Control robot

C course "Logik"

Transdranny

Theoretical Patten: Seductive Melovivod

Tasksi:

A - fiancist;

In - holding services;

C - athlete;

D - student?

4. To hide the shudzhenka, Yak Vіdpovіda, Zaknіyy Formula. Warehouse for n-table: (in ú c) → a

6. Creek by the method of rebounding, an overlooking of the predicate of the non-Overhead of the Okovivodi from such a landmark:

Zhoden ІЗ Touristіv Our Growing without knowing the NIMETSKY Movy.

8. Stop the proven progress to the absurd method:

Organizatsіya Evtusu Фіннасое опродоми.

9. Yak Shape Mislennya Viizijs at Mіrkuvanny:

Winter. Calm. Veschі, singing, pіde sn?

Deaductive conclusions

Conclusions from complex judgments . Other types of deductive conclusions

The conclusions are built not only from ordinary, but also of complex judgments. The conclusions are widely used, the parcels of which are conditional and separating judgments protruding in different combinations with each other or with categorical judgments. These include purely conditional, conditionally categorical, separation and conditional and conventional conclusion.

The peculiarity of these conclusions is that the removal of concluding from the parcels is determined not by relations between terms, as in categorical syllogism, but by the nature of the logical connection between judgments. Therefore, when analyzing the parcels, their subject-predicate structure is not taken into account.

Views of deductive conclusions are also abbreviated, complex and comprehensive syllogism.

Pure conditional and conditional categorical conclusion

Pure conditional conclusion

Purely conditional is called the conclusion, whose wish-containers are conventional judgments

For example:

If the invention has been created by joint creative labor of several citizens (a), they are all recognized by co-author of the invention (b)

If the invention has been created by joint creative labor of several citizens (a), the order of use of the rights for the invention, created in collaboration, is determined by the agreement between co-authors (C).

In the above example, both parcels are conditional judgments, and the investigation of the first parcel is the basis of the second (b), from which, in turn, flows some consequence (C). The total part of the two parcels (b) allows you to bind the basis of the first (a) and the consequence of the second (C). Therefore, the conclusion is also expressed in the form of a conditional judgment.

Scheme of purely conditional conclusion:

The conclusion in purely conditional conclusion is based on the rule: a consequence of the consequence is a consequence of the foundation.

The conclusion in which the conclusion is obtained from two conditional parcels, refers to simple. However, the conclusion may follow from a larger number of parcels that form a chain of conditional judgments. Such conclusions are called complex.

Consider an example:

The first parcel is a conditional judgment that expresses the connection of the base (A) and the consequence (b). The second parcel is a categorical judgment in which the truth of the foundation (a) is approved: the lawsuit is presented with an incapacitated person. Recognizing the trueness of the foundation, we recognize the truth of the investigation (b): the court leaves a lawsuit without consideration.

This conclusion is one of the species of conditionally categorical syllogism - the asserting modus (modus ponens), in which the parcel, expressed by categorical judgment, approves the truth of the foundation, and the conclusion approves the truth of the investigation; The argument is aimed at approving the basis for approval.

Approving modus gives reliable conclusions. It has a scheme:

Another modus that gives reliable conclusions is the denying modus (modus tollens), in which the parcel, expressed by categorical judgment, denies the truth of the investigation, and the conclusion denies the truth of the base. The reasoning is directed from the denial of the investigation to the denial of the base. For example:

It is easy to establish that two more varieties of conditionally categorical syllogism are possible.

(3) The parcel, expressed by categorical judgment, denies the truth of the foundation, conclusion denies the truth of the investigation. The reasoning is directed from the denial of the foundation to the denial of the investigation, i.e.:

However, the conclusion in this mode will not be reliable. So, in the given example, the base of the conditional parcel is denied (it is not true that the lawsuit is presented with a incapable person), it is impossible to deny the truth of the investigation with reliability (it is not necessary that the court leaves a lawsuit without consideration). The court may leave a lawsuit without consideration and for other circumstances, for example, as a result of the expiration of the limitation period.

(4) The parcel, expressed by categorical judgment, approves the truth of the investigation, the conclusion approves the truth of the foundation. The argument is directed from the approval of the investigation to the statement of the foundation, i.e.:

Conclusion in this mode will not be reliable. The approval of the investigation (the court leaves the lawsuit without consideration) does not entail the need to be the truth of the foundation: the court may leave a lawsuit without consideration not only as a result of the incapacity of the plaintiff, but also for other reasons.

So, of the four modes of conditionally categorical conclusions, exhaustive all possible combinations of parcels, reliable conclusions give two: saying (MODUS PONENS) (1) and denying (modus tollens) (2). They express law! logic and are called proper mododules of conditionally categorical conclusion. These modes obey the rule: the approval of the foundation leads to the approval of the investigation and the denying of the investigation - to the denial of the ground. Two other modus (3 and 4) do not give reliable conclusions. They are called incorrect modes and obey the rule: the denial of the base does not lead to the need to negate the investigation and the approval of the investigation does not lead to the need to approve the foundation.

The need to output according to approving and denying modes can be shown using the truth tables.

Approving modus (Fig. 1).

The truth of the implication (column 3) depends on the truth of the antecedent (base) (1) and the consequent (investigation) (2). The implication is considered false if and only if the antecedent is true, and the consexenter is false (2nd Table String). In all other cases, the implication of the truth. The truth or falsity of the conjunction (4th column) also depends on the components of its members (3 and 1).

The conjunction is true if and only if both of its members are true (1st line of the table).

Now establish the truth of the implication (5th Table Stage - Approving Mode). Since the implication of the antecedent (4) and the consexer (2) does not contain the case when the antecedent is true, and the consequent is false, the implication is always true. Therefore, the statement ((P → q) p) → Q is a logical law. Denying modox (Fig. 2).

In the columns 1 and 3, 2 and 4 it is shown that if one statement is false, then its denial is true. The implication of p and q (1 and 2) is false only in one case (2nd table line) - a column 5. Conjunction (column 6) of statements (P → Q) and ˉ | Q (5 and 4) is true only in one case (4th Table String). The implication ((P → Q) ˉ | Q) and ˉ | P (6 and 3) are always true, since it does not contain the case when the antecedent is true, and the consequent is false. Consequently, the statement ((p → q) ˉ | q) → ˉ | p is a logical law.

With the help of truth tables, you can show the unreliability of the conclusions of incorrect modes.

When analyzing conditionally categorical conclusions, it should be borne in mind that the basis and consequence of a greater parcel can be both affirmative and negative judgment: P → Q; ˉ | p → q; P → ˉ | Q; ˉ | p → ˉ | q. For example:

The consequence of the conditional parcel is a negative judgment, the categorical package (affirmative judgment) approves the truth of the foundation, the conclusion (negative judgment) approves the truth of the investigation.

In a symbolic record:

Other varieties of modes are possible.

Sometimes there are conditionally categorical conclusions with outgrowing (equivalent) judgment (if, and only if A, then b).

In a symbolic record: P Q, where - equivalence sign. In such conclusions, reliable conclusions are obtained in all four modes:

Consider for the example the distinguished judgment: "If the person is guilty of committing a crime, then it is subject to criminal responsibility." It is easy to establish that a reliable conclusion is obtained according to any of the above modes.

Simple judgments, of which the separation (disjunctive) judgment consists are called members of disjunction or disjuncts. For example, the separation judgment "Bonds may be presenters or registered" consists of two judgments - disjoints: "Bonds may be the presenters" and "bonds can be registered", connected by the logical union "or".

After approving one member of disjunction, we need to deny the other with the need, and the denying one of them is to assert another. In accordance with this, two modes of separation and categorical conclusions are distinguished: the asserting and denying and denial-claiming.

The scheme of the asserting-denying modus:

In the assertive-denying mode (Modus Ponendo Tollens), a smaller package is a categorical judgment - approves one member of disjunction, the conclusion is also a categorical judgment - denies its other member. For example:

Conclusion in this moduce is always reliably, if the rule is observed: a large package must be excluding-separating judgment, or by the judgment of strict disjunction. If this rule is not respected, it is impossible to gain a reliable conclusion. In fact, from the parcels "theft committed to or l" and "the theft is committed to" the conclusion of "L I did not commit" "with the need. It is possible that l is also involved in the fight against theft, is a partner K.

