Syllogism - Knowledge (XXG)

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problems, Boole's addition of equation solving to logic—another revolutionary idea—involved Boole's doctrine that Aristotle's rules of inference (the "perfect syllogisms") must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle."

585:, in which he discussed the concept of the syllogism, its components and distinctions, and ways to use the tool to expand its logical capability. For 200 years after Buridan's discussions, little was said about syllogistic logic. Historians of logic have assessed that the primary changes in the post-Middle Age era were changes in respect to the public's awareness of original sources, a lessening of appreciation for the logic's sophistication and complexity, and an increase in logical ignorance—so that logicians of the early 20th century came to view the whole system as ridiculous. 989: 6922: 2855: 2275: 3934:

if there are no As, and AeB entails AoB, and AeB entails BeA (which in turn entails BoA) then both AeB and AoB have existential import with respect to both A and B. It follows immediately that all universal categorical statements have existential import with respect to both terms. If AaB and AeB is a fair representation of the use of statements in normal natural language of All A is B and No A is B respectively, then the following example consequences arise:

2922: 2788: 2202: 2989: 2723: 2649: 2589: 2408: 2143: 2530: 918:, is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, one might argue that all lions are big cats, all big cats are predators, and all predators are carnivores. To conclude that therefore all lions are carnivores is to construct a sorites argument. 2468: 2335: 3895:

why he leaves no room for such non-existent entities in his logic. This is a thoughtful choice, not an inadvertent omission. Technically, Aristotelian science is a search for definitions, where a definition is "a phrase signifying a thing's essence." Because non-existent entities cannot be anything, they do not, in Aristotle's mind, possess an essence. This is why he leaves no place for fictional entities like goat-stags (or unicorns).

3801: 3525: 2862: 2282: 94: 3190: 3180: 2929: 2795: 2209: 3400: 3133: 3123: 3275: 2996: 2730: 2656: 2596: 2415: 2150: 304: 3739: 3698: 3463: 3422: 932: 53: 3386: 3358: 3348: 3336: 3319: 3309: 3297: 3240: 3107: 3097: 3257: 510:. His original assertions on this specific component of the theory were left up to a considerable amount of conversation, resulting in a wide array of solutions put forth by commentators of the day. The system for modal syllogisms laid forth by Aristotle would ultimately be deemed unfit for practical use, and would be replaced by new distinctions and new theories altogether. 2537: 3287: 3228: 3212: 3202: 3372: 2475: 2342: 3161: 3145: 196: 630:(1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic that there was to know. (This work is not necessarily representative of Kant's mature philosophy, which is often regarded as an innovation to logic itself.) Kant's opinion stood unchallenged in the West until 1879, when 4097: 3974:

can be represented in first order predicate in every combination of existential import—so it can establish which construal, if any, preserves the square of opposition and the validity of the traditionally valid syllogism. Strawson claims such a construal is possible, but the results are such that, in

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For example, if it is accepted that AiB is false if there are no As and AaB entails AiB, then AiB has existential import with respect to A, and so does AaB. Further, if it is accepted that AiB entails BiA, then AiB and AaB have existential import with respect to B as well. Similarly, if AoB is false

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It is claimed Aristotle's logic system does not cover cases where there are no instances. Aristotle's goal was to develop a logic for science. He relegates fictions, such as mermaids and unicorns, to the realms of poetry and literature. In his mind, they exist outside the ambit of science, which is

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Putting it all together, there are 256 possible types of syllogisms (or 512 if the order of the major and minor premises is changed, though this makes no difference logically). Each premise and the conclusion can be of type A, E, I or O, and the syllogism can be any of the four figures. A syllogism

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The convention here is that the letter S is the subject of the conclusion, P is the predicate of the conclusion, and M is the middle term. The major premise links M with P and the minor premise links M with S. However, the middle term can be either the subject or the predicate of each premise where

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went primarily unused before the 12th century, his textbooks on the categorical syllogism were central to expanding the syllogistic discussion. Rather than in any additions that he personally made to the field, Boethius' logical legacy lies in his effective transmission of prior theories to later

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sentences was considered especially remarkable, with only small systematic changes occurring to the concept over time. This theory of the syllogism would not enter the context of the more comprehensive logic of consequence until logic began to be reworked in general in the mid-14th century by the

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These problems and paradoxes arise in both natural language statements and statements in syllogism form because of ambiguity, in particular ambiguity with respect to All. If "Fred claims all his books were Pulitzer Prize winners", is Fred claiming that he wrote any books? If not, then is what he

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emphasized that experimental verification of axioms must be carried out rigorously, and cannot take syllogism itself as the best way to draw conclusions in nature. Bacon proposed a more inductive approach to the observation of nature, which involves experimentation, and leads to discovering and

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For instance, from the premises some A are B, some B are C, people tend to come to a definitive conclusion that therefore some A are C. However, this does not follow according to the rules of classical logic. For instance, while some cats (A) are black things (B), and some black things (B) are

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said; Boole's 'disagreements', if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced Aristotle's four propositional forms to one form, the form of equations, which by itself was a revolutionary idea. Second, in the realm of logic's

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Next to each premise and conclusion is a shorthand description of the sentence. So in AAI-3, the premise "All squares are rectangles" becomes "MaP"; the symbols mean that the first term ("square") is the middle term, the second term ("rectangle") is the predicate of the conclusion, and the

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televisions (C), it does not follow from the parameters that some cats (A) are televisions (C). This is because in the structure of the syllogism invoked (i.e. III-1) the middle term is not distributed in either the major premise or in the minor premise, a pattern called the "

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Are the existential imports required to satisfy (d) above such that the normal uses in natural languages of the forms All A is B, No A is B, Some A is B and Some A is not B are intuitively and fairly reflected by the categorical statements of forms AaB, AeB, AiB and

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consider the case where there may be no instances. Medieval logicians were aware of the problem of existential import and maintained that negative propositions do not carry existential import, and that positive propositions with subjects that do not

777:, and each categorical proposition contains two categorical terms. In Aristotle, each of the premises is in the form "All S are P," "Some S are P", "No S are P" or "Some S are not P", where "S" is the subject-term and "P" is the predicate-term: 2122:

In the Venn diagrams, the black areas indicate no elements, and the red areas indicate at least one element. In the predicate logic expressions, a horizontal bar over an expression means to negate ("logical not") the result of that expression.

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The first-order predicate calculus avoids such ambiguity by using formulae that carry no existential import with respect to universal statements. Existential claims must be explicitly stated. Thus, natural language statements—of the forms

321:), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that 4018:: The conclusion implicates all members of the major term (P – meaning the proposition is negative); however, the major premise does not account for them all (i.e., P is either an affirmative predicate or a particular subject there). 684:, subsuming syllogistic reasoning, which was, therefore, after 2000 years, suddenly considered obsolete by many. The Aristotelian system is explicated in modern fora of academia primarily in introductory material and historical study. 359:

were usually used interchangeably. This article is concerned only with this historical use. The syllogism was at the core of historical deductive reasoning, whereby facts are determined by combining existing statements, in contrast to

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defines the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so." Despite this very general definition, in

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If it is ruled that no universal statement has existential import then the square of opposition fails in several respects (e.g. AaB does not entail AiB) and a number of syllogisms are no longer valid (e.g. BaC, AaB->AiC).

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building on axioms to create a more general conclusion. Yet, a full method of drawing conclusions in nature is not the scope of logic or syllogism, and the inductive method was covered in Aristotle's subsequent treatise, the

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There are infinitely many possible syllogisms, but only 256 logically distinct types and only 24 valid types (enumerated below). A syllogism takes the form (note: M – Middle, S – subject, P – predicate.):

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It is clear that nothing would prevent a singular term occurring in a syllogism—so long as it was always in the subject position—however, such a syllogism, even if valid, is not a categorical syllogism. An example is

472:, upon rediscovery, was instantly regarded by logicians as "a closed and complete body of doctrine", leaving very little for thinkers of the day to debate, and reorganize. Aristotle's theory on the syllogism for 1694:

can be described briefly by giving the letters for the premises and conclusion followed by the number for the figure. For example, the syllogism BARBARA below is AAA-1, or "A-A-A in the first figure".

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The following table shows all syllogisms that are essentially different. The similar syllogisms share the same premises, just written in a different way. For example "Some pets are kittens" (SiM in

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as they came to be called. Consequently, the propositions of a syllogism should be categorical propositions (both terms general) and syllogisms that employ only categorical terms came to be called

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cannot be predicated of anything. Therefore, for a term to be interchangeable—to be either in the subject or predicate position of a proposition in a syllogism—the terms must be general terms, or

1480: 1349: 1283: 1613: 1417: 3966:—can be represented in first order predicate calculus in which any existential import with respect to terms A and/or B is either explicit or not made at all. Consequently, the four forms 1545: 644:). This introduced a calculus, a method of representing categorical statements (and statements that are not provided for in syllogism as well) by the use of quantifiers and variables. 3915:

In natural language and normal use, which statements of the forms, All A is B, No A is B, Some A is B, and Some A is not B, have existential import and with respect to which terms?

385:; 1879). Syllogism, being a method of valid logical reasoning, will always be useful in most circumstances, and for general-audience introductions to logic and clear-thinking. 4024:: Same as above, but for the minor term (S – meaning the proposition is universal) and minor premise (where S is either a particular subject or an affirmative predicate). 5301: 5167: 4140: 1709:. All but four of the patterns in italics (felapton, darapti, fesapo and bamalip) are weakened moods, i.e. it is possible to draw a stronger conclusion from the premises. 1207:

so the categorical statements can be written succinctly. The following table shows the longer form, the succinct shorthand, and equivalent expressions in predicate logic:

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In the four forms of categorical statements used in syllogism, which statements of the form AaB, AeB, AiB and AoB have existential import and with respect to which terms?

