SYLLOGISM
SYLLOGISM
(from Greek syllogismos) - mediated syllogistics. The most famous form of S. is the so-called. simple S. - a two-premises inference about the relationship between two terms (the larger one - P and the smaller one - S) by indicating their relationship to some third, mediating term, called the middle term - M. Classic example a simple categorical S. is the following conclusion: “All people are mortal, Socrates -; therefore Socrates is mortal."
S. are divided according to the so-called. figures that differ from each other in the location of the middle term in the premises. Up to the order of the premises, the following figures C are distinguished:
M-P
S-M
S - P
Figure 1
R - M
S - M
S - P
Figure 2
M-P
M-S
S - P
Figure 3
P-M
M-S
S - P
Figure 4
If in a figure we indicate statements that stand in the places of premises and conclusion, then we get a variety of this figure, called the mode of the figure. Thus, the above S. refers to the Barbara mode of the first figure, which has the following form:
Every M is P
Every S is M
Every S is P
Those modes for which there is a logical consequence between the premises and the conclusion are called correct. To check the correctness of S. there is a special list of rules. The fulfillment of each rule is necessary, and all together is a sufficient condition to consider one correct. These rules are called general rules S. and are divided into rules of terms and rules of premises.
Rules of terms:
1. There must be , in which the average is distributed.
2. If a term is distributed in the conclusion, then it is distributed in the premise.
Parcel rules:
3. There must be an affirmative premise.
4. If both are affirmative, then - affirmative.
5. If there is a negative premise, then the conclusion is a negative statement.
Philosophy: Encyclopedic Dictionary. - M.: Gardariki. Edited by A.A. Ivina. 2004 .
SYLLOGISM
(Greek) , a form of deductive reasoning in which from two statements (parcels) subject-predicate structure is followed by a statement (conclusion) the same logic. structures. Usually S. called categorical S., consisting of three terms, pairwise connected in statements of S. through one of the traces, four logical. relations: “Everything... is...”, “None... is...”, “Some... is...”, “Some... is not...” (designated respectively by the letters A, E, I, O). For example: “Not a single whale (M) don't eat fish () , every whale (M) has a fish-like shape () ; hence some are fish-shaped () don't eat fish () " Statements containing a term not included in the conclusion S. (middle term, M), make up premises C. Premise containing conclusions (greater term, ), called larger parcel. Parcel containing conclusions (minor term, ), called smaller parcel. According to the position of the middle term in the premises (depending on whether it is a subject or a predicate) S. is divided into four figures. Depending on the logical relations connecting terms in S.'s statements are distinguished by various modes.
Philosophical encyclopedic dictionary. - M.: Soviet Encyclopedia. Ch. editor: L. F. Ilyichev, P. N. Fedoseev, S. M. Kovalev, V. G. Panov. 1983 .
SYLLOGISM
(from Greek sollogismos summarizing)
excretion, inference From general to specific. Syllogistics is the study of inferences.
Philosophical Encyclopedic Dictionary. 2010 .
SYLLOGISM
(Greek συλλογισμός) - a form of deductive inference, in which a certainty is determined from two statements (premises). subject-predicate structure is followed by a new statement (conclusion) of the same logical. structures. S. usually called categorical S., statements (judgments) of which are composed of three terms, and each statement represents two terms by means of one of the following. four logical relations: “Everything... is...”, “None... is...”, “Some... is...”, “Some... is not...” (denoted in logic, respectively, with the letters A, E, I, O). Examples of categorical forms. C: "Every M is P; every S is M; therefore every S is P"; "No P is M, some S are M; then some S are not P." (Or, formulating S. in the form of a conditional statement, which is closer to how S. was understood by the creator of his theory, Aristotle: “If every M is P and every S is M, then every S is P”; “If no P is there is M and some S is M, then some S is not P"). An example of a specific reasoning in the form of S. (in syllogistic form): “If not a single dolphin is a fish, and some living beings in this body of water are fish, then some living beings in this body of water are not dolphins.” Statements containing a term that is not included in the conclusion of the statement (called the middle term and usually denoted by the letter M) constitute two premises of the statement. The premise containing the predicate (logical predicate) of the conclusion (major terms) n, P), called larger parcel. The premise containing the subject (logical subject) of the conclusion (minor term, S), called. smaller parcel. According to the position of the middle term (M), S. is divided into four figures. In the 1st figure M is the subject in the major premise and the predicate in the minor, in the 2nd figure – the predicate in both premises, in the 3rd – the subject in both premises, in the 4th – the predicate in the major and the subject in the minor premises . In figures, depending on the type of constants, logical. relations connecting the terms in the premises and conclusion, various modes of S. are distinguished. In total, from the point of view. all possible combinations in three statements of S. four constant logical. relations, there are 4·4·4=64 modes in each of the figures; a total of 256 modes in four syllogism figures. However, only 24 modes are correct (i.e., such that, reasoning on them, we will always obtain a true conclusion from true premises) of them, incl. so-called weakened modes, i.e. modes, for which there are modes that give a stronger conclusion from the same premises (for example. , the conclusion “Every S is P” instead of “Some S are P”). A list of all (unweakened) modes of the system by figure (indicating the figure of the statement, fixing the logical relationship connecting the terms of the statement in its premises and conclusion, and specifying the order of recording the statements that make up the statement - first the major premise, then the smaller one, and, finally, the conclusion – they unambiguously define the following three-letter “words”): 1st figure – modes AAA, EAE, AII, EIO; 2nd figure – EAE, AEE, EIO, AOO; 3rd figure – AAI, IAI, AII, EAO, OAO, EIO; 4th figure – AAI, AEE, IAI, EAO, EIO; replacing general statements with particular ones in the corresponding modes gives weakened modes. For further information about the theory (categorical) of S., see Art. Syllogistics.
The term "S." also applies in a broader sense - in relation to conditional and conditionally categorical inferences, divisive-categorical inferences and conditionally divisive (lemmatic) inferences (see Dilemma, Lemma).
Lit.: Aristotle, Analysts, first and second, trans. from Greek, [L.], 1952; Culbertson J.T., Mathematics and Digital Devices, trans. from English, M., 1965. See also lit. at Art. Syllogistics.
A. Subbotin. Moscow.
Philosophical Encyclopedia. In 5 volumes - M.: Soviet Encyclopedia. Edited by F. V. Konstantinov. 1960-1970 .
SYLLOGISM
SYLLOGISM (Greek συλλογισμός) - a deductive inference in which from two statements (premises) of a subject-predicate structure a new statement (conclusion) of the same logical structure follows. Usually a syllogism is called a syllogism consisting of three terms connected in pairs in statements through one of the following four logical relations: “Everything... is...”, “None... is...”, “Some... is...”, “Some... is not...” (denoted respectively by the letters A, E, I, O). For example: “Not a single whale (M) is a fish (), every whale (At) has a fish-like shape (5); therefore, some fish-shaped (5) do not eat fish (P).” Statements containing a term that is not included in the conclusion of the syllogism (the middle term, M) constitute the premises of the syllogism. The premise containing the predicate of the conclusion (the major term, ) is called the major premise. The premise containing the subject of the conclusion (the minor term, ) is called the minor premise. According to the position of the middle term in the premises (depending on whether it is a subject or a predicate), the syllogism is divided into four figures. Depending on the logical relations connecting the terms in the statements of a syllogism, its various modes are distinguished.