In the negative-asserting modus (modus Tollendo Ponens), a smaller package denies one disjunct, the conclusion approves the other. For example:

Scheme of denial-claiming modus:

In a symbolic record:

where< ... > - Symbol of closed disjunction.

The affirmative conclusion was obtained by negative: denying one disjoint, we argue another.

Conclusion In this mode, it is always reliably, if the rule is observed: all possible judgments must be listed in a larger package - disjoints, in other words, a large package must be full (closed) with a disjunctive statement. Applying incomplete (open) disjunctive statement, it is impossible to obtain a significant conclusion. For example:

However, this conclusion may be false, since not all possible species of SDE-LB1 are taken into account in a larger package: the parcel is incomplete, or open, disjunctive statement (the transaction may be one-sided, to make a sufficient emotion of the will of one person - the issuance of attorney, drawing up testament, refusal of inheritance, etc.).

The separation package may not include two, but three and more members of the disjunction. For example, in the process of investigating the reasons for a fire in the warehouse, the investigator suggested that the fire could arise either due to careless handling of fire (P), or as a result of self-ignition stored in the warehouse of materials (Q), or as a result of arson (R). In the course of the investigation, it was found that the fire arose as a result of the careless handling of fire (P). In this case, all other disjoints are denied. The conclusion takes the form of an assertive denying modus and is built according to the scheme:

Another course of reasoning is possible. Suppose that the fire arose due to careless handling of fire or as a result of self-ignition materials stored in the warehouse did not confirm. In this case, the conclusion will take the form of a denial-asserting modus and will be built according to the scheme:

The conclusion will be true if all possible cases are taken into account in the conventional parcel.

Conditional separation conclusion

Conclusion, in the engine one parcel conditional, and the other - separation judgment, is called a conditional separator or lemma.

The separation judgment may contain two, three and greater number of alternatives, so lemmatic conclusions are divided into dilemmas (two alternatives), trilems (three alternatives), etc.

Consider on the example of the dilemma structure and types of conditionally separating conclusion. There are two types of dilemmas: constructive (creative) and destructive (destructive), each of which is divided into simple and complicated.

In a simple constructive dilemma, the conditional parcel contains two bases from which the same consequence follows. The separation package approves both possible grounds, the conclusion approves the investigation. The reasoning is directed from the approval of the truth of the grounds for the approval of the truth of the investigation.

Scheme of a simple constructive dilemma:

If the accused is guilty of knowingly unlawful arrest (a), it is subject to criminal responsibility for the crime against justice (C); If he is guilty of a deliberately illegal detention (b), it is also subject to criminal responsibility for the crime against justice (C). The accused is guilty or in a deliberately illegal arrest (a), or in a deliberately illegal detention (b)

The accused is subject to criminal responsibility for the crime against justice (C)

In a complex constructive dilemma, the conditional parcel contains two bases and two consequences. The separation package approves both possible consequences. The reasoning is directed from the approval of the truth of the grounds for the approval of the truth of the consequences.

Scheme of a complex constructive dilemma:

If a savings certificate is a presenter "C (A), it is transmitted to another person by handing (b); if it is nominated (c), then transmitted in the manner prescribed for concessions (D). But the savings certificate may be a presenter ( a) or nominal (s)

Savings certificate is transmitted to another person by handing (b) or in the manner prescribed for assignment of requirements (D)

In a simple destructive dilemma, the conditional parcel contains one base from which two possible consequences flows. The separation package denies both consequences, the conclusion denies the base. The argument is directed from the denial of the truth of the consequences to the denial of the truth of the foundation.

Scheme of a simple destructive dilemma:

If n is a suspect (a), it means that he is or detained on suspicion of committing a crime (b), or is a person to which the preventive measure is applied to the presentation of the charge (C)

N was not detained on suspicion of committing a crime (not -B) or he is not a person to which the preventive measure was applied to the charge (not - c).

H is not suspected (not) In a complex destructive dilemma, the conditional parcel contains two bases and two consequences. The separation package denies both consequences, conclusion denies both grounds. The argument is directed from the denial of the truth of the consequences to the denial of the truth of the grounds.

Scheme of a complex destructive dilemma:

If the company is rental (a), it will carry out entrepreneurial activities based on the lease of the property complex (B); If it is a collective (c), it carries out such activities on the basis of its property property (D) This company does not carry out its activities on the basis of the leased property complex (non-B), nor on the basis of its property owned (not - d). This enterprise is not rental (not) or not collective (not - c)

Abbreviated Sillogism (Entimem)

Sillogism, in which all of its parts are expressed - both parcels and conclusion is called full. Such syllogisms were considered in the previous sections. However, in practice, syllogisms are used more often, in which one of the parcels or conclusion is clearly not expressed, but are meant.

Sillogism with a missed parcel or conclusion is called abbreviated syllogism, or entimible.

Endimensions of simple categorical syllogism are widely used, especially the conclusions on the first figure. For example: "Nikolaev is a student, so he is obliged to pass exams." A large package is missing here: "All students are obliged to pass exams." It is a well-known position, which is optional.

Full Sillogism is based on the 1st figure:

The missed might be not only large, but also a smaller package, as well as conclusion: "All students are obliged to take exams, and Nikolaev - a student" or: "All students are obliged to take exams, it means that Nikolaev is obliged to take exams." Missed pieces of syllogism are meant.

Depending on which part of the Slogism is skipped, there are three types of entimibles: with a minimal parcel, with a smaller premise with a missed conclusion.

The conclusion in the form of entimible can also be built on the 2nd figure; According to the 3rd figure, it is rarely built.

The form of entimibles also accept conclusions, the parcels of which are conditional and separating judgments.

Consider the most common types of entifies.

A large parcel is missing here - the conditional judgment "if the crime event had no place, then the criminal case cannot be initiated." It contains the well-known position of the Criminal Procedure Code, which is meant.

A large package is a separation judgment "in this case, either an exclusive, or convicted" - is not formulated.

Separate-categorical syllogism with lowered conclusion: "Death occurred either as a result of murder, or as a result of suicide, or as a result of an accident, or by virtue of natural reasons. Death occurred as a result of an accident. "

Conclusion that deny all other alternatives is usually not formulated.

The use of abbreviated syllogisms is due to the fact that the missed parcel or conclusion or contains a known position that does not need oral or written expression, or in the context of the expressed parties, it is easily understood. That is why reasoning proceeds, as a rule, in the form of entifies. But, since in the entimiment, not all parts of the conclusion that hides a mistake in it is harder than in complete conclusion. Therefore, to verify the correctness of the reasoning, you should find the missed parts of the conclusion and restore the entimion into full syllogism.

Complex and comprehensive syllogism

In the process of reasoning, simple syllogism performs in a logical connection with each other, forming a chain of syllogisms, in which the conclusion of the previous syllogism becomes sending the subsequent. Preceding Sillogism is called prison, subsequent - episillogism

The compound of simple syllogisms, in which the conclusion of the preceding syllogism (transfer) becomes sending the subsequent (episillogism) is called complex syllogism, or polysillogism.

There are progressive and regressive polysillogs. In progressive polysillogism, the conclusion of the transfer becomes greater premises of episillogism. For example:

In regressive polysillogism, the conclusion of the transfer becomes a smaller package of episillogism. For example:

Both of the above examples are a compound of two simple categorical syllogisms constructed by the AAA model of the 1st Figure. However, polysillogism can be a compound of a larger number of simple syllogism, varied in different mododules of different figures. The chain of syllogisms may include both progressive and regressive communications.

Complicated may be purely conditional syllogisms that have a scheme:

In a symbolic record:

From the scheme it can be seen that, as in the simple purely conditional conclusion, the conclusion is an implicative connection of the foundation of the first parcel with the investigation of the latter.

In the process of reasoning, polysillogism takes usually abbreviated form; Some of his parcels are lowered. The polysillogism in which some parcels are missing is called a duct. Distinguish two types of soots:

1. Progressive polysillogism with missed large parcels of episillogisms. For example:

Epihereira is also refer to comprehensive syllogism. Ephaheyrea is called comprehensive syllogism, both parcels of which are entimibles.

