§ 5. REDUCED CATEGORICAL SYLLOGISM (ENTHYMEME)

The term “enthymeme” translated from Greek means “in the mind”, “in thoughts”.

ENTHYMEME, ORABBREVIATION CATEGORICAL

SYLLOGISM, is a syllogism in which one of the premises or conclusion is missing.

An example of an enthymeme: “All sperm whales are whales, therefore all sperm whales are mammals.” Let's restore the enthymeme:

All whales are mammals.

All sperm whales are whales.

All sperm whales are mammals.

There's a big message missing here.

In the enthymeme “All hydrocarbons are organic compounds, therefore methane is an organic compound” a minor premise is missing. Let us restore the enthymeme to a complete categorical syllogism:

All hydrocarbons are organic compounds.

Methane hydrocarbon.

Methane is an organic compound.

In the enthymeme “All fish breathe with gills, and perch is a fish,” the conclusion is missing - “Perch breathes with gills.”

When restoring the enthymeme, it is necessary to determine which judgment is the premise and which is the conclusion. The premise usually comes after the conjunctions “since”, “because”, “for”, etc., and the conclusion usually comes after the words “therefore”, “therefore”, “therefore”, etc.

The reader is invited to construct an enthymeme from this categorical syllogism.

The release by the creditor of the debtor from his obligations is forgiveness of the debt.

This creditor K. released his debtor M. from his obligations.

This creditor K. forgave his debtor M. the debt.

Enthymemes are used more often than complete categorical syllogisms.

§ 6. COMPLEX AND COMPLEX SYLLOGISMS (POLYSYLLOGISMS, SORITES, EPICHEIREMA)

In thinking there are not only individual complete or abbreviated syllogisms, but also complex syllogisms, consisting of two, three or more simple syllogisms. Chains of syllogisms are called polysyllogisms.

polysyllogism(complex syllogism) are two or more simple categorical syllogisms related to each other in such a way that the conclusion of one of them becomes the premise of the other. There are progressive and regressive polysyllogisms.

IN progressive polysyllogism the conclusion of the previous polysyllogism (prosyllogism) becomes the greater premise of the subsequent syllogism (episyllogism). Let us give an example of a progressive polysyllogism, which is a chain of two syllogisms and has the following scheme:

All A essence B.

All C are D.

This means that all Cs are Bs.

AllD the essence of S.

All D's are IN.

Sports strengthens health(B).

Gymnastics (WITH)- sports (A).

This means that gymnastics improves health.

Aerobics( D ) - gymnastics(WITH).

Aerobics (D) improves health (IN).

Let us give another example of progressive polysyllogism.

This means education is necessary.

Vocational education is a type of education.

Vocational education is necessary.

Legal education for lawyers is a professional education.

IN regressive polysyllogism the conclusion of the prosyllogism becomes the lesser premise of the episyllogism. For example:

All planets (A)- cosmic bodies (IN).

Saturn(WITH) - planet(A).

Saturn (WITH) - cosmic body (IN).

All cosmic bodies (IN) have mass (D).

Saturn(WITH) - cosmic body(IN).

Saturn (WITH) has mass (D).

By connecting them together and without repeating the statement twice, “Everything WITH essence IN", we get a regressive polysyllogism scheme for general affirmative premises:

AllA essence IN.

All C are A

AllIN essence D.

All With the essence of V.

All C are D.

Let us give more examples of regressive polysyllogism.

Consumer fraud (IN) there is an act punishable under Article 200 of the Criminal Code of the Russian Federation (C).

Weighing(A) there is consumer fraud(IN).

Weighing (A) there is an act punishable under Article 200 of the Criminal Code of the Russian Federation (WITH).

Any act punishable under Article 200 of the Criminal Code RF(S), there is a crime.

Weighing(A) there is an act punishable under Article 200 of the Criminal CodeRF (C).

Weighing (A) there is a crime (D).

Sorites (with general parcels)

Progressive and regressive polysyllogisms in thinking are most often used in an abbreviated form - in the form of sorites. There are two types of sorites: progressive and regressive.