A. L. Subbotin
New Philosophical Encyclopedia: In 4 vols. M.: Thought. Edited by V. S. Stepin. 2001 .
Synonyms:
See what "SYLLOGISM" is in other dictionaries:
- [gr. syllogismos] log. a conclusion consisting of two judgments (premises), from which a third judgment follows, a conclusion, a conclusion (for example, every S is M, and every M is P, therefore, every S is P). Dictionary foreign words. Komlev N.G.,... ... Dictionary of foreign words of the Russian language
See the proof... Dictionary of Russian synonyms and similar expressions. under. ed. N. Abramova, M.: Russian Dictionaries, 1999. syllogism inference, proof; reasoning, inference, enthymeme, mode Dictionary r ... Synonym dictionary
Syllogism- Syllogism ♦ Syllogisme A type of deductive reasoning, formulated by Aristotle, combining three terms related in pairs, each mentioned twice, in three propositions. However, the canonical example of a syllogism is... ... Philosophical Dictionary Sponville
- (Greek syllogismos) reasoning in which two premises connecting subjects (subjects) and predicates (predicates) are united by a common (middle) term that ensures the closure of concepts (terms) in the conclusion of the syllogism. Eg: All metals... ... Big Encyclopedic Dictionary
SYLLOGISM, syllogism, man. (Greek syllogismos) (philosophy). In formal logic, an inference in which from two previously established propositions, called premises, a third proposition, called the conclusion, is obtained. Dictionary Ushakova. D.N.... ... Ushakov's Explanatory Dictionary
SYLLOGISM, ah, husband. In logic: inference, in which from two given judgments (premises) a third (conclusion) is obtained. | adj. syllogistic, aya, oh and syllogistic, aya, oh. Ozhegov's explanatory dictionary. S.I. Ozhegov, N.Yu. Shvedova. 1949 1992 … Ozhegov's Explanatory Dictionary
Syllogism an inference in which, based on several judgments, a new judgment, called a conclusion, is necessarily derived. In contrast to S., as a mediocre inference, a direct inference is one in which the conclusion is obtained from a given judgment without the help of another. I. Direct inferences include: a) inferences by submission. One can always infer from the truth of a general judgment to the truth of a particular content of the same content, but not vice versa; one can always conclude from the falsity of a particular judgment to the falsity of a general judgment of the same content, but not vice versa. These conclusions are made on the basis of the dictum de omni et nullo: quicquid de omnibus valet etiam de quibusdam et singulis; quicquid de nullo valet nec de quihusdam nec de singulis valet; b) inferences by identity: from the truth of a known judgment follows the truth of something identical in content; c) inferences on transformation(conversio), based on the relationship between the volumes of the logical subject and the logical predicate and the possibility of their rearrangement. By transformation, generally affirmative judgments turn into generally affirmative ones in the case where the volume of the subject is equal to the volume of the predicate (conversio pura), for example. A = B, therefore, B = A; but the vast majority of general affirmative judgments, through transformation, turn into private affirmative ones (conversio impura) on the basis that the volume of the predicate (defining) is usually greater than the volume of the defined - therefore, during transformation, part of the volume of the defining concept loses its significance for the conclusion. Particular affirmative and general negative judgments give pure transformations. Partial negative judgments do not give a conclusion when transforming. If, when transforming judgments, their qualities are also changed, that is, affirmative ones are turned into negative ones, then the following type of conclusions will be obtained: from generally affirmative ones, generally negative judgments will be obtained; from a general negative - usually a particular affirmative, in cases of equality of the logical subject and predicate - a general affirmative; from partial negative judgments partial affirmative ones are obtained; finally, no conclusions can be drawn from a particular affirmative. Based on the relationship of concepts depicted in the so-called. logical square, one can make conclusions regarding the contradiction and opposition of judgments. II. They distinguish mediocre conclusions from direct inferences, or S.S. are categorical, conditional, and divisive, depending on the nature of the judgment, called in S. the major premise. Premises are those judgments from which the conclusion is derived; the very process of drawing a conclusion is called inference. Simplest form the principle on the basis of which inference is made - two quantities, separately equal to the third, are equal to each other; but since only a small number of judgments represent a real equality of the concepts contained in them, and in most judgments the scope of the predicate is wider than the scope of the logical subject, the above principle accepts the following formula: two concepts related to the third also have some relationship with each other. A correct inference must accurately determine the relationship between these concepts. The relationship of concepts to each other is established thanks to the concept common to the two judgments. Thus, the most general rule of inference is that only from such two judgments can a conclusion be drawn that have one general concept. This general concept in syllogistic is called the middle term; the premise from which the subject of the conclusion is taken is called the minor, and the subject itself is called the minor term; the premise from which the predicate of the conclusion is taken is called the major, and the predicate itself is called the major term. The middle term disappears in conclusion. The nature of the correct conclusion is determined by comparing the volume and quality of terms; Therefore, formal logic distinguishes between figures and types (modi) of inferences. There are four figures of syllogisms, depending on the possible position of the middle term in the premises; all significant modi in these four figures are nineteen. The derivation of meaningful modi in various figures is extremely simple and is determined by comparing the volume and quality of the terms. In the first figure M denotes the middle term, P is the logical predicate, S is the logical subject. The meaning of this figure is to subsume a known concept under a general rule; therefore, the conditions of this figure are as follows: the major premise must be general (affirmative or negative), the minor premise must be affirmative (general or particular). So, in the first figure there can be four significant conclusions, that is, four modi conclusions. In the second figure, two different concepts are assigned the same attribute; it is clear that in the case of two affirmative premises there can be no correct conclusion, for from the fact that two concepts have one common feature, no conclusions can be drawn regarding the connection or lack of connection between the two concepts. Consequently, a conclusion based on the second figure can only be obtained if one of the premises is affirmative, the other negative; in this case, the conclusion will be negative, i.e. we can say that S is not a type of P. The rules of the second figure are as follows. The major premise must be general, one of the premises must be negative This figure has four significant conclusions, all types of conclusions being negative. In the third figure, the middle term takes the place of the subject in both premises: two different characteristics are assigned to one and the same concept; in this case, it is always possible to conclude that these two characteristics are at least occasionally found in one object; or if one premise attributes a certain characteristic to a concept, and the other denies another characteristic, then we can conclude that the connection between these characteristics is not necessary, that is, there are cases when one characteristic appears without the other; So, from this figure, partial conclusions of an affirmative positive or negative form are always possible, depending on the quality of the premises. The only requirement in the third figure, the observance of which is necessary for a correct conclusion, is that the minor premise be affirmative. There are six significant modi in the 3rd figure. The 4th figure is the reverse of the first, and as a result, in it a broader concept is defined by a less broad one: The conclusion is always partial. There are five significant modi. The artificiality of this method of inference is striking, and everyone will prefer to draw a conclusion from the first figure, rearranging the premises. Examples: I. Every crime is punishable deception is a crime cheating is punishable. No man is omniscient scientist - person the scientist is not omniscient. II. No mineral grows plants - growing plants are not minerals. III. All birds lay eggs all birds are vertebrates some vertebrates lay eggs. Snakes don't have legs Snakes are animals Some animals don't have legs. When deriving the various meaningful modi in the four figures, one should keep in mind the following rules arising from consideration of the relationship of concepts. Firstly, a conclusion can only be obtained from two judgments that have one common concept. Secondly, nothing can follow from two negative premises (ex mere negativis nihil sequitur). Thirdly, nothing follows from the two particular premises (ex mere particularibus nihil sequitur). Fourthly, the conclusion always follows the weaker premise (conclusio sequitur partem debiliorem), and a particular judgment is considered weaker in relation to the general, negative - in relation to the positive, possible - in relation to the necessary or actual. The general rules for the formation of syllogisms are expressed in the following 8 Latin rules. 