5976: 4033: 3066:. Columns indicate similarity, and are grouped by combinations of premises. Borders correspond to conclusions. Those with an existential assumption are dashed. 665:(1850). The work of Bolzano had been largely overlooked until the late 20th century, among other reasons, because of the intellectual environment at the time in 4039: 1034:

The premises and conclusion of a syllogism can be any of four types, which are labeled by letters as follows. The meaning of the letters is given by the table:

597:), rather than about verifying the assumptions. However, people over time focused on the logic aspect, forgetting the importance of verifying the assumptions. 6059: 5200: 4917: 593:

The Aristotelian syllogism dominated Western philosophical thought for many centuries. Syllogism itself is about drawing valid conclusions from assumptions (

688: 728:. According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were "to go under, over, and beyond" Aristotle's logic by: 4709:

on validity of syllogisms: "A simple set of rules of validity was finally produced in the later Middle Ages, based on the concept of Distribution."

506:. Aristotle's terminology in this aspect of his theory was deemed vague, and in many cases unclear, even contradicting some of his statements from 4666:

Corcoran, John, and Hassan Masoud. 2015. "Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions."

549:—a discussion of logic based on Boethius' commentaries and monographs. His perspective on syllogisms can be found in other works as well, such as 6373: 4186:

A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation

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is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form:

3995:". Because of this, it can be hard to follow formal logic, and a closer eye is needed in order to ensure that an argument is, in fact, valid. 6531: 802:

More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the

5319: 6386: 5709: 4464:," which mean "I affirm" and "I deny," respectively; the first capitalized letter of each word is for universal, the second for particular' 3924:

What existential imports must the forms AaB, AeB, AiB and AoB have to preserve the validity of the traditionally valid forms of syllogisms?

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is to be considered as true, false, or even meaningless if there are no As. If it is considered as false in such cases, then the statement

206: 1621:

it appears. The differing positions of the major, minor, and middle terms gives rise to another classification of syllogisms known as the

217: 4852: 4827: 4601: 4284: 4009: 3992: 5971: 742:

expanding the range of applications it could handle, such as expanding propositions of only two terms to those having arbitrarily many.

6391: 6381: 6118: 5324: 4767: 5869: 5315: 6527: 4881: 4803: 4726: 4700: 4629: 4614: 4592: 4245: 4225: 3866: 3848: 3782: 3725: 3590: 3572: 3506: 3449: 975: 253: 235: 177: 80: 3749: 3473: 942: 438:. Before the mid-12th century, medieval logicians were only familiar with a portion of Aristotle's works, including such titles as 6624: 6368: 5193: 4910: 4012:: Neither of the premises accounts for all members of the middle term, which consequently fails to link the major and minor term. 3879:

If a statement includes a term such that the statement is false if the term has no instances, then the statement is said to have

5929: 5622: 5363: 4336: 4866: 6885: 6587: 6350: 6345: 6170: 5591: 5275: 4946: 4778: 4546: 3826: 3550: 577:(c. 1300 – 1361), whom some consider the foremost logician of the later Middle Ages, contributed two significant works: 115: 6880: 6663: 6580: 6293: 6224: 6101: 5343: 4027: 1426: 526:(c. 475–526) contributed an effort to make the ancient Aristotelian logic more accessible. While his Latin translation of 5951: 1292: 6956: 6805: 6631: 6317: 5550: 4659: 2127: 1005: 158: 5956: 687:

One notable exception to this modern relegation is the continued application of Aristotelian logic by officials of the

6288: 6027: 5285: 5186: 4903: 130: 6683: 6678: 3811: 3764: 3535: 3488: 1701:

from the premises). The table below shows the valid forms. Even some of these are sometimes considered to commit the

1232: 957: 673:. In the last 20 years, Bolzano's work has resurfaced and become subject of both translation and contemporary study. 1559: 1363: 6612: 6202: 5596: 5564: 5255: 3822: 3711: 3629: 3546: 3435: 490:

did not, however, incorporate such a comprehensive theory on the modal syllogism—a syllogism that has at least one

111: 66: 5329: 4493:"Groarke, Louis F., "Aristotle: Logic", section 7. (Existential Assumptions), Internet Encyclopedia of Philosophy" 3830: 3815: 3760: 3554: 3539: 3484: 953: 104: 6902: 6851: 6748: 6246: 6207: 5684: 4650: 565:

modal sentences, medieval logicians began to shape a more coherent concept of Aristotle's modal syllogism model.

137: 6743: 5358: 6673: 6212: 6064: 6047: 5770: 5250: 4745: 4645: 4399: 4342: 1494: 707: 661:, 1837), the principles of which were applied as a direct critique of Kant, in the posthumously published work 4492: 3684:, so our non-categorical syllogism can be justified by use of the equivalence above and then citing BARBARA. 6575: 6552: 6513: 6399: 6340: 5986: 5906: 5750: 5694: 5307: 5139: 5020: 4951: 4889:

An interactive syllogistic machine for exploring all the fallacies, figures, terms, and modes of syllogisms.

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What existential imports must the forms AaB, AeB, AiB and AoB have for the square of opposition to be valid?

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The use of syllogisms as a tool for understanding can be dated back to the logical reasoning discussions of

424: 144: 6865: 6592: 6570: 6537: 6430: 6276: 6261: 6234: 6185: 6069: 6004: 5829: 5795: 5790: 5664: 5495: 5472: 5114: 4678: 4531: 4057: 792: 440: 4836: 4303: 3672:. To argue that its validity can be explained by the theory of syllogism would require that we show that 3636:. It is clear that Aristotle's syllogism works only for distributive predication, since we cannot reason 1705:, meaning they are invalid if they mention an empty category. These controversial patterns are marked in 6795: 6648: 6440: 6158: 5894: 5800: 5659: 5644: 5525: 5500: 4994: 4989: 4956: 4794: 4082: 4052: 3999: 782: 619: 615: 210:

that states a Knowledge (XXG) editor's personal feelings or presents an original argument about a topic.

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Aristotle's Assertoric Syllogistic (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)

988: 545:(1079–1142), gave his own thorough evaluation of the syllogism concept, and accompanying theory in the 126: 6768: 6730: 6607: 6411: 6251: 6175: 6153: 5981: 5939: 5838: 5805: 5669: 5457: 5368: 5043: 4941: 4383: 4115: 4072: 3941:

If "No men are fire-eating rabbits" is true, then "There are fire-eating rabbits" is true; and so on.

1192: 993: 38: 4860: 6951: 6897: 6788: 6773: 6753: 6710: 6597: 6547: 6473: 6418: 6355: 6148: 6143: 6091: 5859: 5848: 5520: 5420: 5348: 5339: 5335: 5270: 5265: 5129: 4364: 4110: 1702: 1698: 807: 724: 695:, which still requires that any arguments crafted by Advocates be presented in syllogistic format. 607: 533:

logicians, as well as his clear and primarily accurate presentations of Aristotle's contributions.

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In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism.

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Aristotle's theory of the syllogism: a logico-philological study of Book A of the Prior Analytics

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claims true? Suppose Jane says none of her friends are poor; is that true if she has no friends?

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the minor term. The premises also have one term in common with each other, which is known as the

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Chater, N., and M. Oaksford. 1999. "The Probability Heuristics Model of Syllogistic Reasoning."

4030:: Both premises are negative, meaning no link is established between the major and minor terms. 6861: 6668: 6478: 6468: 6360: 6241: 6076: 6052: 5833: 5817: 5722: 5699: 5576: 5545: 5510: 5405: 5240: 5119: 4799: 4763: 4730: 4722: 4696: 4625: 4610: 4588: 4241: 4221: 4145: 4102: 3033: 1697:

The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not

446: 368: 4872:

Development of Fuzzy Syllogistic Algorithms and Applications Distributed Reasoning Approaches

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The Buddhist Philosophy of Universal Flux (Chapter XXIII – Members of a Syllogism (avayava))

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of each term in each statement, meaning whether all members of that term are accounted for.

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with respect to that term. It is ambiguous whether or not a universal statement of the form

3640:. In Aristotle's view singular terms were of type (a), and general terms of type (b). Thus, 736: 735:

extending the class of problems it could treat, as solving equations was added to assessing

677: 394: 4529:

Khemlani, S., and P. N. Johnson-Laird. 2012. "Theories of the syllogism: A meta-analysis."

1682:(Note, however, that, following Aristotle's treatment of the figures, some logicians—e.g., 6856: 6846: 6800: 6783: 6738: 6700: 6602: 6522: 6329: 6256: 6229: 6217: 6123: 6037: 6011: 5966: 5934: 5735: 5537: 5480: 5430: 5395: 5353: 5124: 4847: 4822: 4597: 4583: 4275: 4262: 4135: 4077: 4062: 1161: 718: 712: 681: 670: 653: 648: 636: 528: 419: 377: 317: 31: 4843: 4289: 2854: 2274: 1183:) as term place holders, rather than giving concrete examples. It is traditional to use 6841: 6820: 6778: 6758: 6653: 6508: 6106: 6096: 6086: 6081: 6015: 5889: 5765: 5654: 5649: 5627: 5228: 4773: 4130: 4120: 3717: 3441: 3050: 2977: 2921: 2910: 2843: 2787: 2772: 2698: 2636: 2577: 2518: 2452: 2385: 2319: 2252: 2201: 2190: 1204: 271: 151: 72: 4818: 2988: 2722: 2648: 2588: 2407: 2142: 706:'s unwavering acceptance of Aristotle's logic is emphasized by the historian of logic 6940: 6815: 6493: 6000: 5785: 5775: 5745: 5730: 5400: 4347: 4331: 4200: 4067: 4021: 4015: 3604: 2101: 1683: 909: 631: 623: 601: 542: 372: 2529: 6715: 6562: 6463: 6455: 6335: 6283: 6192: 6128: 6111: 6042: 5901: 5760: 5462: 5245: 5162: 5010: 4895: 4359: 4279: 4150: 3063: 2467: 2334: 2108:

names for the forms as follows: 'Barbara' stands for AAA, 'Celarent' for EAE, etc.