For example:

We will send the parcel epicheram in full syllogism. To do this, we will restore the full syllogism first the 1st Entimem:

As we can see, the first parcel of epicherem makes the conclusion and the smaller package of syllogism. Now restore the 2nd Entimem.

The second parcel epicheremia also make up the conclusion and the smaller parcel of syllogism.

Epicherem's conclusion was obtained from the conclusions of the 1st and 2nd Sillogisms:

Deploying epheherem in polysillogism allows you to check the correctness of the reasoning, avoid logical errors that may remain unnoticed in epheherem.

Concept of statement logic

Modern symbolic logic for analyzing deductive reasoning builds special logical systems; One of them is called the logic of statements or propositional logic, the other - the logic of predicates. Consider briefly the principles for building the logic of statements.

The statement logic is a logical system that analyzes the arguments based on the nature of the relationship between simple judgments, but without taking into account their internal structure.

The language of the statement logic includes: alphabet, determination of correctly constructed expressions, interpretation.

The alphabet of statement logic consists of the following characters.

Symbols for statements: p, q, r, ... (propositional variables).

Symbols for logic ligaments:

(3) Technical signs (,) - brackets.

Permissible expressions in the logic of expressions, called properly constructed formulas or abbreviated PPF, are introduced as follows:

1. Any propositional variable - P, Q, R, ... is PPF.

2. If A and B - PPF (A and B - the symbols of the metalanak, expressing any formulas), then expressions - AV, AV, A → B, AV, ˉ | and are also PPF.

All other expressions, in addition to those provided in paragraph 1 and 2, are not the PPF language of the logic of statements.

The logic of statements can be constructed by a tabular method or as calculus, i.e. as a system that allows you to receive other formulas from some formulas.

Table construction implies semantic determinations of propositional ligaments in the form of matrices showing the dependence of the true value of complex formulas on the values \u200b\u200bof their components of simple formulas. If a and in simple formulas, the true value of the complex formulas constructed using logical ligaments can be represented by a matrix method - in the form of a table.

Among the properly constructed formulas, depending on their truth, the identically true, identically false and executable formulas are distinguished.

Identally true called formulas that make values \u200b\u200bof truth in any - true or false values \u200b\u200bof the components of their propositional variables. Such formulas are laws of logic.

They are identically false called the formulas that take the importance of lies at any - true or false - values \u200b\u200bof propositional variables.

Further refer to formulas that can take values \u200b\u200bof truth or lies depending on the sets of values \u200b\u200bof the components of their propositional variables.

Table construction involves the definition of logical relations between formulas. An essential value for the analysis of reasoning is the ratio of logical follow (symbol), which is defined as follows. From Ai, ..., An as the parcels logically follows in as a conclusion, if with the truth of each AI, ..., ap is true and V. In the language-object, the relative relationship is adequately expressed by implication. It means that if A1, ..., а, ├ in, then the formula, which is the implication of the form (A1 ^ A2 ^ ... ^ An) → V, should be identically true.

Table construction of statement logic allows you to determine the logical relationship between expressions and check the correctness of the conclusions using the above criterion. As an example, we propose to carry out a tabular method to verify the correctness of the formulation of the form (P → Q) ├ (ˉ | Q → ˉ | P). Replacing the sign of the logical following between the package and the implux and constructing the table for the resulting formula, we see that it is identically true. So, reasoning is correct.

If there are more than three variables in the argument, then build a full table for checking its correctness is difficult and then the abbreviated method of checking is used, arguing from the opposite. Since, with the correct reasoning of the formula of the form (A1 ^ ... ^ An) → should be identically true, let's see if it cannot be false with some kind of sets of variables. Suppose that maybe. If we get some contradiction from this assumption, then the assumption is incorrect (and the verifiable reasoning is correct), and if we do not receive contradictions from this assumption, we will see a set of variable values \u200b\u200bin which the formula is false, that is, the set that refutes the verifiable reasoning.

The logic of statements as calculus is primarily the so-called natural output system (START). The device in it serve the rules of the output, each of which is some kind of elementary form of conclusion. Turning through these rules from the parcels or some assumptions to new formulas, gradually reach imprisonment. The output from the parcels was carried out if it was possible to eliminate all the assumptions made. Thus, under the conclusion of the formula in (conclusions) from the formula A1 - AN (parcels), there is a sequence of formulas, each of which is either a package or assumption, or it turns out according to the rules of the output from the previous ones and the last formula of this sequence is the formula B, And all assumptions are eliminated.

STAR rules allow you to operate with all the ligaments available in the language alphabet. They are divided into rules of administration (c) and rules for the exclusion (s) of ligaments.

In addition to these direct rules for obtaining new rows of output, indirect rules are adopted in START, which determine the conveying strategy. For example, if you need to withdraw from the parcels the formula of the implication type (x1 → X2 → ... (xn-1 → xn)))), then after dischargeing the parcels, all the antecedents of the conclusion are discharged as assumptions, starting with the antecedent of the main implication sign, t. e. x1, x2, x3 ..., xn-1. If you manage to display XN, then by indirect rule

collect the formula sequentially: (XN-1 → XN)

(This eliminates the assumption Xn-1), (Xn-2 → (XN-1 → XN) (XN-2 is excluded from the number of assumptions), etc., until we obtain the desired conclusion

X1 → (XN-2 → ... (XN-1 → XN).

This is a rule constructing a direct output.

We give an example of withdrawal using this rule:

((PQ) → R) ├ (P → (Q├ R))

Another indirect rule is used to construct an indirect output, in which the assumption is denial of or denial of the last consequent x. This rule has a view

and it suggests that if from some formulas (R) and assumptions (a), a contradiction is obtained (in ˉ | c), then from these formulas should be ˉ | a. Thus, if the indirect conclusion of the formula form (x1 → (x2 → ... (xn-1 → x n) ...), then after the parcels are issued formulas:

Then, according to the rules of the output, we obtain consequences from all available parcels and assumptions until we obtain two formulas contradictory (B and ˉ | c), which indicates incompatibility of the assumptions of indirect evidence with other assumptions and parcels. Hence the conclusion about his falsity. Then the line fits the line ˉ | ˉ | XNI, thereby the assumption of indirect evidence is excluded. For example, we will implement an indirect conclusion:

The indirect conclusion is considered complete if there is some formula and its denial during the output, that is, the contradiction. Thus, if an indirect conclusion of the formula of the formula X1 → (x2 → ... xn) is built, then all the antetants from x1 to xn-1 are built in line with the assumptions; In the last line, the denial of the last consequent is discharged - ˉ | xn as an assumption of indirect output. According to the rules of the output, we obtain various consequences of all available parcels and assumptions. Obtaining two contradictory consequences speaks of the falsity of the assumptions of indirect output. On this basis, DKD is denied, i.e. we get a double negation. Double denial removal gives the XN formula.

The main logic properties of the natural output system are its consistency and fullness.

Consistency means that only true consequences can be obtained from true parcels and if the formula is removed from an empty set of parcels, it is identically true. This eliminates the ability to derive from an empty set of parcels any formula (a) and its denial (ˉ | a). The completeness of the system means that the deductive means is enough to bring any identically true formula from the empty set of parcels.

The logic of predicates is a more general logical system and includes the logic of statements as its part. It has more efficient logical means for analyzing reasoning in a natural language.

Tasks

1. Chi Correctly Visnaci Vіdyshemnya Mіzh Understavations:

A - fiancist;

In - holding services;

C - athlete;

D - student?

Vіdpovo:

Understat the A, B, with the i d Porivnyannі, is understood, Scho Schіlna in them is an individual, Yaka, to be engaged in the work of Labor Dyalnіsty, є tricky mean.

Ince them Sumynimi understood є a and і in (Zagalna Vidova Measure - Waving Obovo Little Visito Owiti), with І D (Zagalna Vidova Measure - Naddanny Rights Oddorally, read that professionally to engage in sports).

Understat the and і in Nesum_snі, it is understood with the fact that the Finalanist is employed by professional sports meaning not to be engaged in fiscasets (Butt Sumyshchennya in the practitioner is not Maє), for the holding service of the company, Issuynya Dyalnіsty (Kirim Invortenna I and the Science and Pedagogian Dyalnosti) is fear by law.