Progressive sorites(otherwise called by the name of the logician who described this litter Goklenevsky) is obtained from a progressive polysyllogism by throwing out the conclusions of previous syllogisms and the major premises of subsequent ones. The progressive sorites begins with a premise containing the predicate of the conclusion and ends with a premise containing the subject of the conclusion.

All products containing vitamins (A), useful (IN).

Fruits (WITH) - foods containing vitamins (A).

Bananas( D ) - fruits(WITH).

Bananas (D) useful (IN).

Let us give another example of a progressive sorites, formed from the above progressive polysyllogism.

Everything that contributes to the progress of mankind is necessary.

Education contributes to the progress of society.

Vocational education is a type of education.

Legal education for lawyers is a type of professional education.

Legal education for lawyers is necessary.

Progressive sorites scheme:

All A essence IN.

All WITH essence D.

AllD essenceWITH.

All D essence IN.

Regressive sorites(otherwise Aristotelian) is obtained from regressive polysyllogism by throwing out the conclusions of prosyllogisms and the smaller premises of episyllogisms. In a proslogism we swap the premises. A regressive sorites begins with a premise containing the subject of the conclusion and ends with a predicate containing the predicate of the conclusion.

All roses (A)- flowers (B). All flowers (B) are plants (C). All plants (C) breathe (D).

All roses (A) breathe (D).

All A's are B's.

All IN the essence of S.

All C are D.

All A essence D.

Burglary is theft.

Theft is a crime.

The crime is punishable.

Burglary is punishable.

Formalization of epicheirem with general premises

EPICHEREMA In traditional logic, such a complex syllogism is called, both premises of which are abbreviated simple categorical syllogisms (enthymemes).

The scheme of an epicheireme containing only general affirmative statements is usually written as follows:

All A the essence is C, since A essence V.

AllDthe essence is A, sinceDessenceE.

All D the essence of S.

Example of epicheyrema:

Noble work (A) deserves respect (WITH), because noble work (A) contributes to the progress of society CBj. The work of a conscientious lawyer (D) there is noble work (SD), since the work of a conscientious lawyer (D) there is work to establish the truth in the trial (E). The work of a conscientious lawyer fDJ deserves respect).

The first and second premises of the epicheireme are enthymemes, i.e. abbreviated categorical syllogisms in which one of the premises is omitted. Let us fully express the first and second premises of the epicheirema.

Anything that contributes to the progress of society (IN), deserves respect (WITH).

Noble work (SD) contributes to the progress of society (IN).

Noble work (A) deserves respect (WITH).

Establishing the truth in a trial (E) there is noble work (A).

The work of a conscientious lawyer( D ) there is work to establish the truth in the trial(E).

The work of a conscientious lawyer ( D) is noble work.

The conclusions of the first and second syllogisms are made by the premises of the third syllogism.

Noble work (A) deserves respect (WITH).

The work of a conscientious lawyer(C) is noble work (A).

The work of a conscientious lawyer (D) deserves respect (WITH).

Like enthymemes, compound syllogisms greatly simplify our reasoning.

Conclusions based on logical connections between judgments (conclusions of propositional logic)

If in predicate logic simple judgments were divided into subject and predicate, then in propositional logic judgments are not divided into subject and predicate, but are considered as simple judgments, from which complex judgments are formed with the help of logical connectives (logical constants).

The rules of direct inference of propositional logic allow one to derive a true conclusion from given true premises. On their basis, purely conditional and conditionally categorical, purely dividing and dividing-categorical, as well as conditionally dividing (lemmatic) inferences are built.

§ 7. CONDITIONAL CONCLUSIONS

Purely conditional an inference is such an indirect inference in which both premises are conditional propositions. A conditional proposition is one that has the structure: “If A, That b». The structure of a purely conditional inference is as follows:

According to the definition of logical consequence formulated within the framework of propositional calculus, if the formula A With is a logical consequence from these premises, then by connecting the premises with the sign of conjunction and adding the conclusion to them through the sign of implication, we must obtain a formula that is a law of logic, i.e. identically true formula. In this case, the formula will be:

The proof of the identical truth of this formula can be carried out using the tabular method.