1687: 703: 574: 480: 452: 4876: 6825: 6705: 5884: 5874: 5821: 5505: 5425: 5410: 5290: 5235: 5064: 4984: 4635: 4416: 3800: 3524: 837:

Each of the three distinct terms represents a category. From the example above,

491: 458: 428: 348: 344: 297: 93: 3638:

All Greeks are animals, animals are numerous, therefore all Greeks are numerous

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In the 19th century, modifications to syllogism were incorporated to deal with

5755: 5610: 5581: 5387: 5080: 5015: 4974: 4966: 4926: 4886: 4877:

Comparison between the Aristotelian Syllogism and the Indian/Tibetan Syllogism

4871: 4657:— 1994. "The founding of logic: Modern interpretations of Aristotle's logic." 4474: 4092: 3189: 3179: 2861: 2281: 692: 474: 408: 340: 303: 6907: 6810: 5863: 5780: 5740: 5704: 5640: 5442: 5415: 5038: 4578: 4257: 4125: 3399: 3274: 3132: 3122: 3037: 2928: 2794: 2208: 747: 435: 413: 312: 4785:

Smith, Robin. 1986. "Immediate propositions and Aristotle's proof theory."

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terms that could be predicated of others by the use of the copula ("is a").

3385: 3357: 3347: 3335: 3318: 3308: 3296: 3256: 3239: 3106: 3096: 2995: 2729: 2655: 2595: 2414: 2149: 3371: 3286: 3227: 3211: 3201: 2536: 17: 6892: 6690: 6138: 5843: 5437: 5059: 4734: 4381:

van Evra, James. 2004. "'The Laws of Thought' by George Boole" (review).

2105: 555: 523: 423:

Aristotle limits himself to categorical syllogisms that consist of three

322: 285: 3938:"All flying horses are mythical" is false if there are no flying horses. 3160: 3144: 2474: 2341: 6488: 5280: 5152: 5106: 4440:, p. 127: 'The letter names are presumed to come from the Latin words " 4402:. 2003. "Aristotle's 'Prior Analytics' and Boole's 'Laws of Thought'." 4005:

In simple syllogistic patterns, the fallacies of invalid patterns are:

3670:

All Greeks are men, all men are mortal therefore all Greeks are mortals

3044: 1625:. Given that in each case the conclusion is S-P, the four figures are: 666: 5178: 5085: 466:, the work in which Aristotle developed his theory of the syllogism. 3767:. Statements consisting only of original research should be removed. 3666:

Socrates is a man, all men are mortal, therefore Socrates is mortal.

3491:. Statements consisting only of original research should be removed. 2119:) could also be written as "Some kittens are pets" (MiS in Datisi). 960:. Statements consisting only of original research should be removed. 541:

Another of medieval logic's first contributors from the Latin West,

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Aristotle's Syllogistic from the Standpoint of Modern Formal Logic

3398: 3384: 3370: 3356: 3346: 3334: 3317: 3307: 3295: 3285: 3273: 3255: 3238: 3226: 3210: 3200: 3188: 3178: 3159: 3143: 3131: 3121: 3105: 3095: 1179: 1167: 987: 900:. Again, both premises are universal, hence so is the conclusion. 594: 561: 302: 3998:

Determining the validity of a syllogism involves determining the

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is the equivalent of a categorical proposition. It can be argued

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relationship between the two terms is labeled "a" (All M are P).

1203:. It is traditional and convenient practice to use a, e, i, o as 450:, works that contributed heavily to the prevailing Old Logic, or 4861:

Aristotle's Prior Analytics: the Theory of Categorical Syllogism

4437: 4042:: If both premises are affirmative, the conclusion must also be. 1690:—reject the fourth figure as a figure distinct from the first.) 1173: 367:

Within some academic contexts, syllogism has been superseded by

37:"Minor premise" redirects here. For the 2020 thriller film, see 5182: 4899: 4188:, 3rd ed., vol. 1, chap. 2 (London: John W. Parker, 1851), 190. 1165:, Aristotle uses mostly the letters A, B, and C (Greek letters 732:

providing it with mathematical foundations involving equations;

4706: 3794: 3732: 3691: 3518: 3456: 3415: 2307:

Camestres is essentially like Celarent with S and P exchanged.

925: 189: 87: 46: 4036:: If either premise is negative, the conclusion must also be. 275: 4481:

from the original on 2021-12-11 – via www.youtube.com.

2508:

Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4)

992:

Relationships between the four types of propositions in the

865:. Both of the premises are universal, as is the conclusion. 3987:

People often make mistakes when reasoning syllogistically.

2316: No fur bearing animal is a reptile. (SeM) 2130:(consisting of vertices and edges) to evaluate syllogisms. 207:

personal reflection, personal essay, or argumentative essay

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This table shows all 24 valid syllogisms, represented by

2440:

Disamis is essentially like Darii with S and P exchanged.

364:, in which facts are predicted by repeated observations. 27:

Type of logical argument that applies deductive reasoning

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premise, that is, a premise containing the modal words

213: 339:

In antiquity, two rival syllogistic theories existed:

3615:. Aristotle further distinguished types (a) and (b): 1562: 1497: 1429: 1366: 1295: 1235: 716:. Corcoran also wrote a point-by-point comparison of 30:"Epagoge" redirects here. For the genus of moth, see 4863:

an annotated bibliography on Aristotle's syllogistic

2100:

The letters A, E, I, and O have been used since the

1475:{\displaystyle \forall x(A(x)\rightarrow \neg B(x))} 814:(i.e., the subject of the conclusion). For example: 810:

of the conclusion); in a minor premise, this is the

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terms that could be the subject of predication; and

