All people are mortal.
Socrates is a man.
Socrates is dead.
A simple categorical syllogism always contains only three concepts, called terms which are included in its premises and conclusion. The subject of the conclusion ( S) in the syllogism is considered lesser term, conclusion predicate ( P) - big term. The lesser and greater terms are extreme terms syllogism. Each of the extreme terms is contained both in the conclusion and in one of the premises.
Traditionally, the major premise in a syllogism should come first.
Medium(M) it is customary to name a term that is included in both premises, but is not included in the conclusion. Through it, a connection is revealed between those terms-concepts that make up the subject and the predicate of the conclusion (between the extreme terms). Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, a simple categorical syllogism is indirect inference, that is, a conclusion in which the connection between two concepts in the conclusion is established by means of a third one that is present in both premises.
The concepts that occur in the syllogism as terms are content syllogism. The connection that is attached to the terms is the form syllogism.
Example.
All people ( M) are mortal ( P). Major premise of the syllogism
Socrates (S ) - human (M ). Minor premise of the syllogism
Socrates ( S) is mortal ( P).
The terms that make up this syllogism are as follows: ʼʼmortalʼʼ - a larger term (the predicate of the conclusion ( R)); ʼʼSocratesʼʼ - a smaller term (the subject of the conclusion ( S)); ʼʼpeopleʼʼ - middle term ( M) (included in both parcels, but not in the conclusion). Judgment ʼʼSocrates ( S) - human ( M)ʼʼ - lesser package because it contains a smaller term ( S). Judgment ʼʼAll people ( M) are mortal ( R)ʼʼ - big package because it contains a larger term ( R).
Every syllogism has a figure and a mode .
The figure of the syllogism shows the location of the terms ( P, S, M) in parcels. Given the dependence on the location of the middle term, four figures of the syllogism are distinguished (Fig. 18).
Rice. eighteen. Figures of a simple categorical syllogism
Upper the face of the figure always shows the location of the terms in greater parcel, lower- in lesser parcel.
AT first figure in greater MR). AT lesser SM).
In second figure in greater R), the predicate is the middle term ( M). AT lesser in the premise, the subject is the smaller term ( S), the predicate is the middle term ( M).
AT third figure in greater in the premise, the subject is the middle term ( M), the predicate is a larger term ( R). AT lesser in the premise, the subject is the middle term ( MS).
AT fourth figure in greater in the premise, the subject is the larger term ( R), the predicate is the middle term ( M). AT lesser in the premise, the subject is the middle term ( M), the predicate is the smaller term ( S).
Example. To determine the figure of the above syllogism (about Socrates), you need to write out from its premises the letter designations of the terms in the order in which they are located there, connect the middle terms ( M) and draw lines from them to the extreme ones ( S and R). Let's get the first figure:
Modus simple categorical syllogism shows the kind of categorical judgments that make up the syllogism. And first letter in mode always shows view greater parcels, second - lesser parcels, third- view conclusions.
Example. In the syllogism about Socrates, both premises and conclusion are generally affirmative judgments ( BUT), so its mode is AAA.
Simple categorical syllogisms are either right or wrong. The correctness of a syllogism does not depend on its content, but depends only on its form (figure and mode). At the same time, only a syllogism with the correct form ensures the truth of the conclusion with the truth of the premises. Otherwise, even with true premises, the truth of the conclusion is not guaranteed.
To establish whether a syllogism is correct, one can check whether it complies with the general rules of syllogisms and the rules of figures.
General rules of syllogisms:
1. At least one of the premises must be a general proposition.
2. At least one of the premises must be an affirmative judgment.
3. With a private sending, the conclusion must be private.
4. With a negative premise, the conclusion must be negative.
5. With two affirmative premises, the conclusion must be affirmative.
6. The middle term must be distributed in at least one of the premises.
7. A term not distributed in the premise should not be distributed in the conclusion.
Shape rules:
First figure: the minor premise must be affirmative, while the major premise must be general.
Second figure: one of the premises must be negative, and the larger one must be common.
Third figure: the minor premise must be affirmative and the conclusion private.
For fourth figure, no special rules are formulated, since in practice they come down to listing the correct modes of this figure.
Example. Let's check whether the general rules and the rules of figures are observed in the following syllogism:
All lawyers ( R M -).
All present (S +) there are people who know the signs of a crime ( M -).
All present ( S+) there are lawyers ( R -).
It is easy to see that in this case the sixth of the general rules of the syllogism is not observed, since the middle term ( M) turned out to be undistributed in both premises.
The rule of the second figure is also not observed (and this syllogism has exactly the second figure), since both premises are affirmative judgments, and the rule of the second figure requires that one of the premises be negative. Therefore, the above syllogism is not correct.
You can verify the correctness of the syllogism in another way - by looking at whether its mode belongs to the number correct modes of his figure.