If the necessary building materials are delivered on time, the construction of the house will be completed by the planned date.

If the construction of the house is completed by the planned date, then the acceptance of the house by the state commission will take place in a timely manner

If the necessary building materials are delivered on time, the state commission will accept the house in a timely manner.

This type of inference is often used in legal practice. Let us give an example of a purely conditional inference from legal practice.

If there is a secret theft of someone else's car, then a theft has been committed.

If a theft is committed, then the thief of someone else's car will be judged under Art. 158 of the Civil Code of the Russian Federation (theft).

If there was a secret theft of someone else’s car, then the thief of someone else’s car will be tried under Art. 158 of the Civil Code of the Russian Federation (theft).

In a purely conditional inference, there are its varieties (modes). These include, for example:

This formula is a law of logic. In an inference, a judgment b true and regardless of whether it is affirmed or denied A.

If gasoline prices do not rise, we will harvest the crops.

If gasoline prices rise, we will harvest.

Let's harvest the harvest.

Let's give an example from fiction. One of Agatha Christie’s heroes, who found himself on the island, argues: “General MacArthur was in gloomy reverie. Damn it, how strange everything is! Not at all what he expected... If there was even the slightest opportunity, he would have left under any pretext... He would not have stayed here for a minute. But the motorboat left. So whether you like it or not, you’ll have to stay.”

Conditional categorical inference- this is a deductive conclusion in which one of the premises is a conditional proposition, and the other is a simple categorical proposition. It has two correct modes, giving a conclusion that necessarily follows from the premises.

/. APPROVING MODUS(MODUS PONENS)

Formula ((A b) A) b (1) is a law of logic.

Can build reliable conclusions from the statement of the basis to the statement of the consequence. Here are two examples:

If you want to enjoy art, then you must be an artistically educated person.

You want to enjoy art.

You must be an artistically educated person.

To construct another example, let’s use an interesting statement by the great Russian teacher K.D. Ushinsky: “If a person is freed from physical labor and is not accustomed to mental labor, brutality takes possession of him.”* Using this statement, we will construct a conditionally categorical conclusion:

* Ushinsty K.D. Collection Op. M.-L., 1948. T. 2. P. 350.

If a person is freed from physical labor and not accustomed to mental labor, then brutality takes possession of him.

This is a person freed from physical labor and not accustomed to mental labor.

This man is overcome by brutality.

Any use of rules or theorems or laws in mathematics, physics, chemistry and other sciences is based on an affirmative mode that gives a reliable conclusion, therefore it finds the widest application in the practice of thinking. In jurisprudence, this conclusion is used when bringing a particular case under the scope of any article of the Civil Code of the Russian Federation or the Criminal Code of the Russian Federation, or in other situations.

Let's give an example.

If a citizen of the Russian Federation has reached the age of eighteen, then he has full civil capacity.

Citizen of the Russian Federation N.V. Krylov reached the age of eighteen.

For citizen of the Russian Federation N.V. Krylov. civil capacity emerges in full.

II. DENIAL MODUS(MODUS TOLLENS)

Formula ((Ab) )  (2) is also a law of logic.

It is possible to build reliable conclusions from the negation of the consequence to the negation of the basis.

Here are two examples:

If a river overflows its banks, water floods the surrounding areas.

The river water did not wash down the surrounding areas.

The water did not overflow its banks.

To construct the second conditionally categorical conclusion, we will use the following statement: “... He is vile who is angry if he is a witness of a stranger’s valor.” (Dante Alighieri).

The conclusion is constructed as follows:

If a person becomes enraged at the sight of someone else’s valor, then he is vile.

This man is not vile.

This man does not become enraged at the sight of someone else's valor.

In legal practice, this mode is very often used.

For example:

If one citizen of the Russian Federation has 12 m2, then he has a standard living space.

Russian citizen Sidorov does not have living space standards.