Understat the and і in Nesumіsnі s understanding, the Pithenan is revealed to go to the context of one in the Kilkosti Kilkosti Vizhio, Tobto, Whatally, Visiti, Svitti Vuschuє Mozhvyt.

Such a rank, Cola and і in non-reproach Tsecking with Kolomi from І D.

Otvanyo Sumynі Understatya A І V.

In the visionary donutias of the mіzhniy, the calkynimniyniyniyniyniy, the іsnuynnyh reheat, the fact that Scho їx specimen will not locate one one (the spinning of the fiscalist of the Fiscal Dannery of Mіnіsterism є Single-by-Financiste, and the main service).

Understat the first in transitioning correctly.

Otovnoyo Sumynі Understatya with І D.

Vіdnoshennoshtі here is not here, Shaho obviously, Viddoshen Pіdporodnostikno Tseh is not Majmo, the student is understood to reflect on Virmine to understand the A, in the i s, and not about the rendel to the (repentant, student of the Federal Institute of FIZIKIA).

MІZhOVIY Zagalnimi understood Іsnuє in their breath is reheated by the same reasons, Shaho І Mіzh pronounced A І V.

Rysmanno Nesumіsni understood.

Mіzh Nesumіsnimi clearly and і s, and Torzozh in the i with the Supiloshnostі, I am soothing, so the wine, Yak Bulo says the vigor, to the same kind - the profession.

Mіzh incommіsnimi suffices and і d, and Torzozh in the i d Installation of the Predilezhnosti, then Scho Bethi a one-sided fiscalist (by holding the service) with the Oswet of the Ovіtto І Refiruvati Tsu Oswet is inconsisible.

SUI PONTING (A, B, C, D) є Sumynimi dying, Evholeschi, Scho Vinchnya Cych Understand to see the sophisticated people to work to work Diyalnosti (Rodovo means).

Understand to understand (Rosemir Kil Eilera) is promoted correctly.

Understate the "Finanancist" Bіlsh Obєmne, Nіzh Іnshі, Іsnuє in the Usi Galluses of the Georce.

Understate the "Student" to enter the "Holding of the Services" to the touch, to the law "about the service of the service" of Vizhi Ovіt Obovo.

2. Give the real one Nominalna prominent to understand: Constituity, currency, vulice.

Vіdpovo:

Niznalnі Vernacle to understand.

Constitutsіya - the main law of the defense.

Currency - Svіtov Kroshі.

Woolitsa - Miscea Svetrolok, Abo Hello Plan for Zavodіvlі in the population.

Realnі wrenches understand.

Constitutsіya - the law of the dawn, the creepy will stand the main principle of Lyttєdіyalnosti Suspіlyania.

Currency - Groshova Odinyzia, Shahko Vicorovyovyuzuz, Yak Mizhunnaya Rosekunkova Odinitzia і є in the mark of __ payment.

Vulice - Road, Rosetshovana Mіzh Budyligas in the population II is recognized for the proceedings of the іskhodiyv.

Currency - Svіtov Kroshі,

OBRUHTUVENNA: Danish Vnuncheni clear "Currency" Do not river Yoy Zm_st, and s'yovyuzhu іm'ya Tsoye understood, Tobto currency - Tse Gros.

Vulice - Road

Realnі wrenches understand

Constitutsiya - Regulatory-legal document, I amna standing in the regulation of Power Supervisni.

Currency - Socyb Ryanga І payment in the Mizhunniki and MІJersuppinous roses.

3. Visit the appearance of the judge, the term і ї ї rinpodіvenіst for the additional "logic square", the baton of Іnski sudzhenvna, beastly uvara at і іstinnіst:

Deekі Primіshchennya require repair in the center of Rotsi.

Vіdpovo:

Logic Square:

Usi Primіshchennya needs repair from Cyom Rotsi			It is not necessary to repair the approach to the repair of Rotsi
Actsі Primіshchennya require repair at the center of Rotsі	І		ORKI PRIMISTNY NOT REQUIREME REPAIR OF ROTSI

Tse Istinna, as an attribute is meant by the categorical frequenophone sudden.

Istinna - the wrong thing is not Maj Pіdstava to go, shy sudzhevna is not Vіdpovіda, Shaho є Satpravdi.

Simply - this is one sub`.KT Primischennya І one predicate to repair the repair of Rotsi.

Attributes - the fact of the subject of the Primischennya will be partitioned by noma vysno-by -yevosti to repair the repair of Rotsi.

Measure - the word of the leaders of Maє Scho, Tіlki Dereki, and not the SII Primіshchennya.

Frequently hardeningly for Kilkіsti Vono Petroche's leaders, and for Jaclis, it is necessary for the soda.

Thermain S (sub`єT) Primіschennya Nerzpodіlenna, the thermal r (predicate) require repair from the center of Rootsi rosepodіленененене, the predicate of the predicate will turn into a touch of the sub chant (Primіschennya Buvyutn: Yakі do not require repair, yakі require the repair of і yakі vіdremontovyі).

Priimaєmo Sudzhenia І - Istina, Todi on Vidynesya, locked judge about - Hiba. Jacgshchko Sudzhen about - Hiba, then according to the pіdporodkuvanna, the judgment of E - Hiba. Yakschko Sudzhevna E - Hiba, then according to the sophistication of the judgment of the judge, and can Bethi Yak Istina, so I Hiba. Ale knows, Scho Sudzhenna O - Hiba, then on the very well locust Sudzhenna A - Istina. So rank, A - Istina, I - Istina, E - Hiba, Oh - Hiba.

According to the analogue of life, Mіrkuvannya, Yakschko I - Hiba.

Thermin P (predicate) "Require repair from Cyom Rotsі" - Nerzpodіlena, the pose prypodіlenіt of the predicate of the frequency-soluble sudden suggestion of the formal-log cabbages, it is not possible to infant with the inamy to inflate (M.G. Toftool. Logish: Pos. . - K.: ACADEMIA MC, 2002. -368Syu, Stor.84).

Rosovano Meant Istinosti induced judge.

According to the mind of the tasks, we are given the judge І. Yak Vono Istinne Chi Hibna?

Suitably suddensed I - Hiba → E - Istina → O - Istina → A - Hiba.

Alya іz hibnostі and all the sights of the visunok about hibn_st.

Scho, Scho і - Hiba is not proven.

Suddenly sudden to і - Istina → E - Hiba

Dali ZUBUє is inevitable on the Siberian Square Square of the Single Square of the Ostinnocous Destiny Visnka about the Іstinnіst Abo Hibnіst Danish sudden.

4. To hide the shudzhenka, Yak Vіdpovіda, Zaknіyy Formula. Warehouse for ny tables istinnosti:

(In ú c) → a

Vіdpovo:

Jacgshcho posting with the pranks of the Revisiti recipient of the ABO is incomprehensible to the banknote to the bank, then the bank is not rejected by the bank.

Posting the recording of the recipient of the recipient (B) - Istina.

Inconsidately Podachi Platzhenna to Bank (C) - Istina.

Tan, (in ú c) - Istina.

Kutty Bank is not rejected by addressee (a) - Istina.

Tan, (in ú c) → A - Istina.

IN	FROM	(In ú c)	BUT	(In ú c) → a
і	і	і
і	і	і

5. Cancel the look of the dotrimanny formal logic law_vnіn Mіrkuvannya:

Svіddok a.: Firma N. not small Solіdniy Dilovich partnership. Vnaslіddok Tsoy Vona did not remove the great pributkiv.

B. Firma S. Maє Great Dosvіd Roboti і Solіdniy Authority. Two Ryoki Tov Vona Pіdpisal about the SP_V_TERTTVATVOZHTVO Z FIRMU N., Scho brought γ-Solіdnі boutique.

Vіdpovo:

Mіrkuvannya Svіdka A.

The law Tovyznosti is viscous, the partner of the partner of the Great Pributkіv Nobynі is clearly understood.

The law of the SUPERNOSTI is not DIє, the sudidva's sudium is not coming.

The law of the vanished third is not DІє, the obidva is not a supud.