In total, there are 256 modes of simple categorical syllogisms (64 modes in each figure). However, not all of them represent correct conclusions. There are only 24 correct modes (six modes in each figure). Among them, 19 basic, so-called strong modes. The rest - weak modes- are presented as complex conclusions: combinations of conclusions in the form of a categorical syllogism with conclusions according to the rules of the ʼʼlogical squareʼʼ (Table 3).
Table 3
Regular modes of a simple categorical syllogism
Example. The syllogism given (about those present) has a second figure and mode AAA. Moreover, among the correct modes of the second figure there is no mode AAA. This mode exists only in the first figure. This also suggests that the syllogism is incorrect.
Our thinking at the level of inference acquires the ability to carry out without any fundamental restrictions all transformations with classes and relationships and thereby build the most general models of the reality under study. It's called a syllogism...
In mediated inference, the conclusion follows from two or more judgments that are logically related to each other. There are several types of mediated inferences: a) syllogisms; b) conditional inferences; c) disjunctive reasoning. Syllogisms (from gr. syllogismos... .
PLAN PLAN PLAN 1. Complex judgment and its types. 2. Denial of complex judgments. Complex judgments are formed from simple judgments with the help of logical connectives (logical constants): conjunctions, disjunctions, implications and equivalences. Complicated judgments...
From the Greek syllogismos, counting.
New knowledge obtained with the help of a simple categorical syllogism is calculated from the existing judgment.
Composition of the PCS: Consists of two premises and a conclusion.
For example:
All people are mortal.
All logicians are people.
So all logicians are mortal.
Above the line are 2 premises, and then the conclusion.
In turn, the premises and the conclusion consist of 3 terms. These terms are called "PKC terms":
S - the lesser term - is the subject of the conclusion of the syllogism. In our case, these are “logic”. The premise that contains the lesser term is called the lesser premise.
P - the major term - is the predicate of the conclusion of the syllogism. In our case, it is "mortal". The premise that contains the larger term is the big premise.
In a clear logical form of the PCS, the major premise is written at the top, the smaller one under the larger one, and the conclusion under the line.
M - the middle term is a term that is contained in both messages, but is not in the conclusion. In our case, it is "people".
Axiom of the syllogism:
Has two interpretations:
1) Attributive: A sign of a sign of some thing is a sign of that thing itself; that which contradicts the sign of a thing contradicts the thing (the sign of a sign is the sign of a thing).
2) Volumetric: Everything that is affirmed (or denied) in relation to all objects of the class, is affirmed (or denied) in relation to each object and any part of the objects of this class (said about everything and about none).
The attributive interpretation of our example says that the sign of people is "mortal". And the sign "people" of the sign "mortal" is the sign of "logic" things are "mortal".
General PKS rules:
There are 7 rules in total, which are divided into 2 groups.
Group I - rules of terms:
1) There should be only three terms in a syllogism. Error: "Quadruple terms." In another way it is called: "substitution of terms". For example, “All secretaries are busy with their work. Some birds are secretaries. So some birds are minding their own business” is an example of something wrong. The term secretary in the first and second premises has different meanings. In one secretary - there is work. And in the second - a kind of birds. You can't do that.
2) The middle term must be distributed in at least one of the premises. Distribution table:
For example, “All liver flukes eat the liver. Some people in the restaurant also eat liver. So some people in the restaurant are liver flukes." The middle term is "eat the liver". The smaller term is "people in a restaurant". And the bigger term is "liver flukes". That is, it turned out that the middle term in both cases is with a minus. It is not right.
3) If an extreme term (greater or smaller) is not distributed in the premise, then it should not be distributed in the conclusion. Error: "illegal term extension". For example, “I am a person (A). You are not me (E). So you are not human (E)." We find the terms of the syllogism: The middle term is "I". The smaller term is "You". The larger term is "Man". This syllogism is wrong.
Group II - rules for parcels:
1) There must be at least one general premise (no conclusion is made from two private premises). That is, one of the premises must be a general proposition.
2) There must be at least one affirmative premise (no conclusion is drawn from two negative premises).
3) If one of the premises of the syllogism is private, then the conclusion is private.
4) If one of the premises is negative, then the conclusion in the syllogism is also negative.
Solving problems on PCS:
3 types of tasks:
1) Checking the PCS for correctness.
A task:
“Each passionary can change the course of history. Not a single janitor is a passionary. This means that no janitor can change the course of history.”
Define terms and arrange distribution.
Solution:
Define terms:
S - janitor.
P is someone who can change the course of history.
M - passionary.
We arrange the distribution:
A All M+ are P-
E No S+ is M+
E No S+ is P+
Check for correctness (according to the rules): First, it is not violated. The second one is not violated. The third one is violated. That is, the PCS is wrong.
A task:
“All state employees of IJ are students of group 111. Some students of group 111 attend consultations. This means that some students of the state employees of the IJ attend consultations.”
1) We are looking for the conclusion of the syllogism and the terms: “It means that some students of the state employees of the IJ attend consultations”
S - state student IJ.