Citizen of the Russian Federation Sidorov E.V. does not have 12 m2 of living space.

First probabilistic mode

Let's consider the first mode, which does not give a reliable conclusion.

Formula ((A b)  b)  and (3) not is a law of logic. It means that one cannot reliably infer from a statement of a consequence to a statement of a reason. People sometimes incorrectly conclude like this:

If the bay is frozen, then ships cannot enter the bay.

Vessels are not allowed to enter the bay.

The bay is frozen.

The conclusion will be only a probabilistic judgment, i.e. It is likely that the bay is frozen, but it is also possible that there is a strong wind, or the bay is mined, or there is another reason why ships cannot enter the bay.

A probabilistic conclusion can also be obtained in the following conclusions:

If this body is graphite, then it is electrically conductive.

This body is electrically conductive.

This body is probably graphite.

If a citizen of the Russian Federation has moved to another permanent place of residence, then he is removed from the register of those in need of improved housing conditions.

Citizen of the Russian Federation Novikov P.S. removed from the register of those in need of improved housing conditions.

Probably, citizen of the Russian Federation P.S. Novikov. moved to another place of residence.

Think about the reasons (based on Article 32 of the Housing Code of the Russian Federation) that the gr. Novikov P.S.

Second probabilistic mode

This is the second mode, which does not give a reliable conclusion.

Formula ((A b)  A)-> b (4) is not a law of logic. It means that one cannot accept a conclusion as reliable, concluding from the denial of the basis to the denial of the consequence.

Some doctors mistakenly reason like this:

If a person has a fever, then he is sick.

This person does not have a fever.

This person is not sick.

Other people sometimes also make logical errors when drawing conclusions. Here's an example:

If a body is subjected to friction, it will heat up.

The body was not subjected to friction.

The body did not warm up.

The conclusion here is only probabilistic, but not reliable, because the body could have warmed up for some other reason (from the sun, in an oven, etc.).

If one concludes from the statement of the consequence to the statement of the reason, then one can come to a false conclusion due to the multiplicity of causes from which the same consequence can flow. For example, when finding out the cause of a person’s illness, it is necessary to go through all possible causes: he had a cold, was overtired, was in contact with a bacteria carrier, etc. When figuring out the cause of a certain explosion, it is necessary to provide for all possible causes as much as possible: a terrorist attack, a malfunction of something, an accident, arson, criminal showdowns and much more.

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A combination of simple syllogisms in which the conclusion of a previous syllogism (prosyllogism) becomes the premise of a subsequent syllogism (episyllogism) is called a complex syllogism, or polysyllogism.

There are progressive and regressive polysyllogisms.

In progressive polysyllogism, the conclusion of the prosyllogism becomes the greater premise of the episyllogism.

A socially dangerous act (A) is punishable (B) Crime (C) is a socially dangerous act (A)

Crime (C) is punishable (B) Giving a bribe (D) is a crime (C)

Giving a bribe (D) is punishable (B)

In regressive polysyllogism, the conclusion of the prosyllogism becomes the lesser premise of the episyllogism.

For example:

Crimes in the economic sphere (A) - socially dangerous acts (B)

Illegal entrepreneurship (C) - a crime in the economic sphere (A)

Illegal entrepreneurship (C) is a socially dangerous act (B)

Socially dangerous acts (B) are punishable (D) Illegal entrepreneurship (C) is a socially dangerous act (B)

Illegal business (C) is punishable (D)

Both examples given are a combination of two simple categorical syllogisms, constructed according to the AAA mode of the 1st figure. However, a polysyllogism can be a combination of a larger number of simple syllogisms, constructed according to different modes of different figures. A chain of syllogisms can include both progressive and regressive connections.

Purely conditional syllogisms that have the following scheme can be complex:

(r->d)l(d->g)A(g-»5)l...l(G1->51)

From the diagram it is clear that, as in a simple purely conditional inference, the conclusion is an implicative connection of the basis of the first premise with the consequence of the last.