1) Terminus esto triplex, medius majorque minorque. 2) Latius hos quam praemisse conclusio non vult. 3) Aut semel aut iterum medias generaliter esto. 4) Nequaquam capiat medium conclusio fas est. 5) Ambae affirmantes nequeunt generare negantem. 6) Pejorem semper sequitur conclusio partem. 7) Utraque si praemissa neget, nihil inde sequetur. 8) Nihil sequitur geminis ex particularibus unquam. Categorical S. in abbreviated form is called enthymeme; An enthymeme is, therefore, a conclusion in which one of the premises is omitted and implied. Categorical S. in its common form is called epicheirema; epicheyrema means such a conclusion in which each premise is a S. Epicheyrema can be reduced to a simple S., if the conclusions of two syllogisms are considered as premises of the third. A conditional sentence is one whose major premise is a conditional proposition. The minor premise admits or denies the condition, and depending on this, an affirmative or negative conclusion is obtained; the first type of conditional S. is called modus ponens, the second - modus tollens. A disjunctive sentence is one in which the major premise is a disjunctive judgment; a minor premise may deny or affirm some of the parts of the division, and thereby a conclusion may be obtained regarding other parts of the division; by admitting one of the terms of division, we deny the others (modus ponendo tollens) or, by denying one term of division, we admit others (tollendo ponens). Compliance with syllogistic rules does not imply a guarantee of the material truth of the conclusion. From false premises one can accidentally obtain a true conclusion, and, however, as Aristotle notes, it is not clear why the conclusion is true. So, for example, from the premises “Napoleon was a Swede, Napoleon was a painter,” one can draw the conclusion from the third figure that “some painters are Swedes.” On the contrary, from completely correct premises a false conclusion can be drawn if the rules of syllogistic are not followed; for example, if someone from the premises “plants breathe, man breathes” concluded that man is a plant, then he would violate the rule of the second figure of S., which allows only negative conclusions. So, it is necessary to distinguish the formal truth of judgments from the material truth. S. provides only a guarantee of the formal truth of the judgment, while the material truth of the premises depends on the indications of experience or on the axiomatic nature of the premises. Errors in syllogisms are very common and depend on wrong combination premises or from an error in the premises themselves; for example, if the middle term in both premises does not have the same meaning, then an error occurs, called quaternio terminorum. The above brief doctrine of S. has often been subject to changes and criticism. Some denied the usefulness of syllogistics, others tried to get rid of its excessive artificiality, others saw the prototype of S. not in its categorical form, but in a conditional one (Siegwart) and restructured the teaching accordingly. The most serious criticism of S., although not the most thorough, belongs to Mill. A fair reproach made to syllogistics is that the principle of classification of figures, the position of the middle term, is a completely external principle, thanks to which, as Karinsky noted, logic overlooked the internal similarity of the first and third figures and their complete difference from the second. The first and third figures are always affirmative in the process of inference, regardless of whether the conclusion is affirmative or negative, since the process of inference always remains a positive transfer of the predicate from the subject of one judgment to the subject of another; the process of inference in the second figure is always negative, since it consists in the separation of concepts, which is why in the second figure the affirmative minor premise is not at all necessary. Kant also noted that the division of syllogistics into figures contradicts the idea that only the first figure is indisputable, and the rest have this character only because they can be reduced by changing the premises to the first figure. Finally, the third reproach that can be made to syllogistic is the vagueness of its relation to inductive inference. The inductive conclusion from the particular to the general, opposite to the conclusion of the third figure, going from the general to the particular, is most similar to the conclusion of the first figure, but, nevertheless, cannot be identified with it, since the conclusion in the third figure is always particular. These motives have led some to completely deny the significance of syllogistics. Such a negative view of S. was expressed by Bacon, however, on grounds that were not firmly substantiated; Locke also denied syllogistic. Mill argues that S. contains a petitio principii. This reproach applies to the first figure of the categorical S., but has general meaning, since all figures can be reduced to the first, and it is thus the prototype of the others. New truths cannot be derived through S., but only those that the general rule accepts as known. We obtain new truths by inference from particular to particular, and not from general to particular. The general position does not establish a conclusion in the proper sense, but simply interprets special case general position. The incorrectness of this interpretation of the syllogistic process was quite clearly clarified by M.I. Karinsky (in “Classification of Conclusions,” pp. 46-63), who showed that the conclusion really represents new knowledge in comparison with the larger premise, as well as in comparison with the smaller one, and ,next.,S. represents a valid output. “The denial behind the syllogism,” says Karinsky, “of the meaning of the inferential process, whether it was combined with the denial in general of conclusions from the general to the particular, like Bacon, or tried to replace syllogistic formulas with new, non-syllogistic ones, like Locke, or, finally, wanted to reduce conclusions from the general to the particular to induction, as in D. S. Mill, were always entangled in contradictions and thus betrayed their complete inconsistency. The task of the doctrine of inferences, therefore, may not be the elimination of syllogistic formulas from the classification of inferences, but only the transformation of current theories of S." . The doctrine of S. was first expounded by Aristotle in his “First Analytics” (see translation by H. N. Lange, St. Petersburg, 1894). Aristotle speaks of only three figures of categorical S., without mentioning a possible fourth. He examines in particular detail the role of the modality of judgments in the process of inference. Aristotle's successor, the founder of botany, Theophrastus, according to Alexander of Aphrodisius (in his commentary on Aristotle's first Analytics), added five more modi to the first figure of S.; these five modi were subsequently distinguished by Claudius Galen (who lived in the 2nd century after Christ) into a special fourth figure. In addition, Theophrastus and his student Eudemus began analyzing conditional and disjunctive syllogisms. They allowed five types of inferences: two of them correspond to the conditional S., and three - to the dividing one, which they considered as a modification of the conditional S. This ends the development of the doctrine of S. in ancient times, if you do not count the addition that the Stoics made in the doctrine of conditional S. According to Sextus Empiricus, the Stoics recognized some types of conditional and dividing S. αναπόδεικτοι, that is, not requiring proof, and considered them as prototypes of S. (as, for example, Sigwart now looks at S.). The Stoics recognized five types of similar S., coinciding with Theophrastus. Sextus Empiricus gives the following examples for these five species. 