P is a student who attends lectures.
M - student of group 111.
2) We draw up a diagram:
And All S+ is M-.
I Some M- is P-.
I Some S- is P-.
3) Check if the rules are violated:
1) is violated. The rest can not be checked.
A task:
“All geese are grey. Goose Grisha is not gray. So the goose Grisha is not a goose.
1) We are looking for a conclusion and terms: “So the goose Grisha is not a goose.”
R - Goose Grisha
M - be gray.
And All S+ is M-
E All P+ is not M+
E All P+ is not S+
The syllogism is incorrect because the axiom of the syllogism is violated.
2) Deriving a conclusion from premises.
A task:
“All pineapples taste good. A potato is not a pineapple. Means…"
Since there is no conclusion, we cannot define a lesser and a greater term. The mistake is that students try to define terms.
Therefore, we need to start solving this problem by looking for the middle term.
1) Middle term: M - pineapple.
2) We conditionally designate the extreme terms from which we obtain the conclusion:
And things taste good.
B - potatoes.
3) We write the structure of syllogisms:
A All M+ is A-
E All B+ is not M+
O Some S-s are not P+s
We establish the distribution of terms.
The procedure for deriving a conclusion from the premises:
1) Determine the link in the conclusion. The link is determined by the rules and axioms of the premises. The conclusion in our judgment is also negative. If one of the premises is negative, then the conclusion is negative.
2) Determine the type of judgment in the conclusion. The type of judgment in the conclusion is determined by the distribution of extreme terms. Extreme terms A and B. They have a distribution - and +. When deriving a conclusion, you must not violate the 3rd rule of sending. Therefore, we cannot take a general negative judgment as a conclusion, because both terms are distributed there.
3) To demolish the extreme terms of the conclusion. We do according to the distribution of terms. In O S-, and P+, therefore, we substitute: A- \u003d S-, and B + \u003d P +
We change the terms of the judgment to our terms.
We write down the conclusion: "Some things that taste good are not potatoes."
A task:
“All Zelyuks are Momzyuks. Every Snark is a Zeluk. Means…".
1) M - zelyuks.
2) A - momjuki.
B - snark.
3) We write the structure:
And All M+ is A-.
And All B+ is M-.
A All B+ is A-
4) Conclusion - with "is".
Type of judgment - E (general negative).
Conclusion: "Every snark is a momzyuk."
συλλογισμός ) is a reasoning of thought, consisting of three simple attributive statements: two premises and one conclusion. The premises of a syllogism are divided into major (which contains the predicate of the conclusion) and minor (which contains the subject of the conclusion). According to the position of the middle term, syllogisms are divided into figures, and the latter in the logical form of premises and conclusions - on modes.Syllogism example:
Every man is mortal (major premise) Socrates is a man (minor premise) ------------ Socrates is mortal (conclusion)
Structure of a simple categorical syllogism
The syllogism includes exactly three term :
- 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 - middle term: included in both premises, but not included in the conclusion.
Subject S(subject) - something about which we express (divided into two types):
- Specific: Singular, Particular, Plural
- Singular [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"
- Plural propositions are those in which there are several subject class concepts. Note: "insects, spiders, crayfish are arthropods"
- Indefinite. Note: "it's getting light", "it hurts", etc.
Predicate P(predicate) - what we express (2 types of judgments):
- Narrative - this is a judgment regarding events, states, processes or activities of the fleeting. Note: "A rose is blooming in the garden."
- Descriptive - when some property is attributed to one or more objects. The subject is always a certain thing. Note: “Fire is hot”, “snow is white”.
Relationship between subject and verb:
- Judgments of identity - the concepts of subject and predicate have the same scope. Note: "every equilateral triangle is an equiangular triangle"
- Judgments of subordination - a concept with a lesser scope is subordinate to a concept with a wider scope. Note: “A dog is a pet”
- 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 terms is important, since a stray dog, although not domestic in terms of living in a house, still belongs to the class of domestic animals in terms of belonging on a socio-biological basis. That is, it should be understood that a "pet" according to the socio-biological classification in some cases may be a "non-pet" in terms of habitat, that is, from a social and domestic point of view.
Classification of simple attributive statements by quality and quantity
By quality and quantity, four types of simple attributive statements are distinguished:
A- from lat. a ffirmo - General ("All men are mortal") I- from lat. aff i rmo - Partial affirmative ("Some people are students") E- from lat. n e go - All-negative ("None of the whales are fish") O- from lat. neg o- Partial negative ("Some people are not students")Note. For the conditional letter designation of statements, vowels from Latin words are used affirmo(I affirm, I say yes) and nego(I deny, I say no).
Singular statements (those in which the subject is a single term) are equated with general ones.
Distribution of terms in simple attributive statements
The subject is always distributed in a general utterance and never distributed in a particular utterance.
The predicate is always distributed in negative judgments, in affirmative ones it is distributed when, according to the volume P<=S.