In the process of reasoning, polysyllogism usually takes a shortened form;

some of its premises are omitted. A polysyllogism in which some

These premises are called sorites. There are two types of sorites: program polysyllogism with omitted major premises of episyllogisms and per nal polysyllogism with omitted smaller premises. Here is an example of a progressive polysyllogism:

Giving a bribe (D) is punishable (B)

A socially dangerous act (A) is punishable (B) A crime (C) is a socially dangerous act (A) Giving a bribe (D) is a crime (C)

Epicheyrema also belongs to complex abbreviated syllogisms. An epic is called a compound syllogism, both premises of which are;

memes. For example:

1) Dissemination of knowingly false information discrediting the honor and dignity of another person is criminally punishable, since it is slander i.

2) The actions of the accused constitute the spread of

3) The actions of the accused are criminally punishable

Let us expand the premises of the epicheireme into complete syllogisms. To do this, let us restore the complete syllogism first, the 1st enthymeme:

Libel (M) is criminally punishable (R)

Dissemination of deliberately false information discrediting honor

Dissemination of knowingly false information discrediting the honor and dignity of another person (S) is a criminal offense (P)

As we can see, the first premise of the epicheirem consists of a conclusion and a smaller premise of the syllogism.

Now let's restore the 2nd enthymeme.

Deliberate distortion of facts in an application against citizen P. (represents the dissemination of knowingly false information discrediting the honor and dignity of another person (P) The actions of the accused (S) were expressed in deliberate distortion of facts in an application against citizen P. (M)

The actions of the accused (S) constitute the dissemination of deliberately false information discrediting the honor and dignity of another person (P)

From the Greek "heap" (a pile of parcels).

The second premise of the epicheirema also consists of the conclusion and the minor premise of the syllogism.

The conclusion of the epicheirema is derived from the conclusions of the 1st and 2nd syllogisms:

Dissemination of knowingly false information discrediting the honor and dignity of another person (M) is criminally punishable (P) The actions of the accused (S) constitute the dissemination of knowingly false information discrediting the honor and dignity of another person (M)

The actions of the accused (S) are criminally punishable (P)

Expanding the epicheireme into a polysyllogism allows you to check the correctness of the reasoning and avoid logical errors that may go unnoticed in the epicheireme.

Methods for checking the correctness of a simple categorical syllogism can be demonstrated using the following example (second figure, mode AAA):

According to the general rules of syllogism: the rules of syllogism terms are violated: there is a quadruplement of terms, since in the larger premise the term M 1 –“support each other financially”, and in a smaller package M 2 – “support each other”, the middle term is not distributed in any of the premises.

According to the special rules of syllogism figures, the rule of the second figure of the syllogism is violated, namely: according to the rules of the second figure, one of the premises is a negative judgment, and in this example both premises are affirmative judgments.

Using a counterexample: if instead of the concept "G and F“substitute the concept of “true friends”, then a false conclusion will be obtained from true premises.

By modes of figures: mode AAA– incorrect mode of the second figure of the syllogism.

Using diagrams: to do this, we write the structure of premises and conclusion as follows:

Based on this record, we depict the relationships between terms using circular diagrams (Fig. 8.8, 8.9).

Rice. 8.8

Rice. 8.9

As can be seen from the diagrams, the conclusion does not necessarily follow from the premises, i.e. necessary connection between S And R cannot be established, since in our example the middle term M is not distributed in any of the premises and there is a quadruplement of terms.

Violation of at least one of the rules means: the syllogism is incorrect (the conclusion does not necessarily follow from the premises).

Inferences from judgments with relations

An inference whose premises and conclusion are propositions with relations is called an inference with relations.

The most important logical properties of relations are reflexivity, symmetry, transitivity, functionality (uniqueness).

reflective this relationship between objects is called A And IN, in which the object is in the same relation to itself. If R has the property of reflexivity, then it is expressed by the formula

A R B → A R A∩B R B.

For example: "If A ≡ IN, That A ≡ A And IN ≡ IN".

Symmetrical is a relationship that takes place between objects A And IN, and between objects IN And A. The logical property of symmetry can be written as the formula

A R B → B R A.

