Judgments in logic.

click fraud protection

judgment is a form of thinking, affirm or deny anything about the existence of objects, the links between them and their properties, as well as the relationship between objects.

Examples judgment: "The Volga flows into the Caspian Sea", "A.Pushkin wrote a poem "The Bronze Horseman", "Siberian tiger is listed in the Red Book," etc.

structure judgments

judgment includes the following elements: subject, predicate, and a bunch of quantifiers.

  1. subject (lat. Subjektum - «underlying») - that, as stated in the judgment of his subject («S»).
  2. predicate (lat. Praedicatum - «said") - a reflection characteristic of the subject, what is said on the subject of the judgment ("P").
  3. Bundle - relation between the subject («S») and a predicate ("P").It determines the presence / absence of the subject of a property expressed by the predicate.Maybe it implies, and is indicated by a "dash" or the words "a" ("is not"), "has", "have", "essence" and others.
  4. quantifier (quantifier words) defines the scope of the concept, whichIt is the subject of the judgment.It is standing in front of the subject, but it can also be absent in judgment.Represented by words such as "all", "many", "some", "no", "no" and others.

True and false judgments

judgment is true in the case where there is any indication, properties andRelations items approved / denied in judgment, true.For example: "All swallows - birds", "9 for more than 2" and so on. D.

If the statement is contained in the judgment, does not match reality, we are dealing with a false judgment: "The sun revolves around the Earth""A kilo of iron heavier than a kilogram of wool" and others. The correct judgments are the basis of correct reasoning.

However, apart from two-valued logic, in which judgment can be either true or false, there is also a multi-dimensional logic.Under its terms, the judgment can still uncertain.Especially it concerns the future of individual judgments, "Tomorrow there will / will not happen sea battle" (Aristotle, "On the interpretation").Assuming that this is true proposition, the sea battle tomorrow can not happen.Consequently, it is necessary to make it happen.Or vice versa: claiming that the judgment in the present moment is false, we thus do the necessary impossibility of future sea battle.

judgment on the type of statements

As is known, the type of statements are three types of sentences: declarative, interrogative and motive.For example, the sentence "I remember a wonderful moment" refers to the type of narrative.It is advisable to suggest that such a judgment would also be narrative.It contains certain information, according to a specific event.

In turn, the interrogative sentence contains a question, get an answer to: "What does the future hold for me?" In this case, it says nothing and does not deny.Accordingly, the claim that such a judgment is a question incorrectly.Interrogative sentences in principle, does not contain any opinions, because the question can not be differentiated on the basis of truth / falsity.

Incentive type of sentence is formed in the case where there is some incentive to action, or to reject the request: "Arise, O Prophet, and the vid, and attend to."Regarding judgments, that according to some researchers, they are not contained in the proposals of this type.Others believe that it is a variety of modal judgments.

quality judgments

In terms of quality, the judgment can be both assertive (S has P), and negative (S is not P).In the case of the affirmative judgment, by a predicate to a subject is given a certain property (-wa).For example: "Leonardo da Vinci - Italian painter, architect, sculptor, scientist, naturalist and inventor and writer, the largest representative of Renaissance art."

In the negative judgment, on the other hand, the property is taken away from the subject: "The theory of the 25th frame James Vicary has no experimental confirmation."

quantitative characteristic

proposition in logic may be general in nature (related to all subjects in this class), private (some of them) and individual (when talking about the subject, there is only one).For example, it can be argued that such a proposition as "At night all cats are gray" will refer to a common view, because it affects all members of the cat (the subject of the judgment).The statement "Some snakes are not poisonous" - an example of private judgment.In turn, the proposition "Wonderful Dnieper in calm weather," an isolated, since we are talking about one particular river, existing in a single form.

Simple and complex judgments

Depending on the structure, the judgment may be of a simple or complex.The structure of a simple proposition includes two related concepts (SP): «The book - a source of knowledge."There are also judgments with one concept - when the second only meant: "It was getting dark» (P).

complicated form is formed by combining a few simple propositions.

Classification of simple judgments

simple proposition in logic may be of the following types: attributive, judgment with relationships, existential, modal.

Attribute (judgment-properties) sent for approval / denial of the existence of certain properties from an object (attributes) activities.These judgments are categorical form and not questioned "the mammalian nervous system consists of the brain, spinal cord and outgoing nerve pathways."

The judgments with respect of the certain relations between objects.They can have a space-time context, causal, and others. For example: "An old friend is better than two new ones", "Hydrogen is lighter carbon dioxide by 22 times."

existential proposition - a statement of the existence / nonexistence of the subject (both material and ideal), "No prophet in his own country", "The Moon is a satellite of the Earth."

modal proposition - a form of approval, of which consists of a certain modal operator (necessary, good / bad, proved known / unknown, it is forbidden, I believe, and others.).For example:

  • «Russia needs to conduct education reform" (alethic modality - the possibility, the need for something).
  • «Everyone has the right to security of person" (deontic modality - the moral norms of social behavior).
  • «Careless attitude towards public property leads to its loss" (axiological modality - related to the material and spiritual values).
  • «We believe in your innocence" (epistemic modality - the reliability of knowledge).

complex judgments and the types of logical connectives

As already noted, complex judgments consist of a few simple.As the logical connections between them are such techniques as:

  • Conjunction (and ʌ b - connecting judgment).Judgments-conjuncts have a bunch of "and", "Implementation of the rights and freedoms of man and citizen shall not violate the rights and freedoms of others."
  • disjunction (avb - dividing judgment).As constituent elements of judgment-clauses are used as a binder - the conjunction "or".For example: "The plaintiff has the right to increase or decrease the size of the claim."
  • implication (a → b - judgment-effect).If the structure of a complex judgment stands and sending a result, it can be argued that this judgment refers to the implicative.As a ligament in the form used by such alliances as "if ... then".For example: "If through the conductor to miss the electric current, the wire heats up," "You want to be happy - be happy."
  • The equivalence (a ≡ b - identical judgments).It occurs when the value of a and b are the same (either both true or both false): "Man is created for happiness, like a bird to fly."
  • Denial (¬a, ā - judgment-inversion).Each source is associated with the assertion compound statement denying the original.By using ligaments "no".Accordingly, if the original statement is as follows: "The bull reacts to a red light," (a) - the denial will sound like: "the bull reacts to a red light» (¬a).