The law of sufficiently rydstavi is visible to the fact that Schoi is fermented by Ekoniki, Scho Great (Solіdnі) Fіrmi Majut І Great (Solіdnі) BUT.

Mіrkuvannya Svіdka B.

The law notion does not evoke, the pіdmіn is to understand. In the fuddle, the judge is about the power of Fіrmi C, and in the other - Firmi N.

The law of the SUPERNOSTI is not d_, it's not about the same item і not in one and the same hour (two rocks).

The law of the vanished third is not d_, the judge is not superanny.

The law of a tastelessness of it is in order to take advantage of the fact that I am not Maud Loggy, I don't give the agreement about SPIVPRATSY, it is not necessary to give it necessary to the Otriferki).

6. Zrobіt method of rebounding, Obrannya і Sprinkle of the predicate of the non-Overhead of the Umovivodi from such a mischief: Zhoden ІЗ Tourist_v Our Growing without knowing the NIMETSKY Movie.

Vіdpovo:

Cuttering: E \u200b\u200bon A.

Usi Tourishment Our Grup did not know the NIMETSKO Movie.

Obrannya: S - P

Tan, p - s

Maєmo sluggishly locked judge, yak wrapping without a rustle.

Zhoden z Vistzіv Nіmezkoy Movi not Bow Tourist Our Grup.

Scroll of predicate: Calid locally locked in frequency solid. SO NOT є R → ORCINE P є S.

OERSI NOT KNOVTSI NIMETSKU MOVI BULI TURISES NOW GRUPE.

Cutting on: E on a

Tan, the skin tourist of our grup knew not NiMetska Movu.

Running predicate.

Tie, Prinimnі acts of tourists, Šoe didn't know Nіmezzy Movu, s ours

7. Watch a destructive dilemie. Contribute to її correctly.

Vіdpovo:

1. Yakschko Kerіvnittva Acrosioner Comrade to set for METUE Zb_lshnya Statutory Capital, then to rose on the stock rink of Dodaki Aktsії Abo to Accepiate Aktsіionerіv.

2. Kerіvnittva Acrosioner Comrade sent the binding on Viplate Divіdddіv Achtzіonera.

Square, Kerіvnittva Acrosioner Comrade did not put the statutory Cartal Metow.

Bіlinskaya Mastovok (1) є so, shy zho-vibration, zhvalivih housing (Romis_chennya Acrossiya Aboy Vikup).

The marked landmark (2) is locked by the offense of the Hallіdes, I am not a director of Kattalіza, but on Viplate Divіddd_v.

The visunka itself was locked by the Basis itself, from Kotroїni Vivodili (meta is not meta).

Majmo destructive to the Deal.

8. Find the provence of the test by the method of rejected to absurdity: Organizatsiya Evtusu Фіннався опродоров.

Vіdpovo:

Viseno Antithesis. Practically, Istinnim є Theza: Organizatsiya does not need a fiscamation.

The argument for the connoisseurs of one, the branch of the Organizatsiji, Vijliti Finasov Dopcoming є unfallenized by the Organizatsiii Vikonuvati from his function.

Yakschko Organizatsiya is not viscous, then it is not є organіzatsy.

Tavern, organіzatsya, ucho, no need for fiscamation, not є organіzāzyu. And there is absurd.

Tan, hibna antitosis І according to the law of the vulnerable third pinema thesis of Istinna.

9. Yaka Mislennia Shape Priyazhnu at Mіrkuvannі: Winter. Calm. Veschі, singing, pіde sn?

Vіdpovo:

Jacket winter, then, singing, pіde sn?

Yakscho evening, then Buda Nich.

Tan, extr., singing, pіde sn?

Winter (a) - Calidly Cathedrid Sudzhenia Dіisnosti

Orphans (a) - Calidly sinudzhen Jesnostі

Veschі, singing, pіde sn? - Sudzhenna Mozdlyosti.

TSA OPERATIONS OKOVIVID - GіPotez

List of L_Teaturi

1. Zerbankin V.є. Logik. - H.: Basis, 1998.

2. Kirillov V.N., Orlov G.A. Logic exercises. - M.: Mtsupl, 1999.

3. Harutyunov V.Kh., Misshin V.M., Kirik D.P. Logik. - K.: Kneu, 2000.

4. Voloshko І.M., Semenov І.S. Workshop with logiki. - K.: KIEVSKY UN-TU, 1993.

5. Ivlev Yu.V. Logic for universities. - M.: Publishing House Mosk. University, 1997.

6. Ivlev Yu.V. Logic: Collection of exercises. - M.: Book House "University", 1999.

7. Kondakov N.N. Logical dictionary. - M.: OV. Encyclopedia, 1990.

8. Logic exercises: Tutorial. - M.: Lawyer, 1993.

9. Іshmuratov A.T. Introduce to Filosofsky Logiki. - K.: Abris, 1997.

10. Kirillov V.N., Starchenko A.A. Logics. - M.: Lawyer, 1999.

11. Orentarkuk G.O. Base logs. - Ternopil: SMP "Aston", 2001.

12. Ruzavin G.N. Logics. - M.: Uniti, 2002.

Plan

1. Pure conditional syllogism.

2. Reliable and plausible modes of conditionally categorical syllogism.

Exercises

1. Determine the parcels and conclusion in the following conditional and conditionally categorical conclusions; Determine the modus and its correctness:

1.1. If Aristotle was a student of Plato, he studied at his academy, and if he studied at his academy, he received Greek education. So, if Aristotle was a student of Plato, he received Greek education.

1.2. If claustrophobia is a disease, it must be treated. Claustrophobia is a disease, it means it should be treated.

1.3. If this judgment is generally aumed, then its subject is distributed. This judgment is not a secrect. It means that its subject is not distributed.

1.4. If this judgment is generally aumed, then its subject is distributed. The subject is not distributed. It means that this judgment is not a common one.

1.5. If they beat in a nabath, then somewhere a fire. In Nabat do not beat. So there is no fire.

1. Pure conditional syllogism.

The conditional judgment looks like this: "If there is in, then C is D". For example: "If the nose is cold, the animal is great."

Conditional syllogism - This is a syllogism, one of whose parcels is a conditional judgment. Conditional syllogism is divided into two types.

Type 1. Modus Pones (Modus constructive)

P1: If there is b, then with there is D.

P2: A is V.

S: C is D.

For example:

P1: If a man is drunk, he cannot think soberly.

P2: Ignat drunk.

S: Ignat cannot think soberly.

The name "MODUS PONENS" comes from the Latin verb "Ponere" - "Paste". The bottom line is that we argue the basis and, based on this, argue.

Type 2. Modus Tollens (Modus destructive)

Latin verb "Tollere" means "destroying". Unlike modus ponens, we deny the base and, therefore, deny the investigation.

P1: If A is b, then C is D.

P2: C is not D.

S: Consequently, not there

For example:

P1: If the young man often cries, he is emo.

P2: Youth Vasya is not emo.

W: Vasya is crying not often.

Invalid conclusions in conditional syllogisms

It is important to understand that it is possible to conclusted only from the approval of the foundation for the statement of the investigation (modus ponens) or from the negation of the consequence (modus tollens) to the denial of the base.

A characteristic example of an error.

P2: Kohl acquired knowledge.

Can we argue from here that Kohl studied at school? Can not! It is likely that Kohl acquired knowledge reading books, depending on the TV, or in some other way.

Second error.

P1: The one who studied at school acquired knowledge.

P2: Kohl did not study at school.

Is it possible to conclude from these parcels that Kohl did not have acquired knowledge? Not. It is likely that if there is knowledge, but this knowledge of Kolya received outside the school walls.

Purely conditional syllogism consists of two conditional judgments, the structure of each of which is already known: a conditional judgment consists of a foundation, effect and a logical union between them.

Denote by partitioned in the conditional judgment, simple judgments by individual characters, we obtain a conditional judgment formula:

If aIN,thatFROM.

Using the symbol and For a logical union, we get even more abbreviated entry: "B -\u003e C"

Using this abbreviated record, purely conditional syllogism can be submitted to such a scheme:

If in, then with in -\u003e with

If a FROM , tO D C -\u003e D

If in , then d in -\u003e d

In a purely conditional conclusion, the conclusion is based on the rule: the consequence of the consequence is a consequence of the foundation.