1) If day has come, then there is light; but now it’s day, next, there is light. 2) If day has come, then there is light, but there is no light, therefore there is no day. 3) There cannot be day and night (at the same time), but day has come, therefore there is no night. 4) It may be either day or night, but now it is day, therefore there is no night. 5) It can be either day or night, but there is no night, therefore it is now day. In Sextus Empiricus and skeptics in general we also encounter criticism of S., but the purpose of criticism is to prove the impossibility of proof in general, including syllogistic proof. Scholastic logic (see Prantl, "Geschishte d. Logik") did not add anything significant to the doctrine of syllogisms; it only broke the connection with the theory of knowledge that existed in Aristotle and thereby turned logic into a purely formal teaching. The exemplary manual of logic in the Middle Ages was the work of Marcian Capella, and the exemplary commentary was the work of Boethius. Some of Boethius's commentaries deal specifically with the doctrine of S., for example. "Introductio ad categoricos syllogismes", "De syllogisme categorico" and "De syllogismo hypothetico". The writings of Boethius have some historical meaning; they also contributed to the establishment of logical terminology. But at the same time, it was Boethius who gave logical teachings a purely formal character. From the era of scholastic philosophy, in relation to the doctrine of S., Thomas Aquinas († 1274) deserves attention, especially his detailed analysis of false conclusions (“De fallaciis”). A work on logic, which had some historical significance, belongs to the Byzantine Michael Psellus. He proposed the so-called “logical square” (see above), which clearly expresses the relation various types judgments. He owns the names of various modi (τρόποι) figures. These names, Latinized, passed into Western logical literature. Michael Psellus, following Theophrastus, attributed the five modi of the fourth figure to the first. The naming of species had mnemonic purposes in mind. He also owns the commonly used designation by letters of the quantity and quality of judgments (a, e, i, o). Psellus's logical teachings are formal in nature. The work of Psellus was translated by William Shearwood and became widespread thanks to the alteration of Peter of Spain (Pope John XXI). In Peter of Spain, the same desire for mnemotechnical rules is noticeable in his textbook. Latin names The types of figures given in formal logics are taken from Peter of Spain. Peter of Spain and Michael Psell represent the flowering of formal logic in medieval philosophy. Since the Renaissance, criticism of formal logic and syllogistic formalism begins. The first serious critic of Aristotelian logic was Pierre Ramet, who died during the Night of Bartholomew. The second part of his “Dialectics” talks about S.; His teaching about S., however, does not represent significant deviations from Aristotle. Beginning with Bacon and Descartes, philosophy follows new paths and defends methods of research: the unsuitability of the syllogistic method in the sense of a method of research, finding truth, becomes more and more obvious. Nevertheless, the doctrine of S. is still presented in textbooks, although there is no doubt that the listing of all modi is now of only historical interest. Among the works specifically dealing with criticism of S., Kant’s book “Die falsche Spitzfindigkeit der vier Syllogistischen Figuren erwiesen” (1763) stands out. The best presentation of formal logic belongs to the writers of the Herbart school, for example. I'm crushing.
Encyclopedic Dictionary F.A. Brockhaus and I.A. Efron. - S.-Pb.: Brockhaus-Efron. 1890-1907 .
Synonyms:See what “Syllogism” is in other dictionaries:
- (from the Greek syllogismos) indirect inference of syllogistics. The most famous form of S. is the so-called. simple categorical C. a two-premise inference about the relationship between two terms (the major P and the smaller S) by indicating their ... Philosophical Encyclopedia
- [gr. syllogismos] log. a conclusion consisting of two judgments (premises), from which a third judgment follows, a conclusion, a conclusion (for example, every S is M, and every M is P, therefore, every S is P). Dictionary of foreign words. Komlev N.G.,... ... Dictionary of foreign words of the Russian language
Understand the basic structure of syllogisms. A syllogism has three parts: a major premise, a minor premise, and a conclusion. Each part consists of two categorical forms (terms that denote categories, such as the category of birds, animals, etc.), related in the form "Some / all A are / are not. B" Each of the premises has one term in common with by inference: a major term in the major predicate that forms the predicate of the conclusion, and a minor term in the minor premise that forms the subject of the conclusion. The categorical term of the general in the premise is called the “middle term.” For example: Big premise: All birds are animals. Smaller premise: All parrots are birds. Conclusion: All parrots are animals. In this example, "animal" is the major term and the predicate of the conclusion, "parrot" is the minor term and the subject of the conclusion, and "bird" is the middle term.
Think of each term as representing a category. For example, "animal" is a category consisting of anything that can be described as an animal.
Understand that each part is expressed as "some/all A's are/are not B's" with four possible options. The general (symbolized by A) is expressed as "all A's/are B's", abbreviated as AaB. The common negative (symbolized by E) is expressed as "not / A are B", abbreviated as AeB. Partial affirmatives (symbolized by I) are expressed as "some A is/are B", abbreviated Aib. Partial negatives (symbolized by O) are expressed as "some A/are not B", abbreviated AoB.
Define the figure of a syllogism. Depending on whether the middle term serves as subject or predicate in the premises, a syllogism can be classified as one of four possible figures:
- First figure: The middle term serves as the subject of the major premise and the predicate of the minor premise. Thus, the first figure looks like: large premise: M-P .......... for example, “All birds are animals” Small package S-M.......... for example, "All parrots are birds" Conclusion: ...... S-P .......... for example, "All parrots are animals."
- Second figure: the middle term serves as a predicate in the major premise and a predicate in the minor premise. Thus, the second figure takes the form: major premise: P-M.......... e.g., "foxes are not birds" Minor premise: S-M.......... e.g., "All parrots are birds" Conclusion: ...... S-P .......... for example, "Parrots are not foxes."
- Third figure: The middle term serves as the subject of the major premise and the subject of the minor premise. Thus, the third figure takes the form: major premise: M-P .......... e.g., "All birds are animals" Minor premise: M-S.......... e.g., "All birds are mortal" Conclusion: ...... S-P .......... for example, "Some mortals are animals."
- Fourth figure: The middle term serves as a predicate in the major premise and a subject in the minor premise. Thus, the fourth indicator takes the form: major premise: P-M .......... e.g., “birds are not cows” Minor premise: M-S........ e.g., “All cows are animals "Inference: ...... S-P .......... for example, "Some animals are not birds."
Determine whether this syllogism is valid: checking whether it fits into one of the valid syllogism forms for a given figure. A syllogism is valid if and only if the conclusion follows inevitably from the premises, that is, if the premises are true, the conclusion must be true. Although there are 256 possible (all 4 possible options(a, e, I, O) for each part, three parts (major premise, minor premise, conclusion), and four figures, so 4 * 4 * 4 * 4 = 256) syllogism, only 19 of them are valid. The valid forms for each figure are given below, with their mnemonic names (each containing three vowels defining the shape of the side (a, e, I, O) in the order major premise, minor premise, conclusion):
- The first figure has 4 valid shapes: B a rb a r a, C e l a r e nt, D a r ii, F e r io
- B a rb a r a(AAA): e.g.
All birds are animals.
All parrots are birds.
All parrots are animals. - C e l a r e nt (EAE): e.g.
Birds are not foxes.
All parrots are birds.
Parrots are not foxes. - D a r ii(AII): for example,
All dogs are animals.
Some mammals are animals. - F e r io(EIO): e.g.
Dogs are not birds.
Some mammals are dogs.
Some mammals are not birds.
- B a rb a r a(AAA): e.g.
- The second figure has 4 valid shapes: C e s a r e, C a m e str e s, F e st i n o, B a r o c o
- C e s a r e(EAE): e.g.