In some cases, the subject can act as a predicate.
Rules of a simple categorical syllogism
- The middle term must be distributed in at least one of the premises.
- A term not distributed in the premise should not be distributed in the conclusion.
- The number of negative premises must be equal to the number of negative conclusions.
- Each syllogism should have only three terms.
Figures and modes
The figures of the syllogism are the forms of the syllogism that differ in the location of the middle term in the premises:
Each figure corresponds to modes - forms of syllogism, differing in the quantity and quality of premises and conclusions. Modes were studied back in medieval schools, and mnemonic names were invented for the correct modes of each figure:
| Figure 1 | Figure 2 | Figure 3 | Figure 4 | |||
| B a rb a r a | C e s a r e | D a r a pt i | Br a m a nt i p | |||
| C e l a r e nt | C a m e str e s | D i s a m i s | C a m e n e s | |||
| D a r ii | F e st i n o | D a t i s i | D i m a r i s | |||
| F e r io | B a r o c o | F e l a pt o n | F e s a p o | |||
| B o c a rd o | Fr e s i s o n | |||||
| F e r i s o n |
Examples of syllogisms of each type.
All animals are mortal. All people are animals. All people are mortal.
Celarent
None of the reptiles have fur. All snakes are reptiles. None of the snakes have fur.
All kittens are playful. Some pets are kittens. Some pets are playful.
No homework is fun. Some reading is homework. Some reading is not fun.
No healthy food makes you fat. All cakes are full. No cake is healthy food.
Camestres
All horses have bloating. Neither person has bloating. No man is a horse.
No lazy person passes exams. Some students take exams. Some students are not lazy.
All informative things are helpful. Some sites are not helpful. Some sites are not informative.
All fruits are nutritious. All fruits are delicious. Some tasty foods are nutritious
Some mugs are beautiful. All circles are useful. Some useful things are beautiful.
All the diligent boys in this school are red-haired. Some of the studious boys at this school are boarders. All the diligent boarding boys in this school are red-haired.
Felapton
Not a single jug in this cupboard is new. All the jugs in this cupboard are cracked. Some of the cracked items in this closet are not new.
Some cats are tailless. All cats are mammals. Some mammals are tailless.
None of the trees are edible. Some trees are green. Some green things are not edible.
Bramantip
All apples in my garden are useful. All healthy fruits are ripe. Some ripe fruits are apples in my garden.
All bright flowers are fragrant. Not a single fragrant flower is grown indoors. No indoor flower is bright.
Some small birds eat honey. All honey-eating birds are colored. Some colored birds are small.
No person is perfect. All perfect beings are mythical. Some mythical creatures are not human.
Fresison
No competent person makes mistakes. Some wrong people work here. Some people working here are incompetent.
According to the rules, shapes can be converted to other shapes, and all shapes can be converted to one of the shapes of the first figure.
Story
The doctrine of syllogism was first expounded by Aristotle in his First Analytics. He speaks only of 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. The successor of Aristotle, the founder of botany Theophrastus, according to Alexander of Aphrodisias (in his commentary on the first "Analyst" of Aristotle), added five more modes (modi) to the first figure of the syllogism; these five modes were subsequently singled out by Claudius Galen (who lived in the 2nd century AD) into a special fourth figure. In addition, Theophrastus and his student Evdem began to analyze the 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 antiquity, except for the addition that the Stoics made in the doctrine of conditional syllogism. According to Sextus Empiricus, the Stoics recognized some kinds of conditional and disjunctive syllogism αναπόδεικτοι , that is, not requiring proof, and considered them as prototypes of the syllogism (as, for example, Sigwart looks at the syllogism). The Stoics recognized five types of such syllogisms, coinciding with Theophrastus. Sextus Empiricus gives the following examples for these five species:
- If day has come, then there is light; but now it is day, therefore there is light.
- If day has come, then there is light, but there is no light, therefore, there is no day.
- There cannot be (at the same time) day and night, but the day has come, therefore there is no night.
- It may be either day or night, but now it is day, therefore there is no night.
- It may be either day or night, but there is no night, so now it is day.
In Sextus Empiricus and skeptics in general, we also meet with criticism of the syllogism, but the purpose of criticism is to prove the impossibility of proof in general, including the syllogistic one. Scholastic logic has added nothing essential to the doctrine of syllogisms; it only broke the connection with the theory of knowledge that existed in Aristotle and thus turned logic into a purely formal doctrine. The exemplary manual of logic in the Middle Ages was the work of Marcianus Capella, the exemplary commentary was the writings of Boethius. Some of Boethius' commentaries deal specifically with the doctrine of syllogisms, such as "Introductio ad categoricos syllogismos", "De syllogismo categorico", and "De syllogismo hypothetico". The writings of Boethius are of some historical significance; they also contributed to the establishment of logical terminology. But at the same time, it was Boethius who gave the logical teachings a purely formal character.