1344:{\displaystyle \neg \exists x(A(x)\land \neg B(x))} 118:. Unsourced material may be challenged and removed. 5168:The False Subtlety of the Four Syllogistic Figures 4141:The False Subtlety of the Four Syllogistic Figures 2574: Some pets are not mammals. (SoM) 1607: 1539: 1474: 1411: 1343: 1277: 2515: Some reading is homework. (SiM) 791:"Some S are P" and "Some S are not P" are termed 759:A categorical syllogism consists of three parts: 647:A noteworthy exception is the logic developed in 553:. With the help of Abelard's distinction between 4368:, with an introduction by J. Corcoran. Buffalo: 2840: All snakes are reptiles. (SaM) 2313: All snakes are reptiles. (PaM) 2249: All snakes are reptiles. (SaM) 2974: All flowers are plants. (MaS) 2971: No flowers are animals. (MeP) 2904: All horses have hooves. (PaM) 2630: Some cats are not pets. (MoP) 1278:{\displaystyle \forall x(A(x)\rightarrow B(x))} 4327: 4325: 4034:Affirmative conclusion from a negative premise 3975:his view, the answer to question (e) above is 2907: No humans have hooves. (SeM) 2446: Some rabbits are pets. (MiP) 2382: Some pets are rabbits. (SiM) 1608:{\displaystyle \exists x(A(x)\land \neg B(x))} 1412:{\displaystyle \neg \exists x(A(x)\land B(x))} 5194: 4911: 4203:. 1975. "Stoic vs. Peripatetic Syllogistic." 4040:Negative conclusion from affirmative premises 2837: No reptiles have fur. (MeP) 2633: All cats are mammals. (MaS) 2571: All cats are mammals. (PaM) 2449: All rabbits have fur. (MaP) 2379: All rabbits have fur. (MaP) 8: 4648:. 1972. "Completeness of an ancient logic." 3898:However, many logic systems developed since 2769: All men are mortals. (MaS) 4417:"Philosophical Dictionary: Caird-Catharsis" 3829:. Unsourced material may be challenged and 3726:Learn how and when to remove these messages 3553:. Unsourced material may be challenged and 3450:Learn how and when to remove these messages 2766: All Greeks are men. (PaM) 2695: All Greeks are men. (SaM) 2692: All men are mortal. (MaP) 2512: No homework is fun. (MeP) 2246: No reptile has fur. (MeP) 2187: All Greeks are men. (SaM) 2184: All men are mortal. (MaP) 781:"All S are P," and "No S are P" are termed 81:Learn how and when to remove these messages 6020: 5615: 5383: 5201: 5187: 5179: 5102: 5049: 4918: 4904: 4896: 3891:has existential import with respect to A. 3682:All that are identical to Socrates are men 2706: 2393: 2260: 746:More specifically, Boole agreed with what 689:Congregation for the Doctrine of the Faith 3867:Learn how and when to remove this message 3849:Learn how and when to remove this message 3783:Learn how and when to remove this message 3591:Learn how and when to remove this message 3573:Learn how and when to remove this message 3507:Learn how and when to remove this message 1561: 1540:{\displaystyle \exists x(A(x)\land B(x))} 1496: 1428: 1365: 1294: 1234: 976:Learn how and when to remove this message 300:that are asserted or assumed to be true. 254:Learn how and when to remove this message 236:Learn how and when to remove this message 178:Learn how and when to remove this message 3068: 2983: 2916: 2849: 2782: 2717: 2643: 2583: 2524: 2462: 2455:Some fur bearing animals are pets. (SiP) 2402: 2329: 2269: 2196: 2137: 1711: 1627: 1209: 1036: 284:, 'conclusion, inference') is a kind of 4308:The Stanford Encyclopedia of Philosophy 4162: 3632:, as opposed to non-distributive as in 2322:No fur bearing animal is a snake. (SeP) 698: 4516:See, e.g., Evans, J. St. B. T (1989). 462:, arose alongside the reappearance of 4395: 4393: 4302:Lagerlund, Henrik (2 February 2004). 4205:Archive for the History of Philosophy 676:This led to the rapid development of 7: 4844:"Medieval Theories of the Syllogism" 4304:"Medieval Theories of the Syllogism" 4196: 4194: 3827:adding citations to reliable sources 3551:adding citations to reliable sources 3053:Some rhombuses are rectangles. (SiP) 3011: 2944: 2877: 2810: 2745: 2671: 2611: 2552: 2490: 2430: 2357: 2297: 2224: 2165: 691:, and the Apostolic Tribunal of the 116:adding citations to reliable sources 4853:Stanford Encyclopedia of Philosophy 4828:Stanford Encyclopedia of Philosophy 4792:Thom, Paul. 1981. "The Syllogism." 4587:, translated by R. Smith. Hackett. 4564:. Bedford/St. Martin's. p. 39. 4285:Stanford Encyclopedia of Philosophy 4022:Illicit treatment of the minor term 4016:Illicit treatment of the major term 3993:fallacy of the undistributed middle 3603:With Aristotle, we may distinguish 4762:. University of Pittsburgh Press. 4174:. Bedford/St.Martin's. p. 38. 3043: All squares are 2980:Some plants are not animals. (SoP) 2116: 1587: 1563: 1498: 1454: 1430: 1370: 1367: 1323: 1299: 1296: 1236: 25: 4419:. Philosophypages.com. 2002-08-08 3707:This section has multiple issues. 3628:Such a predication is known as a 3431:This section has multiple issues. 2913:Some humans are not horses. (SoP) 710:in an accessible introduction to 311:In its earliest form (defined by 62:This article has multiple issues. 6920: 4721:. New York: Garland Publishers. 4095: 3799: 3737: 3696: 3668:Intuitively this is as valid as 3523: 3461: 3420: 2994: 2987: 2927: 2920: 2860: 2853: 2793: 2786: 2728: 2721: 2654: 2647: 2639:Some mammals are not pets. (SoP) 2594: 2587: 2535: 2528: 2473: 2466: 2413: 2406: 2340: 2333: 2280: 2273: 2207: 2200: 2148: 2141: 930: 194: 92: 51: 4835:Koutsoukou-Argyraki, Angeliki. 4776:. 1973. "What is a syllogism?" 4668:History and Philosophy of Logic 4606:Oxford Dictionary of Philosophy 4562:The Essential Guide to Rhetoric 4404:History and Philosophy of Logic 4218:A Concise Introduction to Logic 4172:The Essential Guide to Rhetoric 3715:or discuss these issues on the 3439:or discuss these issues on the 2709: 2396: 2263: 699:Boole's acceptance of Aristotle 456:. The onset of a New Logic, or 334:Therefore, Socrates is mortal. 103:needs additional citations for 70:or discuss these issues on the 4947:Problem of multiple generality 4779:Journal of Philosophical Logic 4622:Introduction to Medieval Logic 3910:The following problems arise: 2846:Some snakes have no fur. (SoP) 2521:Some reading is not fun. (SoP) 1602: 1599: 1593: 1581: 1575: 1569: 1534: 1531: 1525: 1516: 1510: 1504: 1469: 1466: 1460: 1451: 1448: 1442: 1436: 1406: 1403: 1397: 1388: 1382: 1376: 1338: 1335: 1329: 1317: 1311: 1305: 1272: 1269: 1263: 1257: 1254: 1248: 1242: 1: 6881:History of mathematical logic 4742:Aristotle's Modal Syllogistic 4642:(3rd ed.). Macmillan Company. 3611:, and general terms, such as 2775:Some mortals are Greek. (SiP) 2701:Some Greeks are mortal. (SiP) 2580:Some pets are not cats. (SoP) 669:, which was then part of the 6806:Primitive recursive function 4673:Englebretsen, George. 1987. 4560:Lundberg, Christian (2018). 4170:Lundberg, Christian (2018). 2193:All Greeks are mortal. (SaP) 1006:List of valid argument forms 622:("if A then B") statements. 4624:. Oxford University Press. 4609:. Oxford University Press. 3763:the claims made and adding 3487:the claims made and adding 2126:It is also possible to use 956:the claims made and adding 369:first-order predicate logic 6978: 5870:Schröder–Bernstein theorem 5597:Monadic predicate calculus 5256:Foundations of mathematics 4887:Online Syllogistic Machine 4620:Broadie, Alexander. 1993. 1003: 907: 406: 392: 276: 36: 29: 6916: 6903:Philosophy of mathematics 6852:Automated theorem proving 6023: 5977:Von Neumann–Bernays–Gödel 5618: 4758:Rescher, Nicholas. 1966. 4651:Journal of Symbolic Logic 4600:. 1996. "Syllogism." In 4240:. John Wiley & Sons. 4216:Hurley, Patrick J. 2011. 3083: 3080: 3077: 3074: 2993: 2926: 2859: 2792: 2762:with S and P exchanged: 2727: 2653: 2593: 2534: 2472: 2442:Similar: Dimatis (IAI-4) 2412: 2388:Some pets have fur. (SiP) 2375:Similar: Datisi (AII-3) 2339: 2309:Similar: Calemes (AEE-4) 2279: 2206: 2147: 1153:Some humans are not old. 1127:Some humans are healthy. 