Foxes are not birds.
All parrots are birds.
No parrots are not foxes. - C a m e str e s (AEE): for example,
All foxes are animals.
Trees are not animals.
Trees are not foxes. - F e st i n o(EIO): e.g.
Restaurant food is not healthy.
Some recipes are healthy.
Some recipes are not restaurant grade. - B a r o c o(AOO): for example,
All liars are villains.
Some doctors are not villains.
Some doctors are not liars.
- C e s a r e(EAE): e.g.
- The third figure has 6 valid shapes: *D a r a pt i, D i s a m i s, D a t i s i, F e l a pt o n, B o c a rd o, F e r i s o n
- D a r a pt i(AAI): e.g.
All people are fallible.
All people are animals.
Some animals make mistakes. - D i s a m i s (IAI): for example,
Some books are precious.
All books are perishable.
Some perishable things are valuable. - D a t i s i(AII): for example,
All books are imperfect.
Some books are informative.
Some informative things are imperfect. - F e l a pt o n (EAO): for example,
They don't eat snakes.
All snakes are animals.
Some animals are not eaten. - B o c a rd o(OAO): e.g.
Some websites are not helpful.
All websites are Internet resources.
Some online resources are not useful. - F e r i s o n (EIO): for example,
Lepers are not allowed to enter the church.
All lepers are people.
Some people cannot enter the church.
- D a r a pt i(AAI): e.g.
- The fourth figure has 5 valid forms: Br a m a nt i p, C a m e n e s, D i m a r i s, F e s a p o,Fr e s i s o n
- Br a m a nt i p (AAI): for example,
All pigs are unclean.
All unclean things are best avoided.
Some things to avoid are pigs. - C a m e n e s (AEE): for example,
All trees are plants.
Plants are not birds.
Birds are not trees. - D i m a r i s (IAI): for example,
Some lawyers are villains.
All lawyers are human.
Some people are villains. - F e s a p o(EAO): e.g.
No free food.
All free things are welcome.
Some desirable things are not food. - Fr e s i s o n (EIO): for example,
Dogs are not birds.
Some birds are pets.
Some pets are not dogs.
- Br a m a nt i p (AAI): for example,
- Note that if any of the premises are negative, then the conclusion must also be negative. If both premises are affirmative, the conclusion must also be affirmative.
- For an inference to be valid, at least one of the two premises must contain a universal form. If both premises are particular, then an unjustified conclusion cannot follow. For example, if “some cats are black” and “some black things are tables,” it does not follow that “some cats are tables.”
- Drawing or visualizing a Venn diagram can help in distributing understanding of terms when determining whether a given syllogism is valid or not.
- The general (A) is presented in the form of one circle (subject) completely within another circle (predicate).
- The general negative (E) is represented as two mutually exclusive, non-overlapping circles.
- The quotients (I, O) are represented as two intersecting circles, with a common intersecting area and with separate areas.
- There is another way to mark up a Venn diagram when solving categorical syllogism problems: instead of using them in a purely theoretical manner as described above (also known as "Euler Circles").
***Draw three intersecting circles and shade to indicate absence (or impossibility), leave space blank to indicate “unknown,” and a small “+” sign to indicate presence.
- Now a valid categorical statement will take one of four forms:
- lens, completely shaded
- diagonal fully shaded
- in "+" trace in the lens
- "+" trace in a diagonal
- the syllogism works (in the classical Aristotelian sense) if the circles representing the major and minor premises are one of four shapes: either lenses or bigons completely in shadow, or a "+" trace in the lens or lunula.
- This method is only suitable for syllogisms of three categorical statements: minor premise, major premise and conclusion.
- Now a valid categorical statement will take one of four forms:
- Understand the distribution of conditions. A categorical term is distributed if all individual members of that category are counted, for example, in "All men are mortal", the term "men" is distributed because every member belonging to that category is included in that category as a mortal. Notice how each of the four variations distributes (or not) the terms:
- In "All A's are B" premises, the subject (A) is distributed
- In "A are not B" premises, since the subject (A) and predicate (B) are distributed.
- In "Some A are B" premises, neither the subject nor the predicate is distributed.
- In "Some A are not B" premises, the predicate (B) extends.
- To make a conclusion valid, the middle term must be distributed in at least one of the premises so that the major and minor premises are related. Avoid the fallacy of undistributed middles. For example, from “All dogs love food” and “John loves food,” it does not follow that “John is a dog.”
- For a conclusion to be valid, at least one of the two premises must be positive. If both premises are negative, then an unjustified conclusion cannot follow. If both premises are negative, the average cannot establish any connection between the large and small points.
Warnings
- Beware of the fallacy of illegal major, where the main term is undistributed in the major premise but distributed in the conclusion. An example of this is: Everyone is B; no C are A. Therefore neither C are B. For example, “all cats are animals”; "Dogs are not cats"; Therefore, "Dogs are not animals": this syllogism is invalid since the basic term "animals" is undistributed in the major premise, but is distributed in the conclusion.
- Beware of the fallacy of the minor term, where the minor premise is not distributed in the conclusion. An example of this is: "Everyone is a B; all are C. Thus, all are C B. For example, "All cats are mammals"; "All cats are animals"; Therefore, "all animals are mammals": this syllogism is invalid since the minor term "animals" is undistributed in the lesser parcel (because not all animals are cats), but distributed in custody.
St. Petersburg Institute of Foreign Economic Affairs
Connections between Economics and Law.
Test
discipline: Logic and theory of argumentation
on the topic: The concept of syllogisms
Kaliningrad 2010
Introduction
Main features of a syllogism
History of the concept
Conclusion
Bibliography
Introduction
Syllogism- this is an inference consisting of two judgments, from which a third is necessarily deduced. Moreover, of the two given judgments, one is generally affirmative or generally negative.
Syllogisms are divided into direct and mediocre.
Direct syllogisms are those in which the conclusion is drawn from one premise.
Mediocre syllogisms are those in which the conclusion is drawn from two or more premises.
The rules allow us to systematically eliminate incorrect inferences and justify the acceptability of correct inferences. If it is established that a syllogism follows all the rules, then we can confidently say that it is correct.
My report will discuss the rules for composing a syllogism, because this is logical culture.
Main features of a syllogism
First, every syllogism must consist of two premises and a conclusion. Sometimes one of the premises is omitted and the syllogism is reduced to premises and conclusions. Such a contraction is called entineme. For example, the phrase “All girls love flowers. Masha loves flowers” is an entineme in which the premise “Masha is a girl” is omitted, but we mean it (the premise, not Masha, of course). Please note: this is so like a syllogism is deductive conclusion, then the resulting conclusion cannot be more general than the premises on the basis of which it was made. This statement is verified by comparing terms. For example, in the syllogism “All plants are organisms, flowers are plants, therefore flowers are organisms” we have three terms: “organisms”, “plants” and “flowers”, and “organisms” is the larger term, “plants” is the middle one, and “flowers” is the smaller one. However, the middle term is not included in the conclusion, its function is to be connecting a link between greater and lesser terms for the purpose of comparing them, since they themselves cannot be compared, therefore syllogisms are also called mediocre conclusions.This connection can be expressed by the following principle: “If one thing is in another, and this other is in a third, then the first is also in the third.” Similarly: “If one thing is in another, and this other is outside the third, then and the first is also outside the third." This proposition, obvious at first glance, is called the axiom of syllogism. Based on this axiom, we have the principle: “Everything that is asserted regarding the whole is also affirmed regarding each particular that is contained in it." The situation is similar with negation regarding the whole.