For example, the relation “to be related” has the property of symmetry: if A relative IN, That IN- relative A.

Transitive This property of relations is called when, in the presence of this relationship between objects A And IN, IN And WITH it is possible to establish this relationship between A And WITH, i.e. A R C. The logical property of transitivity can be expressed by the formula

(A R B) ∩ (B R C) → A R C.

For example:

A > B 6 > 4

B > C 4 > 2

A > C 6 > 2

Functional(unambiguous) a relation is called if and only if each value of the relation at relationship x R y corresponds to only one single value X . For example: " x father at ", because every person (at) there is only one father.

The logical property of functionality can be written symbolically as the following axiom:

(A R B ∩ C R B) → A ≡ WITH.

Abbreviated, compound compound syllogisms

The varieties of simple categorical syllogism formed from simple propositions also include abbreviated syllogism (enthymeme), complex (polysyllogism) and complex abbreviated (epicheireme).

Enthymeme

Enthymeme - abbreviated categorical syllogism. Translated from Greek, enthymeme means “in the mind, in thoughts.” This name indicates that this or that part of the syllogism is implied and not stated. In the process of thinking, we often do not express all parts of a syllogism, but think in enthymemes.

An enthymeme is a syllogism in which either one of the premises or the conclusion is missing.

The following types of enthymemes are distinguished:

a) with a missing major premise, for example:

b) with a missing smaller premise, for example:

All chemical elements (M) have an atomic weight (P); (implied)

This means that helium (5) has an atomic weight (P).

c) with a missing conclusion, for example:

All chemical elements (M) have an atomic weight (P)

Enthymeme structure:

Restoring enthymemes to a complete syllogism has enormous educational value. Sophistic tricks, false premises, as a rule, are veiled in the missing part of the enthymeme. This psychological feature is actively used by the enemy when deliberately misleading. For example, the following false conclusions can be found in enthymemes: “He is a pianist because he has long flexible fingers,” “All monkeys love bright things, and all women do too.”

Restoring the missing part of the syllogism allows you to check both the truth and correctness of the enthymemes.

Like any conclusion, an enthymeme can be correct (correct) or incorrect (incorrect).

Enthymema with missed by parcel counts correct , if it is restored into a correct syllogism and the missing premise is not false.

Enthymema with lowered conclusion counts correct , if the conclusion is derived from the premises.

To restore the enthymeme into a complete syllogism, the following rules should be followed.

• 1. Find a conclusion and formulate it in such a way that the major and minor terms are clearly expressed.
• 2. When finding premises and conclusion, one should proceed from the fact that the conclusion is usually placed after the words “means”, “therefore”, etc. or before the words “because”, “for”, “since”. Another judgment, naturally, will be one of the premises.
• 3. If one of the premises is omitted, but the conclusion is present, then it is necessary to establish which of them (the larger or the smaller) is present. This is done by checking which of the extreme terms is contained in a given premise. If the term is larger, then there is a larger premise; if the premise contains a minor term, then it is a minor premise.
• 4. Knowing which of the premises is omitted, and also knowing the middle term, you can determine both terms of the missing premise.

For example: “Jupiter, you are angry, which means you are wrong.” Implicit in this entims, and therefore omitted, is the larger premise: “Whoever is angry is wrong.” Let us restore the entire syllogism in full:

The form of enthymemes can also be taken by inferences, the premises of which are conditional and disjunctive judgments.

For example, let’s check the enthymeme: “He must be an educated person, because he competently answers all the questions that are asked to him.”

Let's determine whether a premise or a conclusion is missing in it and write the conclusion, if any, below the line, the premise (or both) above the line.

The presence of a conclusion in an enthymeme is usually indicated by the words: “since”, “because”, “since”, etc. or “means”, “therefore”, “thus”. The words of the first group show that the conclusion comes before them, and the premise comes after them, the words of the second group show that the conclusion comes after them. If there are no such words, then the conclusion is missing from the enthymeme. There is a conclusion to this topic. The proposition: “He must be an educated man” is a conclusion because it comes before the word “since.” Let us determine the structure of this judgment, i.e. Let's find a subject and a predicate in it. The subject is “he”, the predicate is “an educated person”.