896:, and the middle term is 4867:Fuzzy Syllogistic System 4746:Harvard University Press 4685:Hamblin, Charles Leonard 2242:Similar: Cesare (EAE-2) 1000:red areas are nonempty.) 888:Here, the major term is 833:: All Greeks are mortal. 827:: All Greeks are humans. 821:: All humans are mortal. 427:, including categorical 425:categorical propositions 307:"Socrates" at the Louvre 6553:Self-verifying theories 6374:Tarski's axiomatization 5325:Tarski's undefinability 5320:incompleteness theorems 5140:Sophistical Refutations 4952:Dictum de omni et nullo 4760:Galen and the Syllogism 4518:Bias in human reasoning 4236:Zegarelli, Mark. 2010. 3058:Table of all syllogisms 2255:No snake has fur. (SeP) 1124:particular affirmative 1104:No humans are perfect. 1081:All humans are mortal. 998:(Black areas are empty, 853:is the major term, and 775:categorical proposition 579:Treatise on Consequence 573:The French philosopher 6927:Mathematics portal 6538:Proof of impossibility 6186:propositional variable 5496:Propositional calculus 4751:Patzig, Günter. 1968. 4532:Psychological Bulletin 4475:"Syllogisms Made Easy" 4337:The Great Instauration 4058:Hypothetical syllogism 3658:categorical syllogisms 3404: 3390: 3378: 3364: 3352: 3342: 3323: 3313: 3301: 3291: 3281: 3263: 3244: 3232: 3218: 3206: 3196: 3184: 3165: 3149: 3139: 3127: 3113: 3101: 3032: All 1609: 1541: 1476: 1413: 1345: 1279: 1078:universal affirmative 1001: 914:A polysyllogism, or a 878:: All men are mortals. 583:Summulae de Dialectica 371:following the work of 341:Aristotelian syllogism 337: 308: 216:by rewriting it in an 6796:Kolmogorov complexity 6749:Computably enumerable 6649:Model complete theory 6441:Principia Mathematica 5501:Propositional formula 5330:Banach–Tarski paradox 4740:Malink, Marko. 2013. 4640:Introduction to Logic 4083:Statistical syllogism 4053:Disjunctive syllogism 3983:Syllogistic fallacies 3956:All A is B, No A is B 3644:can be predicated of 3402: 3388: 3374: 3360: 3350: 3338: 3321: 3311: 3299: 3289: 3277: 3259: 3242: 3230: 3214: 3204: 3192: 3182: 3163: 3147: 3135: 3125: 3109: 3099: 1610: 1542: 1477: 1414: 1346: 1280: 1028:Conclusion/Consequent 1004:Further information: 991: 882:Conclusion/Consequent 831:Conclusion/Consequent 769:Conclusion/Consequent 626:famously claimed, in 600:In the 17th century, 551:Logica Ingredientibus 353:categorical syllogism 327: 306: 6744:Church–Turing thesis 6731:Computability theory 5940:continuum hypothesis 5458:Square of opposition 5316:Gödel's completeness 4942:Square of opposition 4755:. Dordrecht: Reidel. 4547:Cognitive Psychology 4384:Philosophy in Review 4346:. Archived from the 4343:Constitution Society 4220:. Cengage Learning. 4116:Argumentation theory 4073:Prosleptic syllogism 4010:Undistributed middle 3823:improve this section 3547:improve this section 1560: 1495: 1427: 1364: 1293: 1233: 1150:particular negative 994:square of opposition 892:, the minor term is 559:modal sentences and 375:, in particular his 112:improve this article 6957:Ancient Greek logic 6898:Mathematical object 6789:P versus NP problem 6754:Computable function 6548:Reverse mathematics 6474:Logical consequence 6351:primitive recursive 6346:elementary function 6119:Free/bound variable 5972:Tarski–Grothendieck 5491:Logical connectives 5421:Logical equivalence 5271:Logical consequence 5130:Posterior Analytics 4842:Lagerlund, Henrik. 4819:"Aristotle's Logic" 4675:The New Syllogistic 4365:The Laws of Thought 4111:Syllogistic fallacy 3634:Greeks are numerous 1703:existential fallacy 1101:universal negative 861:; in this example, 608:Posterior Analytics 362:inductive reasoning 330:All men are mortal. 315:in his 350 BC book 290:deductive reasoning 6696:Transfer principle 6659:Semantics of logic 6644:Categorical theory 6620:Non-standard model 6134:Logical connective 5261:Information theory 5210:Mathematical logic 4927:Aristotelian logic 4787:Ancient Philosophy 4660:Ancient Philosophy 4184:John Stuart Mill, 4028:Exclusive premises 3881:existential import 3748:possibly contains 3688:Existential import 3472:possibly contains 3412:Terms in syllogism 3405: 3391: 3379: 3365: 3353: 3343: 3324: 3314: 3302: 3292: 3282: 3264: 3245: 3233: 3219: 3207: 3197: 3185: 3166: 3150: 3140: 3128: 3114: 3102: 3013:P: rectangle 2264:Camestres (AEE-2) 1605: 1537: 1472: 1409: 1341: 1275: 1002: 941:possibly contains 872:: All mortals die. 654:Wissenschaftslehre 514:Medieval syllogism 332:Socrates is a man. 309: 218:encyclopedic style 205:is written like a 6934: 6933: 6866:Abstract category 6669:Theories of truth 6479:Rule of inference 6469:Natural deduction 6450: 6449: 5995: 5994: 5700:Cartesian product 5605: 5604: 5511:Many-valued logic 5486:Boolean functions 5369:Russell's paradox 5344:diagonal argument 5241:First-order logic 5176: 5175: 5148: 5147: 5120:On Interpretation 5094: 5093: 4744:. Cambridge, MA: 4350:on 13 April 2019. 4310:. Edward N. Zalta 4238:Logic for Dummies 4146:Tautology (logic) 4103:Philosophy portal 3877: 3876: 3869: 3859: 3858: 3851: 3793: 3792: 3785: 3750:original research 3730: 3680:is equivalent to 3678:Socrates is a man 3674:Socrates is a man 3654:categorical terms 3601: 3600: 3593: 3583: 3582: 3575: 3517: 3516: 3509: 3474:original research 3454: 3409: 3408: 3019: 3018: 2952: 2951: 2892:Camestros (AEO-2) 2885: 2884: 2818: 2817: 2781: 2780: 2753: 2752: 2679: 2678: 2619: 2618: 2560: 2559: 2498: 2497: 2483:M: homework 2461: 2460: 2438: 2437: 2365: 2364: 2328: 2327: 2305: 2304: 2232: 2231: 2173: 2172: 2098: 2097: 1680: 1679: 1618: 1617: 1157: 1156: 986: 985: 978: 943:original research 659:Theory of Science 508:On Interpretation 447:On Interpretation 264: 263: 256: 246: 245: 238: 188: 187: 180: 162: 85: 16:(Redirected from 6969: 6925: 6924: 6876:History of logic 6871:Category of sets 6764:Decision problem 6543:Ordinal analysis 6484:Sequent calculus 6382:Boolean algebras 6322: 6321: 6296: 6267:logical/constant 6021: 6007: 5930:Zermelo–Fraenkel 5681:Set operations: 5616: 5553: 5384: 5364:Löwenheim–Skolem 5251:Formal semantics 5203: 5196: 5189: 5180: 5158:Port-Royal Logic 5103: 5050: 4920: 4913: 4906: 4897: 4857: 4848:Zalta, Edward N. 4832: 4823:Zalta, Edward N. 4715:Łukasiewicz, Jan 4598:Blackburn, Simon 4566: 4565: 4557: 4551: 4542: 4536: 4527: 4521: 4514: 4508: 4507: 4505: 4504: 4495:. Archived from 4489: 4483: 4482: 4471: 4465: 4434: 4428: 4427: 4425: 4424: 4413: 4407: 4397: 4388: 4379: 4373: 4370:Prometheus Books 4357: 4351: 4329: 4320: 4319: 4317: 4315: 4299: 4293: 4276:Bobzien, Susanne 4273: 4267: 4255: 4249: 4234: 4228: 4214: 4208: 4198: 4189: 4182: 4176: 4175: 4167: 4105: 4100: 4099: 4098: 3872: 3865: 3854: 3847: 3843: 3840: 3834: 3803: 3795: 3788: 3781: 3777: 3774: 3768: 3765:inline citations 3741: 3740: 3733: 3722: 3700: 3699: 3692: 3596: 3589: 3578: 3571: 3567: 3564: 3558: 3527: 3519: 3512: 3505: 3501: 3498: 3492: 3489:inline citations 3465: 3464: 3457: 3446: 3424: 3423: 3416: 3069: 3015: 3014: 3010: 3005: 2998: 2991: 2984: 2959:Felapton (EAO-3) 2948: 2947: 2943: 2938: 2931: 2924: 2917: 2881: 2880: 2876: 2871: 2864: 2857: 2850: 2825:Celaront (EAO-1) 2814: 2813: 2809: 2804: 2803:M: reptile 2797: 2790: 2783: 2758:is exactly like 2749: 2748: 2744: 2739: 2732: 2725: 2718: 2707: 2675: 2674: 2670: 2665: 2658: 2651: 2644: 2615: 2614: 2610: 2605: 2598: 2591: 2584: 2556: 2555: 2551: 2546: 2539: 2532: 2525: 2494: 2493: 2489: 2488:S: reading 2484: 2477: 2470: 2463: 2434: 2433: 2429: 2424: 2417: 2410: 2403: 2397:Disamis (IAI-3) 2394: 2361: 2360: 2356: 2351: 2344: 2337: 2330: 2301: 2300: 2296: 2291: 2290:M: reptile 2284: 2277: 2270: 2261: 2238:Celarent (EAE-1) 2228: 2227: 2223: 2218: 2217:M: reptile 2211: 2204: 2197: 2169: 2168: 2164: 2159: 2152: 2145: 2138: 2102:medieval Schools 1712: 1699:follow logically 1628: 1614: 1612: 1611: 1606: 1551:Some A is not B 1546: 1544: 1543: 1538: 1481: 1479: 1478: 1473: 