Depending on the nature of the major premise, syllogisms are of three types: - categorical (which are divided into complete, i.e. consisting of two premises - epicheiremes and abbreviated - entinemes); - conditional (major premise - conditional proposition); - divisive (major premise). premise - disjunctive judgment).As noted earlier, each syllogism consists of three propositions. And since one judgment must contain only one term, then there must also be exactly three terms in the syllogism. If the judgments contain more or less three terms, then it will be impossible to draw a conclusion. For example, from the premises “All politicians - deceivers . Roosevelt was a good family man"It is impossible to conclude "Roosevelt was a liar" or "All politicians are good family men" But if the messages sounded like this: “Everything politicians deceivers . Roosevelt was politician", we could draw a completely clear conclusion, because we would have three terms, not four. The next principle of constructing syllogisms sounds like this: no conclusion can be drawn from two negative judgments. For example: A physicist is not a humanist. A historian is not a physicist. From From these statements we cannot conclude that the historian is not a humanist. More precisely, such a conclusion will not satisfy the laws of logic. For comparison: if only one judgment were negative (for example: a physicist is not a humanist, a historian is a humanist), then we could draw a certain conclusion: a historian is not a physicist. From this principle the following follows: if one of the premises is negative, then the conclusion must be negative. Similar laws apply to private statements: if one of the judgments is private, then the conclusion must be private. For example: Some people are envious. All The English are people. Some the English are envious. In addition, a conclusion cannot be drawn from two particular statements. For example, from the premises “Some physicists are romantics” and “Some gardeners are romantics” we cannot draw a conclusion, since the conclusion does not follow necessarily (that is, a gardener does not have to be a physicist at all , and vice versa). This occurs because the middle term is not distributed. This implies next principle: the middle term must be taken in its entirety in at least one premise. That is, if we take as premises the statements “Some people are envious, some Englishmen are envious” (where the term “envious” will be the middle one), then we will not draw a conclusion. Consequently, we have a principle similar to the two previous pairs of principles: terms not taken in premises in their entirety, cannot be taken in their entirety in conclusion. Therefore, from premises like “Some people are envious, all English people” we can only draw the following conclusion: “ Some The English are envious" (may the inhabitants of Foggy Albion forgive me).
This is an argument consisting of three simple attributive statements: two premises and one conclusion. The premises of a syllogism are divided into a major one (which contains the predicate of the conclusion) and a minor one (which contains the subject of the conclusion). According to the position of the middle term, syllogisms are divided into figures, and the latter, according to the logical form of the premises and conclusion, are on modes .
Example of a syllogism:
Every man is mortal (big premise)
Socrates is a man (minor premise)
Socrates is mortal (conclusion)
Structure of a simple categorical syllogism
The syllogism contains exactly three terms:
S - minor term: subject of the conclusion (also included in the minor premise);
P - major term: predicate of the conclusion (also included in the major premise);
M is the middle term: included in both premises, but not included in the conclusion.
Subject S(subject) - that about which we express (divided into two types):
1. Definite: Singular, Particular, Plural
Single [judgments] - in which the subject is an individual concept. Note: “Newton discovered the law of gravity”
Particular judgment - in which the subject of judgment is a concept taken in part of its scope. Note: “Some S are P”
Multiple propositions are those in which there are several subject class concepts. Note: “insects, spiders, crayfish are arthropods”
2. Uncertain. Note: “it’s getting light”, “it hurts”, etc.
Predicate P(predicate) - what we express (2 types of judgments):
Narrative is a judgment regarding events, states, processes or activities that are passing quickly. Note: “A rose is blooming in the garden.”
Descriptive - when some property is attributed to one or many objects. The subject is always a certain thing. Note: “Fire is hot,” “snow is white.”
Relationship between subject and predicate:
1. Judgments of identity - the concepts of subject and predicate have the same scope. Note: “any equilateral triangle there is an equiangular triangle"
2. Judgments of subordination - a concept with a less wide scope is subordinate to a concept with a wider scope. Note: “A dog is a pet”
3. Judgments of relation - namely space, time, relation. Note: “The house is on the street”
When determining the relationship between the subject and the predicate, a clear formalization of the terms is important, since a stray dog, although not a domestic dog from the point of view of living in a house, still belongs to the class of domestic animals from the point of view of belonging on a socio-biological basis. That is, it should be understood that a “domestic animal” according to the socio-biological classification in some cases can be a “non-domestic animal” from the point of view of its habitat, that is, from a social and everyday point of view.
History of the concept
The doctrine of syllogism was first expounded by Aristotle in his First Analytics. He speaks of only three figures of the categorical syllogism, without mentioning a possible fourth. He examines in particular detail the role of the modality of judgments in the process of inference. Aristotle's successor, the founder of botany, Theophrastus, according to Alexander of Aphrodisius (in his commentary on Aristotle's first Analytics), added five more modes (modi) to the first figure of the syllogism; these five modes were subsequently distinguished by Claudius Galen (who lived in the 2nd century AD) into a special fourth figure. In addition, Theophrastus and his student Eudemus began analyzing conditional and disjunctive syllogisms. They allowed five types of inferences: two of them correspond to the conditional syllogism, and three to the disjunctive one, which they considered as a modification of the conditional syllogism. This ends the development of the doctrine of syllogism in ancient times, except for the addition that the Stoics made in the doctrine of conditional syllogism. According to Sextus Empiricus, the Stoics recognized certain types of conditional and disjunctive syllogism αναπόδεικτοι , that is, not requiring proof, and considered them as prototypes of a syllogism (as, for example, Sigwart looks at a syllogism). The Stoics recognized five types of such syllogisms, coinciding with Theophrastus. Sextus Empiricus gives the following examples for these five species:
1. If day has come, then there is light; but now it is day, therefore there is light.
In which, based on several judgments, a new judgment, called a conclusion, is necessarily derived. In contrast to S., as a mediocre inference, a direct inference is one in which the conclusion is obtained from a given judgment without the help of another.
I. Direct conclusions include:
A) inferences by submission. One can always infer from the truth of a general judgment to the truth of a particular content of the same content, but not vice versa; one can always conclude from the falsity of a particular judgment to the falsity of a general judgment of the same content, but not vice versa. These conclusions are made based on dictum de omni et nullo: quicquid de omnibus valet etiam de quibusdam et singulis; quicquid de nullo valet nec de quihusdam nec de singulis valet; b) inferences by identity: from the truth of a known judgment follows the truth of something identical in content; c) inferences on transformation (con version), based on the relationship between the volumes of the logical subject and the logical predicate and the possibility of their rearrangement.
