Rules of figures, Algorithm for complete analysis...

Rule shapes

Each figure has its own regulatory requirements, expressing the specifics of the logical conclusion. Namely:

I figure

1. A large premise should be a general proposition.

2. A smaller premise should be affirmative.

Conclusion on the first figure admits all kinds of categorical judgments (A, I, E, O). This is the most informative figure, Aristotle called it "the most perfect syllogism."

II figure

1. A large premise should be a general proposition.

2. And one of the premises is a negative proposition. The conclusion is a negative judgment of (E, O).

III figure

1. A smaller premise is an affirmative judgment.

2. The conclusion is a private judgment (/, About).

IV figure

General conclusions will not be given. As already mentioned, this is the least informative figure.

Each figure performs its own cognitive tasks:

• The first figure is indispensable in the construction of evidence;

• the second is preferable for rebuttal;

• The third helps avoid hasty generalizations.

Yet most often in our life practice we have to prove something, justify our point of view. And the obvious evidence is only evidence on the first figure (it is based on the axiom of syllogism). Therefore, the importance of information syllogisms to the first figure. This, in the first place. And secondly, with the help of the information to the first figure, the correctness of the modes of the remaining figures also becomes clear, because once with the help of the axiom of syllogism we understand the obviousness of the modes of the first figure, we are also convinced of the correctness of the moduli of the remaining figures, equivalent to the modes of the first figure. How does the reduction of syllogisms occur? By sending packages (of course, if possible). For example, take the syllogism of the second figure:

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(& pound;) Who is too afraid of hatred (P),

can not manage (M) (Seneca). (L) Napoleon (5) was able to manage (M).

(& pound;) Napoleon (5) was not too afraid of hatred (P).

In order to obtain the first figure of the syllogism, it is necessary to draw a large parcel, observing the rules of treatment. Since this premise is a negative negative judgment, both its terms (M and P) are distributed, hence, a pure appeal is possible:

(& pound;) Who can manage (M)

Not too afraid of hatred (P). (A) Napoleon (5) was able to manage (M).

(& pound;) Napoleon (5) was not too afraid of hatred (P).

The same applies to other figures. In the third figure, the smaller parcel is reversed, and in the fourth one, both.

Algorithm for a complete analysis of a simple categorical syllogism (PCS)

The word algorithm comes from the lat. Algorithmi - the spelling of the name of Mohammed al-Khwarizmi (787-850) - an outstanding mathematician of the medieval East and means a precise injunction defining the sequence of actions that ensures obtaining the desired result from the original data. Applied to syllogisms, algorithmic actions are possible. In a concrete-clear form they are reflected in Fig. 6.2.

Consider this for a specific example.

Everything relating to the realm of the mind is an inference. " (G. Hegel). PKS is a conclusion. IIKS refers to the sphere of the mind.

In this argument, from true premises, a true conclusion is obtained that instills and maintains a subjective confidence in the logicality of reasoning. Let's see if this is true.

1. We establish the structure of the syllogism:

• In conclusion (!), we find and denote the subject (5) - the smaller term of the syllogism ( PKC ), and the predicate (P) is the largest term ( that refers to the sphere of the mind );

• We find and denote them in the premises,

• denote the middle term (M) - inference ). All that belongs to the realm of the mind (P) is an inference

(M).

PKC (S) - reasoning (M).

PKC (5) refers to the sphere of the mind is (P);

• we find:

a) a large premise (it includes the predicate of the conclusion):

Algorithm for a complete analysis of a simple categorical syllogism

Fig. 6.2. Algorithm for the complete analysis of a simple categorical syllogism

Everything related to the realm of reason (N) is a conclusion (P) & quot ;;

b) a smaller premise (it includes the subject of the conclusion): "SCC (5) refers to the sphere of the mind (M)"; We are convinced that the syllogism is recorded in the standard form, that a large premise is in the first place. The standard recording of the syllogism provides the convenience of a logical analysis of the syllogism and in many cases avoids typical errors (for example, in determining the shape and mode). In this case, the syllogism is written in the standard form;

• In case of a non-standard entry, it would be necessary to change the parcels in some places (bring them to standard view).

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2. Define the PKC figure: the second figure .

3. Set the mode : ALA

(A) Everything related to the sphere of the mind (P) is a conclusion (M).

(A) PKC (5) is the conclusion (M).

(A) The PKC (5) refers to the sphere of the mind is (P).

4. We establish the distribution of terms :

(A) Everything related to the sphere of the mind (P +) is an inference (M ~).

(л) PKC (5+) - inference (M -).

(l) PKS (5+) refers to the sphere of the mind (P ~).

(Already visible error - the middle term is not distributed in any of the parcels.)

5. We check the syllogism (in Figure 6.3 there are ways to test a simple categorical syllogism).

• By the general rules of the PKC Terms of Terms.

1. There must be three terms in the syllogism. - Yes.

2. The middle term should be distributed at least in one of the parcels. - Disrupted (the middle term is not distributed in any of the parcels).

3. The term, unallocated in the parcel, should not be distributed in custody. - Observed.

Methods for verifying the correctness of a simple categorical syllogism

Fig. 6.3. Methods for verifying the correctness of a simple categorical syllogism

Parcel rules.

1. At least one of the premises must be a general proposition. - Both are common.

2. At least one of the premises must be in the affirmative. - Both are affirmative.

3. If there is a private parcel, the conclusion must be private. Hci private packages.

4. If there is a negative premise, the conclusion must be negative. - There is no negative premise.

The rules of the parcels are observed.

• By the rules of the figure

1. A large premise should be a general proposition. - So it is.

2. One of the premises must be negative. - Violated.

• Modes: ALA - the wrong mode for the second shape.

• Using pie charts:

- we take into account information only from parcels (the conclusion is not taken into account);

- we start building with a larger premise;

- for convenience, we formalize the parcels: All P is M ,

All S is M .

It's better to start scheming with a larger premise: All P is M .

Add to the picture information from the smaller package: All S is M .

As you can see, it is impossible to establish unambiguous relations between the extreme terms 5 and P. • Using a counterexample.

All students (P) are students (M) & quot ;. & lt; • ESS students (5) students (L /) & quot ;. All students (5) are students (P) .

Arguing by the same scheme, from the true premises, we get a false conclusion. This indicates that such a way of communication of thoughts is not logically necessary.

Conclusion: The syllogism is wrong (the conclusion does not follow with the need for parcels).

Conclusion

Inference is a logical operation with judgments that allows you to gain a gain of knowledge without resorting to additional sources of information. Guaranteed truthfulness of conclusions is ensured only by deduction.

Immediate deductive reasoning is, first, the conclusions conditioned by the properties of the relationship between categorical judgments; secondly, ways to identify information implicit in the judgment. These are the simplest ways to obtain reliable new knowledge based on what is already available.

A simple categorical syllogism is the conclusion of one categorical proposition from the other two. In it, the connection between the two concepts (in conclusion) is established by means of the third concept, which exists in both premises. PKS is the basic form of the syllogism underlying several types of complex, shortened and complexly reduced syllogisms.

Conclusions

In the direction of the movement of thought, reasoning is divided into deductive, inductive and transductive.

Modern logic divides inferences by the nature of the connection of parcels and conclusions to demonstrative and plausible.

Demonstrative (deductive) reasoning is divided into two large groups: syllogisms and conclusions of the logic of judgments. In turn, syllogisms are divided into immediate and indirect.

It should be remembered that the basic logical characteristic of inference is logical correctness.

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