Based on the subject and predicate of the conclusion, we establish the nature of the existing premise: “He competently answers all the questions that are asked of him.” It contains the subject of the conclusion: “he”, therefore it is the minor premise. Using the predicate of the conclusion and the middle term, which is included in the minor premise, we restore the major premise missing in the enthymeme: “Anyone who competently answers all the questions that are asked to him is an educated person.”

As a result, we get a complete syllogism:

Let's check the correctness of the resulting syllogism. It is built according to I figure, both rules of this figure (see above) are observed. This means that this syllogism is correct. It can also be verified using a circular diagram (Fig. 8.10), which corresponds to the axiom of the syllogism.

Rice. 8.10

Polysyllogisms, sorites, epicheyrema

In the process of thinking, syllogisms are connected to each other, forming chains of syllogisms - complex syllogisms and polysyllogisms.

Polysyllogisms

A chain of syllogisms in which the conclusion of the previous syllogism becomes the premise of the next one is called a polysyllogism.

A syllogism that precedes another in a chain of syllogisms is called proslogism .

A syllogism following another in a chain of syllogisms is called episyllogism .

There are progressive and regressive polysyllogisms.

Progressive polysyllogism called polysyllogism, in which the conclusion of the previous polysyllogism (prosyllogism) becomes the greater premise of the episyllogism.

For example:

Regressive polysyllogism is called a polysyllogism in which the conclusion of the prosyllogism becomes the smaller premise of the episyllogism.

All counterfeiters (E) – criminals (D)

All criminals(D) – offenders (C)

Hence,

All counterfeiters (E)– offenders (C)

A)

Hence,

All counterfeiters (E) – People ( A)

All people ( A) mortal ( IN)

(E) – mortal (IN)

All E There is D

AllD There is WITH

All E There is WITH

All WITH There isA

All E There is A

All A There is IN

All E There is IN

In each case, we recorded the conclusion by adding the word “therefore.” True, in regressive polysyllogism we changed the usual arrangement of premises, placing the smaller premise first.

Sorites

A polysyllogism in which some premises (major or minor) are missing is called sorites (Greek. soros - heap, heap of parcels), or an abbreviated polysyllogism.

There are two types of sorites: progressive, or Gocklenian, named after the author - the German logician R. Gocklen (1547–1628) and regressive, or Aristotelian.

Sorites, in which, starting from the second syllogism in the chain of syllogisms, a major premise is omitted, is called progressive (Goklenievsky) .

Example.

All people (A) mortal (IN)

All offenders (WITH) - People (A)

All criminals ( D) – offenders (WITH)

All counterfeiters ( E) – criminals(D)

Therefore, all counterfeiters (E) – mortal (IN)

All A There is IN

All WITH There is A

All D There is WITH

All E There isD

All E There is IN

A sorites in which, starting from the second syllogism in a chain of syllogisms, a minor premise is omitted is called regressive (Aristotelian).

Example.

All counterfeiters ( E) – criminals (D)

All criminals (D)– offenders (C)

All offenders (C) are people ( A)

All people (A) mortal (IN )

Therefore, all counterfeiters (E) mortal (IN)

All E There is D

All D There is WITH

All WITH There is A

All A There is IN

All E There is IN

Epicheyrema

Epicheyrema (Greek) epiheirema- inference) is a complex syllogism in which the premises are enthymemes.

Example.

All rhombuses ( A) – parallelograms ( WITH), since they (diamonds) ( A) have pairwise parallel sides (IN)

All squares ( D) – rhombuses ( A), since they are (squares) (ABOUT) have mutually perpendicular diagonals, bisecting at the point of their intersection ( E)

Therefore, all squares (D)– parallelograms (C).

All A is C, since A There is IN - enthymeme

AllD There isA, sinceD There is E – enthymeme

All D There is WITH