By transformation, generally affirmative judgments turn into generally affirmative ones in the case where the volume of the subject is equal to the volume of the predicate ( conversio pura), e.g. A = B, therefore, B = A; but the vast majority of general affirmative judgments, through transformation, turn into particular affirmative ones ( conversio impura) on the basis that the volume of the predicate (defining) is usually greater than the volume of the defined - therefore, during transformation, part of the volume of the defining concept loses its significance for the conclusion. Particular affirmative and general negative judgments give pure transformations. Partial negative judgments do not give a conclusion when transforming. If, when transforming judgments, their qualities are also changed, that is, affirmative ones are turned into negative ones, then the following type of conclusions will be obtained: from generally affirmative ones, generally negative judgments will be obtained; from a general negative - usually a particular affirmative, in cases of equality of the logical subject and predicate - a general affirmative; from partial negative judgments partial affirmative ones are obtained; finally, no conclusions can be drawn from a particular affirmative. Based on the relationship of concepts depicted in the so-called. logical square, one can make conclusions regarding the contradiction and opposition of judgments.
"logical square"
From the truth of a generally affirmative proposition one can conclude (according to the law of contradiction) to the falsity of a particular affirmative one; in the same way, one can infer from the truth of a general negative to the falsity of a particular affirmative. The rule for this kind of conclusion is: contradictory judgments (for example, A - O and E - I) cannot be simultaneously true or false. On the contrary, the following conclusions can be drawn. Two general (and contrary) propositions can be simultaneously false, but cannot be simultaneously true. Two partial (and opposite) propositions can be true at the same time, but cannot be false at the same time. Finally, using the modality of judgments, one can conclude from necessity to reality and possibility, from reality to possibility, but not vice versa; from impossibility one can conclude to invalidity and non-necessity.
II. Mediocre, or syllogisms, are distinguished from direct inferences. S. are categorical, conditional and divisive, depending on the nature of the judgment, called in S. the major premise. Premises are those judgments from which the conclusion is derived; the very process of drawing a conclusion is called inference. The simplest form of the principle on the basis of which an inference is made is that two quantities, separately equal to a third, are equal to each other; but since only a small number of judgments represent a real equality of the concepts contained in them, and in most judgments the scope of the predicate is wider than the scope of the logical subject, the above principle accepts the following formula: two concepts related to the third also have some relationship with each other. A correct inference must accurately determine the relationship between these concepts. The relationship of concepts to each other is established thanks to the concept common to the two judgments. Thus, the most general rule of inference is that only from such two judgments can a conclusion be drawn that have one common concept. This general concept in syllogistic is called the middle term; the premise from which the subject of the conclusion is taken is called the minor, and the subject itself is called the minor term; the premise from which the predicate of the conclusion is taken is called the major, and the predicate itself is called the major term. The middle term disappears in conclusion. The nature of the correct conclusion is determined by comparing the volume and quality of terms; therefore formal logic distinguishes between figures and types ( modi) inferences. There are four figures of syllogisms, depending on the possible position of the middle term in the premises; all significant modi in these four figures there are nineteen. Derivation of significant modi in various figures is extremely simple and is determined by comparing the volumes and quality of terms. In the first figure
M - P S - M S - P
M denotes the middle term, P is the logical predicate, S is the logical subject. The meaning of this figure is to subsume a known concept under a general rule; therefore, the conditions of this figure are as follows: the major premise must be general (affirmative or negative), the minor premise must be affirmative (general or particular). So, in the first figure there can be four meaningful conclusions, that is, four modi conclusions. In the second figure, two different concepts are assigned the same attribute; it is clear that in the case of two affirmative premises there can be no correct conclusion, for from the fact that two concepts have one common feature, no conclusions can be drawn regarding the connection or lack of connection between the two concepts indicated. Consequently, a conclusion based on the second figure can only be obtained if one of the premises is affirmative, the other negative; in this case, the conclusion will be negative, that is, we can say that S is not a type of P. The rules of the second figure are as follows. The major premise must be general, one of the premises must be negative
R - M S-M S-P
This figure has four significant conclusions, all types of conclusions being negative. In the third figure, the middle term takes the place of the subject in both premises:
M - R M -S; S-P
two different characteristics are assigned to one and the same concept; in this case, it is always possible to conclude that these two characteristics are at least occasionally found in one object; or if one premise attributes a certain characteristic to a concept, and the other denies another characteristic, then we can conclude that the connection between these characteristics is not necessary, that is, there are cases that one characteristic appears without the other; So, from this figure, partial conclusions of an affirmative positive or negative form are always possible, depending on the quality of the premises. The only requirement in the third figure, the observance of which is necessary for a correct conclusion, is that the minor premise be affirmative. There are six significant modi in the 3rd figure. The 4th figure is the reverse of the first, and as a result, in it a broader concept is defined by a less broad one:
R - M M - S. S - P
The conclusion is always partial. Meaningful modi five. The artificiality of this method of inference is striking, and everyone will prefer to draw a conclusion from the first figure, rearranging the premises.
Examples:
I. Every crime is punishable
Cheating is a crime; deception is punishable. No man is an omniscient scientist - no man is a scientist omniscient.
II. No mineral grows
Plants - plants that grow are not minerals.
III. All birds lay eggs
All birds are vertebrates; some vertebrates lay eggs. Snakes do not have legs Snakes are animals Some animals do not have legs.
When deriving different signifiers modi in four figures, one should keep in mind the following rules arising from consideration of the relationship of concepts. Firstly, a conclusion can only be obtained from two judgments that have one common concept. Secondly, nothing can follow from two negative premises ( ex mere negativis nihil sequitur). Thirdly, nothing follows from the two particular premises ( ex mere particularibus nihil sequitur). Fourth, the conclusion always follows the weakest premise ( conclusio sequitur partem debiliorem), and a particular judgment is considered weaker in relation to the general, negative - in relation to the positive, possible - in relation to the necessary or actual.
The general rules for the formation of syllogisms are expressed in the following 8 Latin rules.
1) Terminus esto triplex, medius majorque minorque. 2) Latius hos quam praemisse conclusio non vult. 3) Aut semel aut iterum medias generaliter esto. 4) Nequaquam capiat medium conclusio fas est. 5) Ambae affirmantes nequeunt generare negantem. 6) Pejorem semper sequitur conclusio partem. 7) Utraque si praemissa neget, nihil inde sequetur. 8) Nihil sequitur geminis ex particularibus unquam.
A categorical syllogism in abbreviated form is called an enthymeme; An enthymeme is, therefore, a conclusion in which one of the premises is omitted and implied. Categorical S. in its common form is called epicheirema; epicheyrema means such a conclusion in which each premise is a S. Epicheyrema can be reduced to a simple S., if the conclusions of two syllogisms are considered as premises of the third.
A conditional syllogism is one whose major premise is a conditional proposition. The minor premise admits or denies the condition, and depending on this, an affirmative or negative conclusion is obtained; The first type of conditional syllogism is called modus ponens, second - modus tollens. A disjunctive sentence is one in which the major premise is a disjunctive judgment; a minor premise may deny or affirm some of the parts of the division, and thereby a conclusion may be obtained regarding other parts of the division; admitting one of the division terms, we deny the others ( modus ponendo tollens) or, denying one term of division, we admit others ( tollendo ponens).