1418: 1416: 1415: 1410: 1350: 1348: 1347: 1342: 1284: 1282: 1281: 1276: 1219:Predicate logic 1210: 1037: 981: 974: 970: 967: 961: 958:inline citations 934: 933: 926: 680:and first-order 678:sentential logic 395:History of logic 286:logical argument 279: 278: 259: 252: 241: 234: 230: 227: 221: 198: 197: 190: 183: 176: 172: 169: 163: 161: 120: 96: 88: 77: 55: 54: 47: 21: 6977: 6976: 6972: 6971: 6970: 6968: 6967: 6966: 6937: 6936: 6935: 6930: 6919: 6912: 6857:Category theory 6847:Algebraic logic 6830: 6801:Lambda calculus 6739:Church encoding 6725: 6701:Truth predicate 6557: 6523:Complete theory 6446: 6315: 6311: 6307: 6302: 6294: 6014: and 6010: 6005: 5991: 5967:New Foundations 5935:axiom of choice 5918: 5880:Gödel numbering 5820: and 5812: 5716: 5601: 5551: 5532: 5481:Boolean algebra 5467: 5431:Equiconsistency 5396:Classical logic 5373: 5354:Halting problem 5342: and 5318: and 5306: and 5305: 5300:Theorems ( 5295: 5212: 5207: 5177: 5172: 5144: 5125:Prior Analytics 5090: 5069: 5048: 5025: 4999: 4961: 4930: 4924: 4893: 4841: 4816: 4813: 4774:Smiley, Timothy 4584:Prior Analytics 4575: 4570: 4569: 4559: 4558: 4554: 4543: 4539: 4528: 4524: 4515: 4511: 4502: 4500: 4491: 4490: 4486: 4473: 4472: 4468: 4435: 4431: 4422: 4420: 4415: 4414: 4410: 4398: 4391: 4380: 4376: 4358: 4354: 4330: 4323: 4313: 4311: 4301: 4300: 4296: 4274: 4270: 4263:Prior Analytics 4256: 4252: 4235: 4231: 4215: 4211: 4199: 4192: 4183: 4179: 4169: 4168: 4164: 4159: 4136:Logical fallacy 4101: 4096: 4094: 4091: 4078:Quasi-syllogism 4063:Legal syllogism 4049: 3985: 3964:Some A is not B 3931: 3873: 3862: 3861: 3860: 3855: 3844: 3838: 3835: 3820: 3804: 3789: 3778: 3772: 3769: 3754: 3742: 3738: 3701: 3697: 3690: 3626: 3597: 3586: 3585: 3584: 3579: 3568: 3562: 3559: 3544: 3528: 3513: 3502: 3496: 3493: 3478: 3466: 3462: 3425: 3421: 3414: 3060: 3029: 3026:Darapti (AAI-3) 3021: 3012: 3008: 3007: 3006: 3004:M: square 3003: 2962: 2954: 2946:P: animal 2945: 2941: 2940: 2939: 2937:M: flower 2936: 2899:Calemos (AEO-4) 2895: 2887: 2878: 2874: 2873: 2872: 2870:M: hooves 2869: 2828: 2820: 2811: 2807: 2806: 2805: 2802: 2746: 2743:S: mortal 2742: 2741: 2740: 2737: 2711:Bamalip (AAI-4) 2689: 2686:Barbari (AAI-1) 2681: 2673:P: mortal 2672: 2668: 2667: 2666: 2663: 2642: 2627: 2625:Bocardo (OAO-3) 2621: 2612: 2609:S: mammal 2608: 2607: 2606: 2603: 2568: 2562: 2553: 2549: 2548: 2547: 2545:M: mammal 2544: 2506: 2500: 2491: 2487: 2486: 2485: 2482: 2441: 2431: 2427: 2426: 2425: 2423:M: rabbit 2422: 2373: 2367: 2358: 2354: 2353: 2352: 2350:M: rabbit 2349: 2308: 2298: 2294: 2293: 2292: 2289: 2240: 2234: 2225: 2221: 2220: 2219: 2216: 2181: 2179:Barbara (AAA-1) 2175: 2167:P: mortal 2166: 2163:S: Greeks 2162: 2161: 2160: 2157: 2136: 1558: 1557: 1493: 1492: 1425: 1424: 1362: 1361: 1291: 1290: 1231: 1230: 1205:infix operators 1162:Prior Analytics 1008: 999: 997: 996: 982: 971: 965: 962: 947: 935: 931: 924: 912: 906: 773:Each part is a 757: 755:Basic structure 725:Laws of Thought 719:Prior Analytics 713:Laws of Thought 701: 682:predicate logic 671:Austrian Empire 649:Bernard Bolzano 637:Begriffsschrift 618:("A or B") and 591: 571: 539: 529:Prior Analytics 521: 516: 488:Prior Analytics 470:Prior Analytics 464:Prior Analytics 420:Prior Analytics 411: 405: 397: 391: 378:Begriffsschrift 345:Stoic syllogism 336: 333: 331: 318:Prior Analytics 292:to arrive at a 260: 249: 248: 247: 242: 231: 225: 222: 214:help improve it 211: 199: 195: 184: 173: 167: 164: 121: 119: 109: 97: 56: 52: 45: 35: 32:Epagoge (genus) 28: 23: 22: 15: 12: 11: 5: 6975: 6973: 6965: 6964: 6959: 6954: 6949: 6939: 6938: 6932: 6931: 6917: 6914: 6913: 6911: 6910: 6905: 6900: 6895: 6890: 6889: 6888: 6878: 6873: 6868: 6859: 6854: 6849: 6844: 6842:Abstract logic 6838: 6836: 6832: 6831: 6829: 6828: 6823: 6821:Turing machine 6818: 6813: 6808: 6803: 6798: 6793: 6792: 6791: 6786: 6781: 6776: 6771: 6761: 6759:Computable set 6756: 6751: 6746: 6741: 6735: 6733: 6727: 6726: 6724: 6723: 6718: 6713: 6708: 6703: 6698: 6693: 6688: 6687: 6686: 6681: 6676: 6666: 6661: 6656: 6654:Satisfiability 6651: 6646: 6641: 6640: 6639: 6629: 6628: 6627: 6617: 6616: 6615: 6610: 6605: 6600: 6595: 6585: 6584: 6583: 6578: 6571:Interpretation 6567: 6565: 6559: 6558: 6556: 6555: 6550: 6545: 6540: 6535: 6525: 6520: 6519: 6518: 6517: 6516: 6506: 6501: 6491: 6486: 6481: 6476: 6471: 6466: 6460: 6458: 6452: 6451: 6448: 6447: 6445: 6444: 6436: 6435: 6434: 6433: 6428: 6427: 6426: 6421: 6416: 6396: 6395: 6394: 6392:minimal axioms 6389: 6378: 6377: 6376: 6365: 6364: 6363: 6358: 6353: 6348: 6343: 6338: 6325: 6323: 6304: 6303: 6301: 6300: 6299: 6298: 6286: 6281: 6280: 6279: 6274: 6269: 6264: 6254: 6249: 6244: 6239: 6238: 6237: 6232: 6222: 6221: 6220: 6215: 6210: 6205: 6195: 6190: 6189: 6188: 6183: 6178: 6168: 6167: 6166: 6161: 6156: 6151: 6146: 6141: 6131: 6126: 6121: 6116: 6115: 6114: 6109: 6104: 6099: 6089: 6084: 6082:Formation rule 6079: 6074: 6073: 6072: 6067: 6057: 6056: 6055: 6045: 6040: 6035: 6030: 6024: 6018: 6001:Formal systems 5997: 5996: 5993: 5992: 5990: 5989: 5984: 5979: 5974: 5969: 5964: 5959: 5954: 5949: 5944: 5943: 5942: 5937: 5926: 5924: 5920: 5919: 5917: 5916: 5915: 5914: 5904: 5899: 5898: 5897: 5890:Large cardinal 5887: 5882: 5877: 5872: 5867: 5853: 5852: 5851: 5846: 5841: 5826: 5824: 5814: 5813: 5811: 5810: 5809: 5808: 5803: 5798: 5788: 5783: 5778: 5773: 5768: 5763: 5758: 5753: 5748: 5743: 5738: 5733: 5727: 5725: 5718: 5717: 5715: 5714: 5713: 5712: 5707: 5702: 5697: 5692: 5687: 5679: 5678: 5677: 5672: 5662: 5657: 5655:Extensionality 5652: 5650:Ordinal number 5647: 5637: 5632: 5631: 5630: 5619: 5613: 5607: 5606: 5603: 5602: 5600: 5599: 5594: 5589: 5584: 5579: 5574: 5569: 5568: 5567: 5557: 5556: 5555: 5542: 5540: 5534: 5533: 5531: 5530: 5529: 5528: 5523: 5518: 5508: 5503: 5498: 5493: 5488: 5483: 5477: 5475: 5469: 5468: 5466: 5465: 5460: 5455: 5450: 5445: 5440: 5435: 5434: 5433: 5423: 5418: 5413: 5408: 5403: 5398: 5392: 5390: 5381: 5375: 5374: 5372: 5371: 5366: 5361: 5356: 5351: 5346: 5334:Cantor's 5332: 5327: 5322: 5312: 5310: 5297: 5296: 5294: 5293: 5288: 5283: 5278: 5273: 5268: 5263: 5258: 5253: 5248: 5243: 5238: 5233: 5232: 5231: 5220: 5218: 5214: 5213: 5208: 5206: 5205: 5198: 5191: 5183: 5174: 5173: 5171: 5170: 5165: 5160: 5155: 5149: 5146: 5145: 5143: 5142: 5137: 5132: 5127: 5122: 5117: 5111: 5109: 5100: 5096: 5095: 5092: 5091: 5089: 5088: 5083: 5077: 5075: 5071: 5070: 5068: 5067: 5062: 5056: 5054: 5047: 5046: 5041: 5035: 5033: 5027: 5026: 5024: 5023: 5018: 5013: 5007: 5005: 5001: 5000: 4998: 4997: 4992: 4987: 4982: 4977: 4971: 4969: 4963: 4962: 4960: 4959: 4954: 4949: 4944: 4938: 4936: 4932: 4931: 4925: 4923: 4922: 4915: 4908: 4900: 4891: 4890: 4884: 4879: 4874: 4869: 4864: 4858: 4839: 4833: 4817:Smith, Robin. 