For example:

1. If this act is theft (b), then it is a crime (C)

2. If this act is a crime (C), it is punishable by law (e)

3. If this act is theft (B), then it is punishable by law (e)

It is easy to see that the role of the average term in purely conditional syllogism performs a simple judgment, which is in the first premise by the consequence, and in the second parcel the base of this conditional judgment.

2. Reliable and plausible modes of conditionally categorical syllogism.

Conditionally categorical is a conclusion in which one of the parcels is conditional, and the other package and conclusion are categorical judgments. A logical basis for such a conclusion is a certain relationship between the base and consequence (antecedent and consequent).

1) from the approval of the basis for the approval of the investigation;

2) from the denial of the base to the denial of the investigation;

3) from the approval of the investigation to the approval of the foundation;

4) from the denial of the investigation to the denial of the base.

Of the four modes of conditionally categorical conclusion, exhaustive all possible parcel combinations, reliable conclusions give two: saying (modus ponens) (1) and denying (modus tollens) (2).

In the assertion of the modus, the thought is moving from the approval of the grounds for approval of the investigation. In the denying mode, the thought proceeds from the negation of the investigation to the denial of the base.

They express the laws of logic and are called correct mododules of conditionally categorical conclusion. These modes obey the rule:

- The approval of the foundation leads to the approval of the investigation and the denying of the investigation - to the denial of the ground.

Two other modus (3 and 4) do not give reliable conclusions. They are called incorrect mododules and obey the rule:

- The denial of the foundation does not lead to the need to negate the investigation and the approval of the investigation does not lead to the need to approve the foundation.

If a IN, then with in -\u003e with

This conclusion is an asserting modus (modus roune) of the conditionally categorical syllogism (from the approval of the basis for the approval of the investigation).

If in the conditionally categorical syllogism, the thought moves from the denial of the investigation (recognition, the establishment of its inconsistency of reality, i.e. falsehood) of conditional judgment in a smaller premise, then it is necessary to deny the base of conditional judgment in the conclusion of Silogism:

If in, then with in -\u003e with

This conclusion is a denying modus (modus tollens) of the conditionally categorical syllogism (from the denying effect to the denial of the base).

Both modus (approving and denying) guarantee the need and truth of the output with the truth of the parcels. The two remaining modes of this type of syllogism do not give the true output, because Their structural features do not comply with the rules, logic laws. These modes are called incorrect, unauthorized, problematic, plausible. They give knowledge, which in one case (which is determined by the package content) can be false, in another true. The formulas of these modes are written as:

In -\u003e with in -\u003e with

(maybe not-c) (possibly in)

3. Exercises.

Determine the parcels and conclusions in the following conditional and conditionally categorical conclusions, determine the mode and its correctness:

if Aristotle was a pupil of Plato, he studied at his academy, and if he studied at his academy, he received Greek education, which means that Aristotle was a pupil of Plato, he received Greek education

Parcel:

If Aristotle was a student of Plato, he studied at his academy,

If he studied at his academy, he received Greek education,

Conclusion:

If Aristotle was a student of Plato, he received Greek education.

Modus constructive

if claustrophobia is a disease, it must be treated. Claustrophobia disease, it means to treat it.

Parcel:

Claustrophobia is a disease, it must be treated,

Claustrophobia disease

Conclusion:

So it must be treated.

Modus constructive.

Reconnecting correctly, because Built according to the correct mode.

If this judgment is generally aumed, then its subject is distributed. This judgment is not a secrect. It means that its subject is not distributed.

Parcels:

- This judgment is not a common

Conclusion:

- So, its subject is not distributed

Modus destructive

Reconnecting correctly, because Built according to the correct mode.

If this judgment is generally aupportitive, then the subject is distributed. The subject is not distributed. It means that this judgment is not a common one.

Parcels:

- If this judgment is a secrecy, then the subject is distributed.

- The subject is not distributed.

Conclusion:

- it means that this judgment is not a common

The conclusion is based on the principle "from denial of investigation to denial of conclusion."

This (fourth) modus does not give a reliable conclusion.

If they beat in a nabath, then somewhere a fire. In Nabat do not beat. So there is no fire.

Parcels:

- If they beat into the Nabat, then somewhere a fire.

- Nabat does not beat.

Conclusion:

- So there is no fire.

Modus destructive.

Reconnecting correctly, because Built according to the correct mode.

4. List of used literature

Getmanova A. D. Logic. - M.: Publishing house "Omega-L", 2007.

Ivin A.A. Practical logic. Tasks and exercises. - M., 1996.

Kobzar V.I. Logics. Study Guide for students of humanitarian faculties. - SPb.: St. Petersburg State University, 2001.

Romanov V.V. Logics. Lecture course. - Ekaterinburg: Publishing House of the Ekaterinburg Higher School of the Ministry of Internal Affairs of Russia, 1995.

Chernyak N.A. Logic: Tutorial. - Omsk: Omsk. State University, 2004.

Logic: Textbook for legal universities Kirillov Vyacheslav Ivanovich

§ 1. Pure conditional and conditional categorical conclusion

§ 1. Pure conditional and conditional categorical conclusion

Pure conditional conclusion

Purely conditional is called conclusion, the parcel and the conclusion of which are conditional judgments. For example:

r), all of them are recognized by co-authors of the invention ( q.).

______________________

If the invention is created by joint creative labor of several citizens ( r), then the procedure for using the rights for the invention, created in collaboration, is determined by the agreement between co-authors ( r.).

In the example above, both parcels are conditional judgments, and the investigation of the first parcel is the basis of the second ( q.), from which, in turn, follows some consequence ( r.). Common part of two parcels ( q.) allows you to link the basis of the first ( r) and the investigation of the second ( r.). Therefore, the conclusion is also expressed in the form of a conditional judgment.

Scheme of purely conditional conclusion:

The conclusion in purely conditional conclusion is based on the Rule: the consequence of the consequence (R) is a consequence of the foundation (P).

The conclusion in which the conclusion is obtained from two conditional parcels, refers to simple. However, the conclusion may follow from a larger number of parcels that form a chain of conditional judgments. Such conclusions are called complex. They will be discussed in § 5.

This conclusion has two correct modes: 1) Approving and 2) denying. They give reliable conclusions.

1. In the statement of the mods (modus ponens) Parcel, expressed by categorical judgment, approves the truth of the base of the conditional parcel, and the conclusion approves the truth of the investigation; reasoning directed from the approval of the truth of the foundation for the approval of the truth of the investigation.

Scheme modus:

rq.).

The lawsuit is presented with an incapacitated person ( r).

___________________________

The court leaves a lawsuit without consideration ( q.).

The first parcel is a conditional judgment that expresses the basis of the foundation ( r) and the investigation ( q.). The second parcel is a categorical judgment in which the trueness of the foundation is approved ( r): The lawsuit is presented with an incapable person. Recognizing the truth of the foundation ( r), we recognize the truth of the investigation ( q.): The court leaves a lawsuit without consideration.

2. In the denying mode (modus tollens) The parcel, expressed by categorical judgment, denies the truth of the consequence of the conditional parcel, and the conclusion denies the truth of the base. Reasoning directed from denial of the truth of the investigation to the denial of the truth of the foundation.

Scheme modus:

If the claim is presented with an incapable person ( r), the court leaves a claim without consideration ( q.).

The court did not leave a claim without consideration ( non-Q.).

_________________________

It is not true that the lawsuit is presented with an incapable person ( non-R.).

It is easy to establish that two more varieties of conditionally categorical syllogism are possible: from denial of the truth of the foundation for the denial of the truth of the investigation (3) and on the approval of the truth of the investigation to the approval of the truth of the foundation (4), i.e.:

However, the conclusion of these modes will not be reliable. So, if in the example above, the base of the conditional parcel is denied: it is incorrect that the lawsuit is presented with an incapacitated person (Scheme 3), it is impossible to deny the truth of the investigation with reliability: it is not true that the court leaves a lawsuit without consideration. The court may leave a lawsuit without consideration and for other circumstances, for example, as a result of the expiration of the limitation period.