Compliance with syllogistic rules does not imply a guarantee of the material truth of the conclusion. From false premises one can accidentally obtain a true conclusion, and, however, as Aristotle notes, it is not clear why the conclusion is true. So, for example, from the premises “Napoleon was a Swede, Napoleon was a painter,” one can draw the conclusion from the third figure that “some painters are Swedes.” On the contrary, from completely correct premises a false conclusion can be drawn if the rules of syllogistic are not followed; for example, if someone from the premises “plants breathe, man breathes” concluded that man is a plant, then he would violate the rule of the second figure of S., which allows only negative conclusions. So, it is necessary to distinguish the formal truth of judgments from the material truth. S. provides only a guarantee of the formal truth of the judgment, while the material truth of the premises depends on the indications of experience or on the axiomatic nature of the premises. Errors in syllogisms are very frequent and depend on an incorrect combination of premises or on an error in the premises themselves; for example, if the middle term in both premises does not have the same meaning, then an error occurs, called quaternio terminorum.
The above brief doctrine of syllogisms has often been subject to changes and criticism. Some denied the usefulness of syllogistics, others tried to get rid of its excessive artificiality, others saw the prototype of S. not in its categorical form, but in a conditional one (Siegwart) and restructured the teaching accordingly. The most serious criticism of S., although not the most thorough, belongs to Mill. A fair reproach made to syllogistics is that the principle of classification of figures, the position of the middle term, is a completely external principle, thanks to which, as Karinsky noted, logic overlooked the internal similarity of the first and third figures and their complete difference from the second. The first and third figures are always affirmative in the process of inference, regardless of whether the conclusion is affirmative or negative, since the process of inference always remains a positive transfer of the predicate from the subject of one judgment to the subject of another; the process of inference in the second figure is always negative, since it consists in the separation of concepts, which is why in the second figure the affirmative minor premise is not at all necessary. Kant also noted that the division of syllogistics into figures contradicts the idea that only the first figure is indisputable, and the rest have this character only because they can be reduced by changing the premises to the first figure. Finally, the third reproach that can be made to syllogistic is the vagueness of its relation to inductive inference. The inductive conclusion from the particular to the general, opposite to the conclusion of the third figure, going from the general to the particular, is most similar to the conclusion of the first figure, but, nevertheless, cannot be identified with it, since the conclusion in the third figure is always particular. These motives have led some to completely deny the significance of syllogistics. Such a negative view of S. was expressed by Bacon, however, on grounds that were not firmly substantiated; Locke also denied syllogistic. Mill argues that S. contains a petitio principii. This reproach applies to the first figure of the categorical S., but has a general meaning, since all figures can be reduced to the first, and it is thus the prototype of the others. New truths cannot be derived through S., but only those that the general rule accepts as known. We obtain new truths by inference from particular to particular, and not from general to particular. The general proposition does not establish a conclusion in the proper sense, but simply interprets a particular case with a general proposition. The incorrectness of this interpretation of the syllogistic process was quite clearly clarified by M.I. Karinsky (in “Classification of Conclusions,” pp. 46 - 63), who showed that the conclusion truly represents new knowledge in comparison with the larger premise, as well as in comparison with the smaller one, and ,next.,S. represents a valid output. “The denial of the syllogism,” says Karinsky, “the meaning of the inferential process, whether it was combined with the denial in general of conclusions from the general to the particular, like Bacon, or tried to replace syllogistic formulas with new, non-syllogistic ones, like Locke, or, finally, wanted to reduce conclusions from the general to the particular to induction, as in D. S. Mill, were always entangled in contradiction and thus betrayed their complete inconsistency. The task of the doctrine of inferences, therefore, may not be the elimination of syllogistic formulas from the classification of inferences, but only the transformation of current S. theories.”
The doctrine of syllogisms was first expounded by Aristotle in his “First Analytics” (see translation by H. N. Lange, St. Petersburg,). Aristotle speaks of only three figures of a categorical syllogism, without mentioning a possible fourth. He examines in particular detail the role of the modality of judgments in the process of inference. Aristotle's successor, the founder of botany, Theophrastus, according to Alexander of Aphrodisius (in his commentary on Aristotle's first Analytics), added five more modi to the first figure S.; these five modi were subsequently singled out by Claudius Galen (who lived in the 2nd century after R.H.) into a special fourth figure. In addition, Theophrastus and his student Eudemus began analyzing conditional and disjunctive syllogisms. They allowed five types of inferences: two of them correspond to the conditional syllogism, and three to the disjunctive syllogism, which they considered as a modification of the conditional S. This ends the development of the doctrine of S. in ancient times, if you do not count the addition that the Stoics made in the doctrine of the conditional S. According to Sextus Empiricus, the Stoics recognized certain types of conditional and divisive S. αναπόδεικτοι, that is, not requiring proof, and considered them as prototypes of S. (as, for example, Sigwart now looks at S.). The Stoics recognized five types of similar S., coinciding with Theophrastus. Sextus Empiricus gives the following examples for these five species.
1) If day has come, then there is light; but now it’s day, next, there is light. 2) If day has come, then there is light, but there is no light, therefore there is no day. 3) There cannot be day and night (at the same time), but day has come, therefore there is no night. 4) It may be either day or night, but now it is day, therefore there is no night. 5) It can be either day or night, but there is no night, therefore it is now day.
In Sextus Empiricus and skeptics in general we also encounter criticism of S., but the purpose of criticism is to prove the impossibility of proof in general, including syllogistic proof. Scholastic logic (see Prantl, “Geschishte d. Logik”) did not add anything significant to the doctrine of syllogisms; it only broke the connection with the theory of knowledge that existed in Aristotle and thereby turned logic into a purely formal teaching. The exemplary manual of logic in the Middle Ages was the work of Marcian Capella, and the exemplary commentary was the work of Boethius. Some of Boethius's commentaries deal specifically with the doctrine of S., for example. “Introductio ad categoricos syllogismes”, “De syllogisme categorico” and “De syllogismo hypothetico”. Boethius's writings have some historical significance; they also contributed to the establishment of logical terminology. But at the same time, it was Boethius who gave logical teachings a purely formal character. From the era of scholastic philosophy, in relation to the doctrine of S., Thomas Aquinas (†) deserves attention, especially his detailed analysis of false conclusions (“De fallaci is”). A work on logic, which had some historical significance, belongs to the Byzantine Michael Psellus. He proposed the so-called “logical square” (see above), which clearly expresses the relationship between different types of judgments. He owns the names of various modi(τρόποι) figures. These names, Latinized, passed into Western logical literature. Michael Psellus, following Theophrastus, five modi the fourth figure was related to the first. The naming of species had mnemonic purposes in mind. He also owns the commonly used designation by letters of the quantity and quality of judgments ( a, e, i, o). Psellus's logical teachings are formal in nature. The work of Psellus was translated by William Shearwood and became widespread thanks to the alteration of Peter of Spain (Pope John XXI). In Peter of Spain, the same desire for mnemotechnical rules is noticeable in his textbook. The Latin names of the types of figures given in formal logics are taken from Peter of Spain. Peter of Spain and Michael Psell represent the flowering of formal logic in medieval philosophy. Since the Renaissance, criticism of formal logic and syllogistic formalism begins. The first serious critic of Aristotelian logic was Pierre Ramet, who died during the Night of Bartholomew. The second part of his Dialectics talks about S.; His teaching about S., however, does not represent significant deviations from Aristotle. Beginning with
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