the defined field of his own science. If,
438 I, 14| and in most cases in this figure-a second proof that this figure
439 II, 7 | or by pointing with the finger, what other method remains?~
440 I, 2 | of the basic truths and a firmer conviction of them than
441 I, 2 | inheres in the subject more firmly than that attribute; e.g.
442 I, 32| transferred terms could only fit in as middle terms or as
443 I, 33| necessary. This view also fits the observed facts, for
444 I, 19| if the extreme terms are fixed, can there be an infinity
445 I, 13| why the Scythians have no flute-players; namely because they have
446 I, 19| stated, and proof is bound to follow-proof that A inheres in C through
447 I, 10| line which he draws is a foot long or straight, when it
448 II, 5 | replies "Animal, mortal, footed, biped, wingless"; and when
449 II, 4 | predicate essence-i.e. definable form-C’s definable form will appear
450 I, 4 | which are contained in the formulae defining triangle and line): (
451 II, 14| 14~In order to formulate the connexions we wish to
452 II, 13| indifference alike to good and ill fortune, I take these two results
453 I, 34| borrowing money, or that the friendship of these people sprang from
454 I, 3 | demonstrations, it is clearly frivolous and impossible to say that
455 II, 5 | indeed we cannot fail to fulfil these conditions if what
456 I, 24| demonstrable there will be fuller demonstration. Hence the
457 I, 8 | not eternal they are not fully commensurate. Other subjects
458 I, 24| creates the opinion that its function is conditioned by something
459 I, 2 | most universal causes are furthest from sense and particular
460 I, 15| the series BEF...,and if G-a term in the former series-is
461 I, 19| If our reasoning aims at gaining credence and so is merely
462 I, 3 | C must be", which above gave the conclusion "if A is,
463 II, 13| species to the universal genera-this for the further reason too
464 II, 19| a step towards a further generalization.~Thus it is clear that we
465 II, 4 | conclusion is drawn.~We may generalize by supposing that it is
466 I, 15| the first, B will have a genus-for the premiss containing it
467 I, 11| limits, that is, of the genus-the genus, I mean (as I have
468 I, 12| among those who are not geometers, for in such a company an
469 I, 31| we saw the pores in the glass and the light passing through,
470 II, 11| the preservation of one’s goods. The end in view is in the
471 II, 8 | nature; for we have not got genuine knowledge even of
472 I, 24| of knowledge-a potential grasp-of the posterior as well. For
473 II, 4 | impossible on the following grounds:-(a) syllogism proves an
474 II, 12| instance, not every man can grow a beard, but it is the general
475 I, 19| aiming at truth, one must be guided by the real connexions of
476 II, 13| subject.~The author of a hand-book on a subject that is a generic
477 I, 22| substances. On the other hand-in proof of the impossibility
478 I, 3 | series): if on the other hand-they say-the series terminates
479 I, 4 | of any figure selected at haphazard, nor in demonstrating does
480 I, 17| inference are liable to happen and through what kinds of
481 I, 8 | occurrences-e.g. of eclipse as happening to the moon-are, as such,
482 I, 33| their distribution under the heads of discursive thought, intuition,
483 I, 13| know that circular wounds heal more slowly, the geometer’
484 I, 24| demonstration but with the hearer.~(4) Demonstration is syllogism
485 I, 10| contended that the pupil’s hearing is also an hypothesis required
486 II, 12| namely total failure of heat. Then B is attributed to
487 I, 9 | science in a higher or the highest degree. But, as things are,
488 II, 11| instance if thunder be a hiss and a roar necessarily produced
489 I, 34| Quick wit is a faculty of hitting upon the middle term instantaneously.
490 II, 14| species does the possession of horns attach?~Yet a further method
491 I, 32| justice is cowardice"; "man is horse", and "man is ox"; "the
492 II, 14| the subgenera-man, e.g. or horse-possess their properties. Let A
493 II, 7 | nature? He who knows what human-or any other-nature is, must
494 I, 19| being white" coincides with "humanity" within one substratum-therefore
495 I, 25| from fewer postulates or hypotheses-in short from fewer premisses;
496 I, 17| been true; but it is ex hypothesi false.~When the erroneous
497 I, 10| only in a limited sense hypothesis-that is, relatively to the pupil;
498 I, 10| understood, and this is not hypothesis-unless it be contended that the
499 II, 6 | and substantially is, but hypothetically, i.e. by premising (1) that
500 I, 22| of certain premisses-i.e. hypothetically-the series of intermediate predications