"logical square"
From the era of scholastic philosophy, in relation to the doctrine of syllogism, 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 Psellos. He proposed the so-called "logical square", in which the relationship of various types of judgments is clearly expressed. He owns the names of various modi (Greek. 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 name of the 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). The logical teachings of Psellus are formal. The work of Psellos was translated by William of Sherwood and made popular by the recasting of Peter of Spain (Pope John XXI). Peter of Spain in his textbook shows the same desire for mnemonic rules. The Latin names of the types of figures given in formal logics are taken from Peter of Spain. Peter of Spain and Michael Psellos represent the flowering of formal logic in medieval philosophy. From the Renaissance begins criticism of formal logic and syllogistic formalism
The first serious critic of Aristotelian logic was Pierre Ramet, who died during Bartholomew's Night. The second part of his "Dialectic" deals with the syllogism; his doctrine of syllogism, however, does not represent significant deviations from Aristotle. Beginning with Bacon and Descartes, philosophy follows new paths and defends research methods: the unsuitability of the syllogistic method in the sense of a method of research, finding the truth, becomes more and more obvious.
Syllogism in modern logic
Syllogism predominated in logic until the 19th century and had limited application, in part because of its attachment to categorical syllogism. The syllogism is replaced by a simpler and more powerful
Inferences in which a conclusion is necessarily drawn from knowledge of a greater degree of generality to knowledge of a lesser degree of generality, as already mentioned, are called deductive (from lat. deductio - "extraction").
Example: All flowers are plants.Rose is a flower.
Rose is a plant.
A typical form of deductive reasoning is the simple categorical syllogism ( from gr. syllogismos - "receiving a conclusion").
The analysis of a syllogism always begins with a conclusion. The subject of judgment, which is the conclusion, is lesser term conclusions (S), predicate - larger term (R).
The premise containing the larger term is called greater premise, package with lesser term - lesser premise.
A concept that is contained in each of the premises, but not in the conclusion, is called with redter min (M)
In the example above: rose (S). plant (R), and flowers - (M).
Let's graph this:
The scheme graphically presents us with the axiom of the syllogism, which underlies the conclusion on the categorical syllogism: "Everything that is inherent in the genus is also inherent in its species."
In order to obtain a true conclusion by means of a syllogism, we must have true premises and follow the rules of terms, premises, and figures.
I. Rules of terms.
1. Each syllogism should have only 3 terms (S, R. M). If the rule is violated, then the error is called "term quadrupling".
An example of such an error
: Labor is the basis of life.
The study of logic - labor .
The study of logic is the basis of life.
Here the term "labor" is interpreted in a different sense: in a larger premise - broadly, and in a smaller one - narrowly.
2. The middle term must be distributed in at least one of the premises:
All useful things have a pleasant smell.
Perfume "Chanel" has a pleasant smell .
Perfume "Chanel" useful.
Here the middle term "have a pleasant smell" (it is convenient to write it like this: "there are those who have a pleasant smell") is not distributed in any of the premises. Therefore the conclusion is false. Let's explain this graphically:
As we see and S and R affect only part of the scope of the middle term - "having a pleasant smell." Therefore, a reliable conclusion cannot be drawn here.
If a term is not distributed in the premise, then it cannot be distributed in the conclusion:
All soldiers know how to shoot.
All children - not soldiers .
All children cannot shoot.
The output predicate (“they know how to shoot”) is distributed, but in the premise it is not distributed. The meaning of this rule is that if it is violated, the conclusion about a larger range of objects than is contained in the premises.
II. Parcel rules.
It is impossible to draw a conclusion from two negative premises:
All blacks are not white.
No piece of coal is white .
The term “blacks” and the term “piece of coal” are in no way connected with the average term “white”. All three terms are in relation to incompatibility, so no conclusion is possible here.
2. It is impossible to draw a conclusion from two private premises:
Some students are excellent students.
Some students are good chess players .
Here the middle term is not distributed in both premises.
3. If one of the premises is negative, then the conclusion must also be negative:
All students have record books.
Dmitriev is not a student.
Dmitriev has no record book.
Any negative premise indicates that the middle term is incompatible with S or R. Hence the incompatibility with each other of the greater and the lesser terms.
4. If one of the premises is private, then the conclusion must be private:
All paratroopers can skydive.
Some military personnel are paratroopers .
Some military personnel can skydive.
Syllogism figures and their rules
Syllogism figures- these are its forms, which differ in the position of the middle term M in parcels. There are four figures in total.
Each of the figures has its own rules. I. The first figure.
All metals conduct electricity.
Copper - metal .
Copper conducts electricity.
Rules of the first figure: the major premise must be general, the minor premise must be affirmative.
A common mistake: the conclusion is made on the first figure with a smaller negative premise. For example.
All children love chocolate.
Petrova is not a child .
Petrova doesn't like chocolate.
The rule of terms is violated here: a term that is not distributed in the premise cannot be distributed in the conclusion.
II . Second figure.
All adventure films are interesting.