Approval of the investigation: The court leaves a lawsuit without consideration (Scheme 4) does not entail with the need for the truth of the foundation: the court may leave a lawsuit without consideration not only as a result of the incapacity of the plaintiff, but also for other reasons.

So, of the four modes of conditionally categorical conclusions, exhaustive all possible combinations of parcels, reliable conclusions give two: saying (MODUS PONENS) (1) and denying (modus tollens) (2). They express the laws of logic and are called correct mododules of conditionally categorical conclusion. These modes obey the rule: the approval of the foundation leads to the approval of the investigation and the denial of the investigation - to the denial of the ground. Two other modus (3 and 4) do not give reliable conclusions. They are called incorrect modes and obey the rule: the denial of the base does not lead to the need to negate the investigation and the approval of the investigation does not lead to the need to approve the foundation.

When analyzing conditionally categorical conclusions, you need to keep in mind the following. First, the basis and consequence of a greater parcel can be both affirmative and negative judgment: p? q; ? P? q; P? ? q; ? P? ? Q.. For example:

If the composition of the crime is absent ( r), then the criminal case cannot be initiated ( ? Q.).

The composition of the crime is absent ( r).

__________________

The criminal case cannot be initiated ( ? Q.).

The consequence of the conditional parcel is a negative judgment, the categorical package (affirmative judgment) approves the truth of the foundation, conclusion (negative judgment) approves the truth of the investigation, that is,

This is an asserting modus.

Other varieties of modes are possible.

Secondly, if b? The extended parcel is equivalent judgment: r? Q. (if, and only if rT. q.), where ? - equivalence sign, then reliable conclusions are obtained in all four modes:

; ; ;

Consider for the example the distinguished judgment: "If the person is guilty of committing a crime, then it is subject to criminal responsibility." It is easy to establish that a reliable conclusion is obtained according to any of the above modes.

The need to output according to the approving and denying modes can be shown using the truth tables.

Approving Modeus (Table 15).

The truth of the implication (column 3) depends on the truth of the antecedent (base) (1) and the consequent (investigation) (2). The implication is considered false if and only if the antecedent is true, and the consexenter is false (2nd Table String). In all other cases, the implication of the truth. The truth or falsity of the conjunction (4th column) also depends on the components of its members (3 and 1). The conjunction is true then and only if both of its member are true (1st line of the table).

Table 15.

Now establish the truth of the implication (5th Table Stage - Approving Mode). Since the implication of the antecedent (4) and the consexer (2) does not contain the case when the antecedent is true, and the consequent is false, the implication is always true. Therefore, the statement ((r? q)? P)? Q. is a logical law.

Denying modus (Table 16).

In columns 1 and 3.2 and 4, it is shown that if one statement is false, then its denial is true. Amplication r and q. (1 and 2) is false only in one case (2nd Table String) - Stage 5. Conjunction (Column 6) of statements ( r? Q.) I. ? Q. (5 and 4) True only in one case (4th line of the table). Amplication ((p? q)?? q) and ?R (6 and 3) is always true, since it does not contain the case when the antecedent is true, and the consequent is false. Therefore, the statement ((P? Q)?? q)? P. is a logical law.

With the help of truth tables, you can show the unreliability of the conclusions of incorrect modes.

Table 16.

Questions for self-test

1. What kind of conclusion is called conditional? How is it built? What rule is its conclusion based on?

2. What kind of conclusions are called conditionally categorical? What modes are correct and what are wrong? Give them schemes.

3. Is it possible to get a reliable conclusion on the wrong models if a large package is equivalent to the judgment?

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From the book theory of justice Author Rolz John

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From the book Logic Tutorial Author Chelpanov Georgy Ivanovich

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From the book Personality and Eros Author Yannaras Christ

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From the book logic. Volume 1. Doctrine on judgment, concept and conclusion Author Sigvart Christof

From the book Philosophical Dictionary Author Conte Sponvil Andre

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From the book Logic: Tutorial for students of legal universities and faculties Author Ivanov Evgeny Akimovich

II. Conditional judgment

From the book Logic for lawyers: Textbook author Ivlev Yu. V.

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From the book Logic: Textbook for legal universities Author Kirillov Vyacheslav Ivanovich

1. The conditional conclusion of conditional is called a conclusion in which at least one package is a conditional judgment. Depending on whether one or both parcels are conditional, distinguish two types of conditional conclusions -

From the book of the author

1. Conditional conclusions of conditionally categorical conclusions1. Are the rules of conditionally categorical conclusion in the following examples: "If N. is a customs officer, then he is a state employee. N. - Customs officer. Consequently, N. - State

From the book of the author

2. Separating conclusions separating and categorical conclusions1. Are the rules of separation and categorical conclusions in the following examples: "I can go to the public service or to do commercial activities. I decided to go on

From the book of the author

A. Deaductive conclusions in the process of reasoning are sometimes for deductive accept the conclusions that are not. The latter are called incorrect deductive conclusions, and (actually) deductive - correct. The method of reasoning methods,

From the book of the author

§ 2. The separation and categorical conclusion of the separation-categorical conclusion is called a conclusion in which one of the parcels is divided, and the other parcel and conclusion are categorical judgments. Exploded judgments from which the separation consists

From the book of the author

§ 3. Conditional conclusion conclusion The conclusion in which one parcel is conditional, and the other is a separation judgment, called a conditionally separating, or lemmatic. The separation judgment may contain two, three and greater number of alternatives, so

Relative conclusions- The conclusions in which the conclusion is derived from a certain set of statements and parcels.

Usually four types of direct conclusions are distinguished (mainly two-silk):

1) purely conditional conclusions They are called such conclusions, in which both parcels and conclusion are conditional statements, i.e. Complex statements made up of simple statements using the logical Union "If ..., then ...", which in logic is often indicated by the symbol →. Taking into account this designation and replacement of simple statements by the capital letters of the Latin alphabet, the conditional conclusion scheme is as follows:

"If the student does well during the semester, he gives the session well. If the student gives the session well, he receives a scholarship. Consequently, if the student does well during the semester, he gets a scholarship "

2) conditionally categorical conclusion A two-sufficient conclusion is called, in which one of the parcels is a conditional statement, and the other parcel, and the conclusion is either the first simple statement of the conditional statement (first parcel), or the second or the denial of both. These include, for example, the conclusion of the following type:

3) In tradition, coming from medieval logic, this conclusion was called modus Ponens.What does the "approving reasoning method" mean. The conclusions of this type are very simple and the examples look trivially. For example: "If you drink coffee every day, a good idea comes to mind. This man drinks coffee every day. Consequently, he soon or later a good idea will come to mind. "

More interesting is the second type of conditional dividing conclusions, called modus tollens. (denying way of reasoning) the scheme of which can be depicted as follows:

Here the SECC is used to record the logical union "incorrectly that ..." (denial). An example of such a conclusion can be found, for example, in Augustine blessed when he writes "if any of the elects dies, then God is mistaken, but none of the elects do not die, for God is not mistaken."

Frequently performed errors when using conventional conclusions are to use the following incorrect ways of reasoning:

A certain investigator reasoned: "If this man is a criminal, he was at the crime scene. This man was at the crime scene. Consequently, this man is a criminal. "

The conclusion that doctors often use: "If a person has increased the temperature, he is sick. This person has no temperature. Consequently, he is not sick. "

4) separation and categorical conclusion A two-way conclusion is called, in which one package (separation) is a complex statement formed from two simple statements using the separation union "... or ..." (disjunction, usually indicated by the symbol of Kommersant), while the second parcel and conclusion are simple statements. . Taking into account the adopted designation scheme of separation and categorical conclusions, it looks like this:

They got a name modus Tollendo Ponens., which means "denial-claiming method of reasoning." An example of such a conclusion is as follows: "This person is mistaken or deliberately misleading others. But this person himself is not mistaken. Consequently, he deliberately misleads others. "

At the same time, the following separation and categorical conclusions are not true:

However, if you replace the "... or ..." separation alliance in these conclusions to the strict separation alliance "either ... or ..." (strict or alternative disjunction), then these methods of reasoning are transformed into correct. The conclusions of this type have a traditional name modus Ponendo Tollens.. With the use of such conclusions, you can face, for example, at the rally, when the speaker says: "Either we will win, or everything will go to all the hell! But we will win! ", I mean that" everything will not go to all the hell. "

5) Conditional conclusions The conclusions are called, in which one of the parcels is a dividing statement, and the rest - conditional statements. Another name of the conditionally separating conclusions - lemmatic, originating from the Greek word Lemma - offer, assumption. This name is based on the fact that there are various assumptions and their consequences in these conclusions. Depending on the number of conditional parcels, conditionally dividing conclusions are called dilemmas (two conditional parcels) trilems (three), polymems (Four or more). In the practice of reasoning, dilemmas are most often used.