4812: 4811:External links 4809: 4808: 4807: 4790: 4783: 4771: 4768:978-0822983958 4756: 4749: 4738: 4712: 4711: 4710: 4682: 4671: 4664: 4655: 4646:Corcoran, John 4643: 4633: 4618: 4595: 4574: 4571: 4568: 4567: 4552: 4537: 4522: 4520:. London: LEA. 4509: 4484: 4466: 4429: 4408: 4400:Corcoran, John 4389: 4374: 4352: 4332:Bacon, Francis 4321: 4294: 4268: 4250: 4229: 4209: 4201:Frede, Michael 4190: 4177: 4161: 4160: 4158: 4155: 4154: 4153: 4148: 4143: 4138: 4133: 4131:Formal fallacy 4128: 4123: 4121:Buddhist logic 4118: 4113: 4107: 4106: 4090: 4087: 4086: 4085: 4080: 4075: 4070: 4065: 4060: 4055: 4048: 4045: 4044: 4043: 4037: 4031: 4025: 4019: 4013: 3984: 3981: 3943: 3942: 3939: 3930: 3929: 3925: 3922: 3919: 3916: 3912: 3875: 3874: 3857: 3856: 3807: 3805: 3798: 3791: 3790: 3745: 3743: 3736: 3731: 3705: 3704: 3702: 3695: 3689: 3686: 3625: 3624: 3621: 3617: 3605:singular terms 3599: 3598: 3581: 3580: 3531: 3529: 3522: 3515: 3514: 3469: 3467: 3460: 3455: 3429: 3428: 3426: 3419: 3413: 3410: 3407: 3406: 3396: 3394: 3392: 3382: 3380: 3368: 3366: 3354: 3344: 3332: 3330: 3326: 3325: 3315: 3305: 3303: 3293: 3283: 3271: 3269: 3267: 3265: 3253: 3251: 3247: 3246: 3236: 3234: 3224: 3222: 3220: 3208: 3198: 3186: 3176: 3174: 3172: 3168: 3167: 3157: 3155: 3153: 3151: 3141: 3129: 3119: 3117: 3115: 3103: 3093: 3089: 3088: 3085: 3082: 3079: 3076: 3073: 3059: 3056: 3055: 3054: 3048: 3041: 3028: 3023: 3017: 3016: 3009:S: rhomb 3000: 2999: 2992: 2982: 2981: 2975: 2972: 2966:Fesapo (EAO-4) 2961: 2956: 2950: 2949: 2942:S: plant 2933: 2932: 2925: 2915: 2914: 2908: 2905: 2894: 2889: 2883: 2882: 2879:P: horse 2875:S: human 2866: 2865: 2858: 2848: 2847: 2841: 2838: 2832:Cesaro (EAO-2) 2827: 2822: 2816: 2815: 2808:S: snake 2799: 2798: 2791: 2779: 2778: 2777: 2776: 2770: 2767: 2751: 2750: 2747:P: Greek 2734: 2733: 2726: 2714: 2713: 2703: 2702: 2696: 2693: 2688: 2683: 2677: 2676: 2669:S: Greek 2660: 2659: 2652: 2641: 2640: 2634: 2631: 2626: 2623: 2617: 2616: 2600: 2599: 2592: 2582: 2581: 2575: 2572: 2567: 2566:Baroco (AOO-2) 2564: 2558: 2557: 2541: 2540: 2533: 2523: 2522: 2516: 2513: 2505: 2502: 2496: 2495: 2479: 2478: 2471: 2459: 2458: 2457: 2456: 2450: 2447: 2436: 2435: 2419: 2418: 2411: 2399: 2398: 2390: 2389: 2383: 2380: 2372: 2369: 2363: 2362: 2346: 2345: 2338: 2326: 2325: 2324: 2323: 2317: 2314: 2303: 2302: 2299:P: snake 2286: 2285: 2278: 2266: 2265: 2257: 2256: 2250: 2247: 2239: 2236: 2230: 2229: 2222:S: snake 2213: 2212: 2205: 2195: 2194: 2188: 2185: 2180: 2177: 2171: 2170: 2154: 2153: 2146: 2135: 2132: 2096: 2095: 2078: 2062: 2045: 2027: 2026: 2010: 1993: 1977: 1960: 1959: 1942: 1928: 1914: 1903: 1902: 1887: 1872: 1858: 1847: 1846: 1831: 1816: 1801: 1785: 1784: 1769: 1755: 1741: 1726: 1725: 1722: 1719: 1716: 1678: 1677: 1674: 1671: 1668: 1665: 1664:Minor premise 1661: 1660: 1657: 1654: 1651: 1648: 1647:Major premise 1644: 1643: 1640: 1637: 1634: 1631: 1616: 1615: 1604: 1601: 1598: 1595: 1592: 1589: 1586: 1583: 1580: 1577: 1574: 1571: 1568: 1565: 1555: 1552: 1548: 1547: 1536: 1533: 1530: 1527: 1524: 1521: 1518: 1515: 1512: 1509: 1506: 1503: 1500: 1490: 1487: 1483: 1482: 1471: 1468: 1465: 1462: 1459: 1456: 1453: 1450: 1447: 1444: 1441: 1438: 1435: 1432: 1408: 1405: 1402: 1399: 1396: 1393: 1390: 1387: 1384: 1381: 1378: 1375: 1372: 1369: 1359: 1356: 1352: 1351: 1340: 1337: 1334: 1331: 1328: 1325: 1322: 1319: 1316: 1313: 1310: 1307: 1304: 1301: 1298: 1274: 1271: 1268: 1265: 1262: 1259: 1256: 1253: 1250: 1247: 1244: 1241: 1238: 1228: 1225: 1221: 1220: 1217: 1214: 1155: 1154: 1151: 1148: 1145: 1139: 1136: 1133: 1129: 1128: 1125: 1122: 1119: 1116: 1113: 1110: 1106: 1105: 1102: 1099: 1096: 1093: 1090: 1087: 1083: 1082: 1079: 1076: 1073: 1070: 1067: 1064: 1060: 1059: 1056: 1053: 1050: 1047: 1044: 1041: 1032: 1031: 1030:: All S are P. 1025: 1024:: All S are M. 1019: 1018:: All M are P. 984: 983: 938: 936: 929: 923: 920: 908:Main article: 905: 902: 886: 885: 884:: All men die. 879: 873: 835: 834: 828: 822: 800: 799: 789: 771: 770: 767: 764: 756: 753: 744: 743: 740: 733: 700: 697: 642:Concept Script 634:published his 590: 589:Modern history 587: 570: 567: 538: 535: 520: 517: 515: 512: 407:Main article: 404: 401: 393:Main article: 390: 387: 383:Concept Script 328: 262: 261: 244: 243: 202: 200: 193: 186: 185: 100: 98: 91: 86: 60: 59: 57: 50: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 6974: 6963: 6960: 6958: 6955: 6953: 6950: 6948: 6945: 6944: 6942: 6929: 6928: 6923: 6915: 6909: 6906: 6904: 6901: 6899: 6896: 6894: 6891: 6887: 6884: 6883: 6882: 6879: 6877: 6874: 6872: 6869: 6867: 6863: 6860: 6858: 6855: 6853: 6850: 6848: 6845: 6843: 6840: 6839: 6837: 6833: 6827: 6824: 6822: 6819: 6817: 6816:Recursive set 6814: 6812: 6809: 6807: 6804: 6802: 6799: 6797: 6794: 6790: 6787: 6785: 6782: 6780: 6777: 6775: 6772: 6770: 6767: 6766: 6765: 6762: 6760: 6757: 6755: 6752: 6750: 6747: 6745: 6742: 6740: 6737: 6736: 6734: 6732: 6728: 6722: 6719: 6717: 6714: 6712: 6709: 6707: 6704: 6702: 6699: 6697: 6694: 6692: 6689: 6685: 6682: 6680: 6677: 6675: 6672: 6671: 6670: 6667: 6665: 6662: 6660: 6657: 6655: 6652: 6650: 6647: 6645: 6642: 6638: 6635: 6634: 6633: 6630: 6626: 6625:of arithmetic 6623: 6622: 6621: 6618: 6614: 6611: 6609: 6606: 6604: 6601: 6599: 6596: 6594: 6591: 6590: 6589: 6586: 6582: 6579: 6577: 6574: 6573: 6572: 6569: 6568: 6566: 6564: 6560: 6554: 6551: 6549: 6546: 6544: 6541: 6539: 6536: 6533: 6532:from ZFC 6529: 6526: 6524: 6521: 6515: 6512: 6511: 6510: 6507: 6505: 6502: 6500: 6497: 6496: 6495: 6492: 6490: 6487: 6485: 6482: 6480: 6477: 6475: 6472: 6470: 6467: 6465: 6462: 6461: 6459: 6457: 6453: 6443: 6442: 6438: 6437: 6432: 6431:non-Euclidean 6429: 6425: 6422: 6420: 6417: 6415: 6414: 6410: 6409: 6407: 6404: 6403: 6401: 6397: 6393: 6390: 6388: 6385: 6384: 6383: 6379: 6375: 6372: 6371: 6370: 6366: 6362: 6359: 6357: 6354: 6352: 6349: 6347: 6344: 6342: 6339: 6337: 6334: 6333: 6331: 6327: 6326: 6324: 6319: 6313: 6308:Example 6305: 6297: 6292: 6291: 6290: 6287: 6285: 6282: 6278: 6275: 6273: 6270: 6268: 6265: 6263: 6260: 6259: 6258: 6255: 6253: 6250: 6248: 6245: 6243: 6240: 6236: 6233: 6231: 6228: 6227: 6226: 6223: 6219: 6216: 6214: 6211: 6209: 6206: 6204: 6201: 6200: 6199: 6196: 6194: 6191: 6187: 6184: 6182: 6179: 6177: 6174: 6173: 6172: 6169: 6165: 6162: 6160: 6157: 6155: 6152: 6150: 6147: 6145: 6142: 6140: 6137: 6136: 6135: 6132: 6130: 6127: 6125: 6122: 6120: 6117: 6113: 6110: 6108: 6105: 6103: 6100: 6098: 6095: 6094: 6093: 6090: 6088: 6085: 6083: 6080: 6078: 6075: 6071: 6068: 6066: 6065:by definition 6063: 6062: 6061: 6058: 6054: 6051: 6050: 6049: 6046: 6044: 6041: 6039: 6036: 6034: 6031: 6029: 6026: 6025: 6022: 6019: 6017: 6013: 6008: 6002: 5998: 5988: 5985: 5983: 5980: 5978: 5975: 5973: 5970: 5968: 5965: 5963: 5960: 5958: 5955: 5953: 5952:Kripke–Platek 5950: 5948: 5945: 5941: 5938: 5936: 5933: 5932: 5931: 5928: 5927: 5925: 5921: 5913: 5910: 5909: 5908: 5905: 5903: 5900: 5896: 5893: 5892: 5891: 5888: 5886: 5883: 5881: 5878: 5876: 5873: 5871: 5868: 5865: 5861: 5857: 5854: 5850: 5847: 5845: 5842: 5840: 5837: 5836: 5835: 5831: 5828: 5827: 5825: 5823: 5819: 5815: 5807: 5804: 5802: 5799: 5797: 5796:constructible 5794: 5793: 5792: 5789: 5787: 5784: 5782: 5779: 5777: 5774: 5772: 5769: 5767: 5764: 5762: 5759: 5757: 5754: 5752: 5749: 5747: 5744: 5742: 5739: 5737: 5734: 5732: 5729: 5728: 5726: 5724: 5719: 5711: 5708: 5706: 5703: 5701: 5698: 5696: 5693: 5691: 5688: 5686: 5683: 5682: 5680: 5676: 5673: 5671: 5668: 5667: 5666: 5663: 5661: 5658: 5656: 5653: 5651: 5648: 5646: 5642: 5638: 5636: 5633: 5629: 5626: 5625: 5624: 5621: 5620: 5617: 5614: 5612: 5608: 5598: 5595: 5593: 5590: 5588: 5585: 5583: 5580: 5578: 5575: 5573: 5570: 5566: 5563: 5562: 5561: 5558: 5554: 5549: 5548: 5547: 5544: 5543: 5541: 5539: 5535: 5527: 5524: 5522: 5519: 5517: 5514: 5513: 5512: 5509: 5507: 5504: 5502: 5499: 5497: 5494: 5492: 5489: 5487: 5484: 5482: 5479: 5478: 5476: 5474: 5473:Propositional 5470: 5464: 5461: 5459: 5456: 5454: 5451: 5449: 5446: 5444: 5441: 5439: 5436: 5432: 5429: 5428: 5427: 5424: 5422: 5419: 5417: 5414: 5412: 5409: 5407: 5404: 5402: 5401:Logical truth 5399: 5397: 5394: 5393: 5391: 5389: 5385: 5382: 5380: 5376: 5370: 5367: 5365: 5362: 5360: 5357: 5355: 5352: 5350: 5347: 5345: 5341: 5337: 5333: 5331: 5328: 5326: 5323: 5321: 5317: 5314: 5313: 5311: 5309: 5303: 5298: 5292: 5289: 5287: 5284: 5282: 5279: 5277: 5274: 5272: 5269: 5267: 5264: 5262: 5259: 5257: 5254: 5252: 5249: 5247: 5244: 5242: 5239: 5237: 5234: 5230: 5227: 5226: 5225: 5222: 5221: 5219: 5215: 5211: 5204: 5199: 5197: 5192: 5190: 5185: 5184: 5181: 5169: 5166: 5164: 5161: 5159: 5156: 5154: 5151: 5150: 5141: 5138: 5136: 5133: 5131: 5128: 5126: 5123: 5121: 5118: 5116: 5113: 5112: 5110: 5108: 5104: 5101: 5097: 5087: 5084: 5082: 5079: 5078: 5076: 5072: 5066: 5063: 5061: 5058: 5057: 5055: 5051: 5045: 5042: 5040: 5037: 5036: 5034: 5032: 5028: 5022: 5019: 5017: 5014: 5012: 5009: 5008: 5006: 5002: 4996: 4993: 4991: 4988: 4986: 4983: 4981: 4978: 4976: 4973: 4972: 4970: 