This movie is uninteresting .
This movie is not an adventure.
Rules for the second figure: the major premise must be a general proposition, and the minor premise and conclusion must be negative propositions. A common mistake: the conclusion is made on the second figure with two affirmative premises. For example:
All rabbits eat carrots.
Egorov eating carrots .
Egorov - a hare?!
Here the rule of terms is violated: the middle term is not distributed in both premises.
III. Third figure
All bamboos bloom once in a lifetime.
All bamboos are perennials. .
Some perennials bloom once in a lifetime. Rule of the third figure: the minor premise must be affirmative, and the conclusion must be particular.
A common mistake: the conclusion is a universally affirmative judgment. For example:
All foxes love cheese.
All foxes have a long tail .
All. who has a long tail, love cheese.
It's clear, that foxes are not the only ones with long tails.
IV. Fourth figure.
All whales swim.
All swimmers live in water .
Some that live in the water are whales.
The fourth figure does not give general affirmative conclusions. This figure is rarely used.
Rules of the fourth figure.
a) if the major premise is affirmative, then the minor must be general;
b) if one of the premises is negative, then the larger premise must be common. A possible error when using the fourth figure: the smaller premise is a quotient with an affirmative larger one. For example:
All cats have whiskers.
Some who have mustaches write poetry.
Are some of the poetry writers cats?
modes categorical syllogism- these are varieties of syllogism that differ from each other in the quantitative and qualitative characteristics of its premises and conclusions.
In four figures of regular modes 19:
1st figure - AAA, EAE,AN,EY;
2nd figure - BUT HER, JSC O, EAE, EY;
3rd figure - AAI. EAO, IAI, AL, JSC, EY;
4th figure - AAL AEE, IAI, EAO, EY.
All fish do not have lungs.
All whales have lungs .
No fish is a whale.
Big premise - universally affirmative judgment (BUT). Minor premise - general negative proposition (E). The conclusion is a general negative judgment (E).
Thus, the mode of this syllogism is EAE(1st figure). By identifying the mode and figures of the syllogism, and by relating the mode to the table of correct modes, we can quickly determine whether the syllogism is true.
3. OTHER KINDS OF SILLOGISMS Abbreviated syllogism
In everyday life, we often use syllogisms that have some parts left out. These syllogisms are called contractions or enthymemes (from Greek- "in the mind"). Depending on what we need to focus on, we can leave only one premise or remove the conclusion.
Example. If we say about someone: “You need to be a dishonorable person to do such things,” then this expression is a syllogism. When we give this syllogism its full form, it will take the following form:
All people who do such things are dishonorable.
This person does things like this. .
Therefore, this person is dishonest.
To restore the enthymeme to a full syllogism, the following rules must be followed:
Find a conclusion and formulate it in such a way that the minor and major terms are clearly expressed. The conclusion usually comes after the words: “means”, “therefore”, etc. or before the words "because", "because", "because". If there are no such words, then the conclusion is missing in the enthymeme.
If there is a conclusion, but not one of the premises, then it is necessary to establish whether a larger or smaller premise is present. Conclusion predicate is a bigger term. The subject of the conclusion is a lesser term. According to which term is contained in the premise, we determine which premise.
So we know which premise is missing, we know the middle term. Proceeding from this, we define both terms of the missing premise.
Enthymemes are widely used in everyday colloquial speech, but one should be careful, because it is not always possible to notice an error that can be clearly fixed in a complete syllogism. For example: "He is an uncultured person, since he has not read Joyce's novel Ulysses." Expanding the enthymeme into a complete syllogism:
All uncultured people have not read Joyce's Ulysses.He hasn't read Joyce's novel Ulysses .
He is an uncultured person.
No conclusion follows from two negative premises.
Complex syllogism (polysyllogism)
These are two or more simple categorical syllogisms connected to each other in such a way that the conclusion of one becomes the premise of another syllogism, and so on. The general formula of polysyllogism is as follows.
M- PEverything that improves health (M) is useful (P).
S - M. Physical education (S) strengthens health (M).
C - P Physical education (C) is useful (P).
S - FROM Swimming ( S ) is physical education (C) .
Consequently, S- R: Swimming (S) - useful (P).
Any scientific thinking in an expanded or hidden form is a polysyllogism, which follows from a whole system of inferences.
An abbreviated complex polysyllogism is called a sorite. In the sorite, all intermediate conclusions are omitted, and only the last conclusion is given.
A complex abbreviated syllogism in which enthymemes serve as premises is called epicheirema.
Epicheirema scheme:
All BUT essence of C, because BUT essence AT.
All D essenceBUT . becauseD essenceE.
Therefore, all D the essence of S. Separating-categorical syllogism
In a dividing-categorical inference, one premise is a divisive judgment, and the second premise and conclusion are categorical judgments. The dividing-categorical syllogism has two modes:
a) affirmative-denying:
b) denying-asserting. General modal formula a).
BUT have or AT, or with.