The following main types of dilemmas can be distinguished:

- Simple constructive dilemma,

– complex structural dilemma,

– simple destructive dilemma,

– difficult destructive dilemma.

An example of a simple constructive dilemma (Socrates argument):

"If death is a transition to non-existence, then it is benefit. If death - the transition to the world is different, then it is benefit. Death - the transition to non-existence or into the world of others. Consequently, death is benefit. "

An example of a complex constructive dilemma:

Young Afinyanin addressed Socrates for advice: Is it worth marrying? Socrates replied: "If a good wife comes you, then you will be happy if you are bad, then you will be like me, a philosopher. But you get a good or bad wife. Therefore, or to be you happy exception, or philosopher. "

An example of a simple destructive dilemma:

"In the modern world, if you want to be happy, you need to have a lot of money. However, it was always so that if you want to be happy, then you need to have a clean conscience. But we know that life is arranged so that it is impossible to have money and conscience at the same time, i.e. Or no money, or no conscience. Consequently, leave hope for happiness. "

An example of a complex destructive dilemma:

"If he is a smart, he will see his mistake. If he is sincere, he is confessed in it. But he or does not see his mistake, or is not recognized in it. Consequently, he or not a smart, or not sincere. "

40.Scluded syllogism (entimible) and its restoration to full form.

Abbreviated syllogism (entimible) -slimogism in which it is released (not expressed express) any of its parts (parcel or conclusion)

Abbreviated (entimatic) may be the conclusions of the logic of judgments. Parcels or conclusion may also be missed there. Therefore, more general definition of entimibles is possible:

Enthymeme - This is a conclusion in which one of the parcels or conclusion is missed.

The meaning of this name (from Greek ẻν θυμφ - in the mind) is that some part of the Slogism is not expressed expressly, but as it were in the mind.

The possibility of an abbreviated expression of conclusions is due to the fact that if there are two some parts of the syllogism, it is always possible to accurately completely set the missed part.

In discussions and disputes, when the interlocutor expresses his thought in the form of an abbreviated syllogism, it is always necessary to accurately realize what kind of judgment is not expressed, but only meant in this reasoning. Otherwise it is impossible to fully understand this reasoning and refute if it is incorrect. Often, people proceed in their arguments from false or dubious positions, but not express them clearly, using abbreviated forms of conclusions. To find a mistake in such a reasoning and refute it, it is necessary to establish what is supposed to be in it, but not expressed clearly.

In simple cases, the implies implied in the argument or conclusion can be installed without resorting to special techniques - according to the general meaning of reasoning. But in many cases, it is not so easy to restore the missing part of the syllogism. However, this can be done by performing the operation of recovery of syllogism to a full form, which consists of several stages:

1) Determining the missed Slitogism element (parcel or conclusion). If there are expressions in the entimiment, denoting a logical connection ("consequently", "because", "since", etc.), it means that there is a conclusion in the entimible. If these words are not, then, most likely, the conclusion is missing;

2) definition of terms of syllogism (smaller, greater and medium);

3) determining the type of missed parcel (if the parcel is missing) - large or smaller;

4) the definition of the figure and the Slimogism modus;

5) The formulation of syllogism in full form.

The difficulties of restoration of syllogisms by entimiment may be related to the fact that to properly determine the concepts (terms), from which the missed element will be formulated (parcel or conclusion), you must know the logical forms of existing elements (two packages or parcels and conclusion). However, in real arguments, standard logical forms of categorical judgments (of which and consist of syllogism) are not always used. Before bringing judgments to standard form, it is necessary to understand their sense, which may be not easy.

Example. We will restore the syllogism from the entimible "This syllogism has three terms, and therefore it is correct."

In this entimiment there is a word denoting a logical connection ("Therefore"), it means that there is a conclusion. The conclusion is the judgment that follows the word "therefore": "It is correct." The remaining judgment is "This syllogism has three terms" - one of the parcels. You need to restore the second, missing parcel.

We define the subject and predicate of the conclusion, formulating it in a logical form and considering that it consists of "this syllogism" and under the pronomation of "he" is meant "this syllogism":

The parcel in the entimible contains a subject of concluding or a smaller term ("this syllogism"), i.e. is a smaller package. And since any package always contains one of the extreme terms and the average term, therefore, the second term of the parcel ("Sillogism, having three terms") is the average term of Slogatogism (M):

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This syllogism (S) is the right Slimogism (P).

We restore a large package. A large package always contains a larger term (P) and an average term (m). However, they can be located in different sequences: Rth or Mr. To determine the sequence of terms, as well as the type of parcel (secrect, general-negative, particularly approved or partly negative), we define the figure and modus of the Slogism. In this case, we take into account that the restored syllogism should be correct.

In a smaller premise, the terms are located in the S-M. Such a location of terms in a smaller parcel is possible either in the first or in the second figure (in the third and fourth, the terms are located in the reverse order - M-S). It means that Sillogism will have either the first or a second shape.

Now we find the Slimogism modus. Since a smaller package and conclusion is a secrect judgment (a), the modus will end on ... AA. We look at which of the pre-selected figures (first or second) there is a correct modus ending with ... aa. Such a modus is in the first figure, and this is a AAA mode.

The desired large parcel is a generally affordative judgment (a), and the terms in it must follow M-p, as it is in this way they are located in a greater parcel in the first figure. We get the following syllogism:

All syllogisms having three terms (M) are the correct Sloghisms (P).

This syllogism (S) is a syllogism having three terms (M).

This syllogism (S) is the right Slimogism (P).

The received parcel is not a true judgment, because the number of terms, as we already know, is not the only condition for the correctness of the Slogism. Consequently, the conclusion of the entimible about the correctness of "this Silogism" is unreasonable

conditional The conclusion is called such mediated conclusion, in which both parcels are conditional judgments. Conditional is a judgment that has a structure: "If but, that b."Structure of purely conditional conclusion is such:

If a, then B scheme:

If b, then with.

If a, then a → B, B → C

According to the definition of a logical investigation, formulated as part of the calculation of statements, if the formula and → C is The logical consequence of these parcels, then by connecting the parcel by the sign of conjunction and attaching to them by the implication sign, we must obtain a formula that is the law of logic, i.e. The identity-true formula. In this case, the formula will be as follows:

((A → C) ^ (B → c)) → (A → C).

The conditional judgment is shaped: if A is b, then C is D, for example: if the Earth revolves around his axis, then there is a change of day and night. The first judgment is the basis ( antecedent), and the second is the investigation ( conceiver).

There are two modes of conditionally categorical conclusions. The first one is called modus Ponens., that is, setting, asserting, constructive modus; The second is called modus Tolens., that is, the destroyer, denying, destructive modus.

Constructive modus It has the following form.

If A is b, then C is D;

A is B.;

Consequently, C is D.

• In the conditionally categorical conclusion in the constructive mode

Destructive modus It has the following form.

If A is b, then C is D;

C is not D;

Therefore, A is not b.

• In conventionally categorical conclusion in the destructive modus, the consequent is denied.

End of work -

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History and subject of logic

Whatever analysis of the term Term Square Significant .. Logic operations with a scope of concept .. Generalization of concept This is a logical transition operation from the concept with a smaller volume, but with a great content to the concept ..

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History and subject of logic
In its development, the logic passed two stages: 1) with IV century. BC e. until the XIX century n. e. During this period, the appearance of formal logic occurred, the author of which is traditionally considered

Language and logic. Name
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Concept
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Refable
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Difficult judgment
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Review
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Refutation. Structure and form
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