4968: 4964: 4958: 4957:Syncategorema 4955: 4953: 4950: 4948: 4945: 4943: 4940: 4939: 4937: 4933: 4929:(syllogistic) 4928: 4921: 4916: 4914: 4909: 4907: 4902: 4901: 4898: 4894: 4888: 4885: 4883: 4880: 4878: 4875: 4873: 4870: 4868: 4865: 4862: 4859: 4855: 4854: 4849: 4845: 4840: 4838: 4834: 4830: 4829: 4824: 4820: 4815: 4814: 4810: 4805: 4804:3-88405-002-8 4801: 4797: 4796: 4791: 4788: 4784: 4781: 4780: 4775: 4772: 4769: 4765: 4761: 4757: 4754: 4750: 4747: 4743: 4739: 4736: 4732: 4728: 4727:0-8240-6924-2 4724: 4720: 4716: 4713: 4708: 4705: 4704: 4702: 4701:0-416-70070-5 4698: 4694: 4690: 4686: 4683: 4680: 4676: 4672: 4669: 4665: 4662: 4661: 4656: 4653: 4652: 4647: 4644: 4641: 4637: 4634: 4631: 4630:0-19-824026-0 4627: 4623: 4619: 4616: 4615:0-19-283134-8 4612: 4608: 4607: 4604: 4599: 4596: 4594: 4593:0-87220-064-7 4590: 4586: 4585: 4580: 4577: 4576: 4572: 4563: 4556: 4553: 4549: 4548: 4541: 4538: 4534: 4533: 4526: 4523: 4519: 4513: 4510: 4499:on 2017-02-04 4498: 4494: 4488: 4485: 4480: 4476: 4470: 4467: 4463: 4462: 4457: 4456: 4451: 4450: 4445: 4444: 4439: 4436:According to 4433: 4430: 4418: 4412: 4409: 4405: 4401: 4396: 4394: 4390: 4386: 4385: 4378: 4375: 4371: 4367: 4366: 4361: 4360:Boole, George 4356: 4353: 4349: 4345: 4344: 4339: 4338: 4333: 4328: 4326: 4322: 4309: 4305: 4298: 4295: 4291: 4287: 4286: 4281: 4280:Ancient Logic 4277: 4272: 4269: 4265: 4264: 4259: 4254: 4251: 4247: 4246:9781118053072 4243: 4239: 4233: 4230: 4227: 4226:9780840034175 4223: 4219: 4213: 4210: 4206: 4202: 4197: 4195: 4191: 4187: 4181: 4178: 4173: 4166: 4163: 4156: 4152: 4149: 4147: 4144: 4142: 4139: 4137: 4134: 4132: 4129: 4127: 4124: 4122: 4119: 4117: 4114: 4112: 4109: 4108: 4104: 4093: 4088: 4084: 4081: 4079: 4076: 4074: 4071: 4069: 4068:Polysyllogism 4066: 4064: 4061: 4059: 4056: 4054: 4051: 4050: 4046: 4041: 4038: 4035: 4032: 4029: 4026: 4023: 4020: 4017: 4014: 4011: 4008: 4007: 4006: 4003: 4001: 3996: 3994: 3988: 3982: 3980: 3978: 3973: 3969: 3968:AaB, AeB, AiB 3965: 3961: 3957: 3951: 3947: 3940: 3937: 3936: 3935: 3926: 3923: 3920: 3917: 3914: 3913: 3911: 3908: 3906: 3901: 3896: 3892: 3890: 3886: 3882: 3871: 3868: 3853: 3850: 3842: 3832: 3828: 3824: 3818: 3817: 3813: 3808:This section 3806: 3802: 3797: 3796: 3787: 3784: 3776: 3766: 3762: 3758: 3752: 3751: 3746:This section 3744: 3735: 3734: 3729: 3727: 3720: 3719: 3714: 3713: 3708: 3703: 3694: 3693: 3687: 3685: 3683: 3679: 3675: 3671: 3667: 3661: 3659: 3655: 3651: 3647: 3643: 3639: 3635: 3631: 3622: 3619: 3618: 3616: 3614: 3610: 3606: 3595: 3592: 3577: 3574: 3566: 3556: 3552: 3548: 3542: 3541: 3537: 3532:This section 3530: 3526: 3521: 3520: 3511: 3508: 3500: 3490: 3486: 3482: 3476: 3475: 3470:This section 3468: 3459: 3458: 3453: 3451: 3444: 3443: 3438: 3437: 3432: 3427: 3418: 3417: 3411: 3401: 3397: 3395: 3393: 3387: 3383: 3381: 3377: 3373: 3369: 3367: 3363: 3359: 3355: 3349: 3345: 3341: 3337: 3333: 3331: 3328: 3327: 3320: 3316: 3310: 3306: 3304: 3298: 3294: 3288: 3284: 3280: 3276: 3272: 3270: 3268: 3266: 3262: 3258: 3254: 3252: 3249: 3248: 3241: 3237: 3235: 3229: 3225: 3223: 3221: 3217: 3213: 3209: 3203: 3199: 3195: 3191: 3187: 3181: 3177: 3175: 3173: 3170: 3169: 3162: 3158: 3156: 3154: 3152: 3146: 3142: 3138: 3134: 3130: 3124: 3120: 3118: 3116: 3112: 3108: 3104: 3098: 3094: 3091: 3090: 3086: 3071: 3070: 3067: 3065: 3064:Venn diagrams 3057: 3052: 3049: 3046: 3042: 3039: 3035: 3031: 3030: 3027: 3024: 3022: 3002: 3001: 2997: 2990: 2986: 2985: 2979: 2976: 2973: 2970: 2969: 2968: 2967: 2960: 2957: 2955: 2935: 2934: 2930: 2923: 2919: 2918: 2912: 2909: 2906: 2903: 2902: 2901: 2900: 2893: 2890: 2888: 2868: 2867: 2863: 2856: 2852: 2851: 2845: 2842: 2839: 2836: 2835: 2834: 2833: 2826: 2823: 2821: 2801: 2800: 2796: 2789: 2785: 2784: 2774: 2771: 2768: 2765: 2764: 2763: 2761: 2757: 2736: 2735: 2731: 2724: 2720: 2719: 2716: 2715: 2712: 2708: 2705: 2700: 2697: 2694: 2691: 2690: 2687: 2684: 2682: 2662: 2661: 2657: 2650: 2646: 2645: 2638: 2635: 2632: 2629: 2628: 2624: 2622: 2602: 2601: 2597: 2590: 2586: 2585: 2579: 2576: 2573: 2570: 2569: 2565: 2563: 2543: 2542: 2538: 2531: 2527: 2526: 2520: 2517: 2514: 2511: 2510: 2509: 2504:Ferio (EIO-1) 2503: 2501: 2481: 2480: 2476: 2469: 2465: 2464: 2454: 2451: 2448: 2445: 2444: 2443: 2421: 2420: 2416: 2409: 2405: 2404: 2401: 2400: 2395: 2392: 2387: 2384: 2381: 2378: 2377: 2376: 2371:Darii (AII-1) 2370: 2368: 2348: 2347: 2343: 2336: 2332: 2331: 2321: 2318: 2315: 2312: 2311: 2310: 2288: 2287: 2283: 2276: 2272: 2271: 2268: 2267: 2262: 2259: 2254: 2251: 2248: 2245: 2244: 2243: 2237: 2235: 2215: 2214: 2210: 2203: 2199: 2198: 2192: 2189: 2186: 2183: 2182: 2178: 2176: 2156: 2155: 2151: 2144: 2140: 2139: 2133: 2131: 2129: 2124: 2120: 2118: 2113: 2109: 2107: 2103: 2094: 2092: 2088: 2084: 2079: 2077: 2076: 2072: 2068: 2063: 2061: 2059: 2055: 2051: 2046: 2044: 2042: 2038: 2034: 2029: 2028: 2025: 2024: 2020: 2016: 2011: 2009: 2007: 2003: 1999: 1994: 1992: 1991: 1987: 1983: 1978: 1976: 1975: 1971: 1967: 1962: 1961: 1958: 1956: 1952: 1948: 1943: 1941: 1937: 1933: 1929: 1927: 1923: 1919: 1915: 1913: 1909: 1905: 1904: 1900: 1896: 1892: 1888: 1885: 1881: 1877: 1873: 1871: 1867: 1863: 1859: 1857: 1853: 1849: 1848: 1844: 1840: 1836: 1832: 1829: 1825: 1821: 1817: 1814: 1810: 1806: 1802: 1799: 1795: 1791: 1787: 1786: 1782: 1778: 1774: 1770: 1768: 1764: 1760: 1756: 1754: 1750: 1746: 1742: 1740: 1736: 1732: 1728: 1727: 1723: 1720: 1717: 1714: 1713: 1710: 1708: 1704: 1700: 1695: 1691: 1689: 1685: 1684:Peter Abelard 1675: 1672: 1669: 1666: 1663: 1662: 1658: 1655: 1652: 1649: 1646: 1645: 1641: 1638: 1635: 1632: 1630: 1629: 1626: 1624: 1596: 1590: 1584: 1578: 1572: 1566: 1556: 1553: 1550: 1549: 1528: 1522: 1519: 1513: 1507: 1501: 1491: 1488: 1485: 1484: 1463: 1457: 1445: 1439: 1433: 1422: 1400: 1394: 1391: 1385: 1379: 1373: 1360: 1357: 1354: 1353: 1332: 1326: 1320: 1314: 1308: 1302: 1288: 1266: 1260: 1251: 1245: 1239: 1229: 1226: 1223: 1222: 1218: 1215: 1212: 1211: 1208: 1206: 1202: 1201:All As are Bs 1198: 1194: 1190: 1186: 1182: 1181: 1176: 1175: 1170: 1169: 1164: 1163: 1152: 1149: 1146: 1144: 1140: 1137: 1134: 1131: 1130: 1126: 1123: 1120: 1117: 1114: 1111: 1108: 1107: 1103: 1100: 1097: 1094: 1091: 1088: 1085: 1084: 1080: 1077: 1074: 1071: 1068: 1065: 1062: 1061: 1057: 1054: 1051: 1048: 1045: 1042: 1039: 1038: 1035: 1029: 1026: 1023: 1022:Minor premise 1020: 1017: 1016:Major premise 1014: 1013: 1012: 1007: 995: 990: 980: 977: 969: 959: 955: 951: 945: 944: 939:This section 937: 928: 927: 921: 919: 917: 911: 910:Polysyllogism 904:Polysyllogism 903: 901: 899: 895: 891: 883: 880: 877: 876:Minor premise 874: 871: 870:Major premise 868: 867: 866: 864: 860: 856: 852: 848: 844: 840: 832: 829: 826: 825:Minor premise 823: 820: 819:Major premise 817: 816: 815: 813: 809: 805: 797: 795: 790: 787: 785: 780: 779: 778: 776: 768: 766:Minor premise 765: 763:Major premise 762: 761: 760: 754: 752: 749: 741: 738: 734: 731: 730: 729: 727: 726: 721: 720: 715: 714: 709: 708:John Corcoran 705: 696: 694: 690: 685: 683: 679: 674: 672: 668: 664: 663:New Anti-Kant 660: 656: 655: 650: 645: 643: 639: 638: 633: 632:Gottlob Frege 629: 625: 624:Immanuel Kant 621: 617: 612: 610: 609: 603: 602:Francis Bacon 598: 596: 588: 586: 584: 580: 576: 568: 566: 564: 563: 558: 557: 552: 548: 544: 543:Peter Abelard 537:Peter Abelard 536: 534: 531: 530: 525: 518: 513: 511: 509: 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5895:inaccessible 5801:Grothendieck 5685:intersection 5572:Higher-order 5560:Second-order 5506:Truth tables 5463:Venn diagram 5452: 5246:Formal proof 5163:Sum of Logic 5030: 5004:Propositions 4892: 4851: 4826: 4793: 4786: 4777: 4759: 4752: 4741: 4718: 4688: 4674: 4670:36(1):39–61. 4667: 4658: 4649: 4639: 4636:Copi, Irving 4621: 4605: 4602: 4582: 4561: 4555: 4545: 4540: 4530: 4525: 4517: 4512: 4501:. 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