BUT there isAT .
Therefore, A is not C. Example:
Wars are either reactionary or progressive
. Wars, the purpose of which is the seizure of foreign lands, are not progressive Consequently, wars of conquest are not progressive.
General formula of mode b):
BUT have or AT, or with.
BUT do not eatAT .
Consequently, BUT is C. Example:
Mineral fertilizers are either nitrogen or phosphorus.This fertilizer is not nitrogen .
Therefore, this fertilizer is phosphoric.
Conditional (hypothetical) syllogism
As we remember, in addition to categorical judgments, there are conditional and disjunctive judgments. Therefore, there may be syllogisms whose premises include conditional propositions, disjunctive propositions, or both.
Conditional Scheme: If BUT there is AT, then C is D.
First Judgment (If BUT there is AT) is called the "base", and the second (C is D)- "consequence".
If in a syllogism both premises and conclusion are conditional propositions, then it is called conditional. Conditional Inference Structure: If BUT, then AT.
If aAT. thenFROM.
If a BUT, then S.
For example:
If an electric current is passed through the conductor, then a magnetic field is formed around the conductor.
If a magnetic field forms around the conductor, then the iron filings are located in this magnat field along the lines of force .
Therefore, if an electric current is passed through the conductor, then the iron filings are located in its magnetic field along the lines of force.
This is a syllogism, where one premise is a conditional proposition, and the second is a simple categorical one. In this case, the categorical premise usually consists of the same terms as the basis or consequence of the conditional premise.
If there is BUT, that is AT.
BUT there is.
Therefore, there is AT.
Example: If this tree is spruce, then it does not lose needles for the winter.
This is a spruce tree .
Therefore, this tree does not lose needles for the winter.
Diagram of the negating mode:
If there is BUT, that is AT.
AT no.
Consequently, BUT no.
Example: If Bogdanov is a good skier, then he will fulfill the standard of a master of sports.
Bogdanov did not fulfill the standard of the master of sports in skiing . Consequently, Bogdanov is not a good skier.
Let's pay attention to the following fact. In conditional syllogisms, one can draw a conclusion only from the statement of the reason to the statement of the consequence. And from the denial of the consequence to the denial of the foundation. It is impossible to draw a conclusion from the affirmation of the consequence to the affirmation of the foundation and from the negation of the foundation to the negation of the consequence. The fact is that the same phenomenon can be caused by different reasons. If I deny that a given cause brought into existence this or that phenomenon, this does not mean that some other cause could not produce it. If I say that a given action has occurred, then this does not mean that it is generated by this cause - there could be many other reasons that could have generated it.
Example 1. Let's try to assert the consequence:
Kuznetsov broadened his horizons.
Does it follow from this that Kuznetsov read good books? No, because Kuznetsov could attend lectures, talk with good specialists, and so on. That is, there are many reasons for expanding horizons.
Example 2. Let's try to negate the base:
If someone reads good books, then he expands his horizons.
Kuznetsov doesn't read good books.
Can we say that Kuznetsov is not expanding his horizons? No, because the considerations given in example 1 are correct in this case. Separative inference
Dividing Inference is called a conclusion in which one or more premises are separating. There are purely divisive and dividing-categorical inferences.
As we remember, the general form of a disjunctive judgment is as follows: BUT have or AT, or C or D or E. Each term of a disjunctive judgment is called an alternative.
In a purely disjunctive syllogism, both premises are disjunctive judgments.
The formula for a purely disjunctive syllogism is:
S there is BUT, or AT, or with,
BUT have orBUT , , orBUT .
S have or A, or BUT 2 , or AT, or with.
Example: Every philosophical system is either idealism or materialism.
Idealist philosophy is either objective idealism or subjective idealism. .
Consequently, every philosophical system is either objective idealism, or subjective idealism, or materialism.Conditional disjunctive syllogism
Conditional-separative inference- this is a conclusion in which one premise consists of two or more conditional propositions, and the other is a disjunctive proposition.
Depending on the number of terms in the distributive premise, this conclusion can be dilemma(if the separating premise contains two members), trilemma(if the separating premise contains three terms) and polylemma(the number of separating terms is more than two).
Dilemmas and trilemmas are of two kinds: constructive and destructive; both forms of dilemma and trilemma can be simple or complex.
A simple design dilemma. This conclusion has two premises. The first asserts that the same consequence follows from two different reasons. The second premise, which is a disjunctive proposition, states that one or the other of these grounds is true.
Diagram of a simple constructive dilemma:
If a BUT is B, then C is D; if E there is F, then C is D.
BUT there isAT orE there isF .
Consequently, FROM there is D.
Example: If a student goes to lectures, then he knows logic.
If a student reads a textbook of logic, then he knows logic.
A student attends lectures or reads a logic textbook . The student knows logic.
Difficult design dilemma. This is a conclusion, where in the first premise there are two grounds from which two consequences follow. The second premise (the disjunctive judgment) speaks of the truth of one or the other reason. The conclusion asserts the truth of one or the other consequence. The difference between a complex constructive dilemma and a simple one is that both consequences of its conditional premise are not the same, but different.
Diagram of a complex design dilemma:
If a BUT there is AT, then C is D: if E there is F, then G there is N.
But orBUT there isAT. orE there isF .
Therefore, either C is D, or G is N.
Example: Stirlitz's reasoning in the novel "Seventeen Moments of Spring" (see: Semenov Yu. Sobr. works in 8 vols. T. 3. - M .. 1991. - C 567-574).
If I return to Berlin, the Gestapo may arrest me, if I go to Moscow, I will not complete the task to the end.
But I can go to Berlin or return to Moscow.
Therefore, either I can be arrested by the Gestapo, or I will not complete the task to the end.
More complex situations are expressed in the logical form of a trilemma or even a polymemma.
An example of a complex constructive trilemma;
Many Russian folk tales speak of a stone that lies at the crossroads of three roads. On the stone is an inscription containing a trilemma:
If you go straight, you will lose your life;
If you go to the left, you will lose your horse;
If you go to the right, you will fall into bondage.
The hero of a fairy tale can go straight, or to the right, or to the left .
Consequently, he will either lose his life, or lose his horse, or fall into captivity.
The reliability of a lemmatic inference depends on the correctness of the conditional propositions in the larger premise and on the completeness of the terms of the division in the smaller one.
Often these conditions are not met, then the lemmatic inference becomes a source of errors.
The cause of errors most often is an incomplete enumeration of division members. It is not always possible to exhaust all possible cases with two alternatives - there can be many more alternatives. An example of such an error:
If a student loves learning, then he does not need encouragement. If the student is disgusted with learning, then any encouragement is ineffective.
The student may love the teaching or be disgusted with it. .
Therefore, encouragement in the matter of learning is either superfluous or useless.
The mistake here is that, in addition to “love of learning” and “disgust for learning,” a student may have, so to speak, a neutral position - for such students, encouraging learning in any form can be effective.
1. The concept of syllogism. Simple categorical syllogism
The word "syllogism" comes from the Greek syllogysmos, which means "conclusion". It's obvious that syllogism- this is the derivation of a consequence, a conclusion from certain premises. A syllogism can be simple, compound, abbreviated, and compound abbreviated.
A syllogism whose premises are categorical propositions is called, respectively, categorical. There are two premises in the syllogism. They contain three terms of the syllogism, denoted by the letters S, P and M. P is the major term, S is the minor, and M is the middle, connecting. In other words, the term P is wider in scope (although narrower in content) than both M and S. The narrowest term in the syllogism is S. At the same time, the larger term contains the predicate of the judgment, the smaller one its subject. S and P are interconnected by the middle concept (M).
All boxers are athletes.
This man is a boxer.
This person is an athlete.
The word "boxer" here is the middle term, the first premise is the greater term, the second is the lesser. To avoid mistakes, we note that this syllogism refers to a given, specific person, and not all people. Otherwise, of course, the second premise would be much broader in scope.
In the first case, the major premise must be general, while the minor premise must be affirmative. The second form of the categorical syllogism gives a negative conclusion, and one of its premises is also negative. The larger concept, as in the first case, must be general. The conclusion of the third form must be private, the minor premise must be affirmative. The fourth form of categorical syllogisms is the most interesting. From such conclusions it is impossible to draw a generally affirmative conclusion, and there is a natural connection between the premises. So, if one of the premises is negative, the larger one should be general, while the smaller one should be general, if the larger one is affirmative.
In order to avoid possible errors, when constructing categorical syllogisms, one should be guided by the rules of terms and premises. The term rules are as follows.
Distribution of the middle term (M). Means that the middle term, the link, must be distributed in at least one of the other two terms - greater or less. If this rule is violated, the conclusion is false.
The absence of unnecessary terms of the syllogism. Means that the categorical syllogism should contain only three terms - the terms S, M and P. Each term should be considered in only one meaning.
Distribution in detention. In order to be distributed in the conclusion, the term must also be distributed in the premises of the syllogism.
Parcel rules.
1. Impossibility of withdrawal from private parcels. That is, if both premises are private judgments, it is impossible to draw a conclusion from them. For example:
Some cars are pickups.
Some mechanisms are machines.
No conclusion can be drawn from these premises.
2. Impossibility of inference from negative premises. Negative premises make it impossible to draw a conclusion. For example:
People are not birds.
Dogs are not people.
Conclusion is not possible.
3. The next rule says that if one of the premises of the syllogism is particular, then its consequence will also be particular. For example:
All boxers are athletes.
Some people are boxers.
Some people are athletes.
4. There is another rule that says that if only one of the premises of the syllogism is negative, the conclusion is possible, but it will also be negative. For example:
All vacuum cleaners are household appliances.
This technique is not household.
This technique is not a vacuum cleaner.
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