What is inference? This is a certain form of thinking and the only correct conclusion. The specifics are as follows: in the process of cognition, it becomes clear that the statements prompted by evidence are not all true, but only a certain part of them.
To establish the full truth, a thorough investigation is usually carried out: clearly identify questions, correlate already established truths with each other, collect the necessary facts, conduct experiments, check all the conjectures that arise along the way and derive the final result. Here it will be - the conclusion.
In logic, the form of thinking looks no different: from true judgments - one or more - subject to certain rules for deriving the result, the following, new judgment is obtained, which directly follows from the previous ones.
Structure
So, what is an inference and what does it consist of? From judgments (premises), conclusion (new judgment) and logical connection between judgments and conclusion. The logical rules by which the conclusion appears,indicate a logical connection. In other words, a conclusion (any) consists of simple or complex judgments that equip the mind with new knowledge. The same judgments, if recognized as true and able to give birth to a new, generalizing one, are called premises of an inference.
The judgment obtained by processing the premises, where the methods of inference have worked, is called a conclusion (and also either a conclusion or a logical consequence). Let's see how judgment and inference are related. Formal logic establishes rules that ensure true inference. How is a conclusion drawn? We will give examples on several premises.
- Student of the conservatory Natalia plays the piano wonderfully.
- Elizaveta has been taking part in piano ensemble competitions for the second year in a duet with Natalia.
- Conclusion: Elizabeth is a successful student at the conservatory.
By example, you can easily learn what a conclusion is, and what is its connection with the premise (judgment). The main thing is that the premises must be true, otherwise the conclusion will be false. One more condition: the connections between judgments must be logically correctly built in order to gradually and accurately build the path further - from the premises to the conclusion.
Three groups of inferences
The division into groups is made after checking the degree of generality of judgments.
- Deductive reasoning, where thought moves from the general to the particular, from the big to the small.
- Inductive, where thought goes from one knowledge to another, increasing the degree of generality.
- Conclusion onanalogy, where both the premises and the conclusion have knowledge of the same degree of generality.
The first group of inferences is built to the particular and from the singular, if it is equated to the general. That is, in any case, there is only one method: from the general to the particular. Deductive reasoning is called deductio - "inference" (from the general rules, the investigation moves to a particular case). The logical judgments of any unions work for deduction: categorical inference, dividing-categorical and conditionally dividing. All of them are deductively obtained.
Deduction begins to be studied from the most typical forms, and this categorical conclusion is a syllogism, which means "counting" in Greek. Here begins the analysis of reasoning, which consists of judgments and concepts.
Analysis of simple structures
The study of complex mental structures always begins with the simplest elements. All human reasoning in everyday life or in a professional environment is also inference, even arbitrarily long chains of inference - everyone extracts new knowledge from existing ones.
The environment - nature - gave humanity a little more than animals, but on this foundation a magnificent colossal building has grown, where a person recognizes the cosmos, and elementary particles, and high-mountain formations, and the depths of ocean depressions, and disappeared languages, and ancient civilizations. None of the available knowledge would have been obtained if mankind had not been given the abilitydraw a conclusion.
Examples of extracting output
To draw conclusions from incoming information is not the whole mind in full, but without this a person cannot live a day. The most important side of the human mind is the ability to understand what a conclusion is and the ability to build it. Even the simplest phenomena and objects require the application of the mind: upon waking up, look at the thermometer outside the window, and if the mercury column on it drops to -30, dress accordingly. It would seem that we do it without thinking. However, the only information that has emerged is the air temperature. Hence the conclusion: it is cold outside, although this is not reliably confirmed by anything other than a thermometer. Maybe we won't be cold in a summer sarafan? Where does knowledge come from? Naturally, such a chain of efforts of the mind does not require. And additional parcels too. These are direct inferences. A smart person can have a maximum of information from a minimum of knowledge and foresee the situation with all the consequences of his actions. A good example is Sherlock Holmes with his faithful Watson. Syllogisms are made up of two or more premises and are also subdivided based on the nature of the constituent judgments. There are simple and complex, abbreviated and compound abbreviated syllogisms.
Immediate inferences
As shown above, direct inferences are conclusions that can be drawn from a single premise. Through transformation, conversion, opposition, a logical conclusion is created. Transformation - changing the quality of the package without changingquantities. The judgment in the bundle changes to the opposite, and the statement (predicate) - to a concept that completely contradicts the conclusion. Examples:
- All wolves are predators (generally affirmative). None of the wolves is not a predator (general negative proposition).
- None of the polyhedra is flat (generally negative judgment). All polyhedra are non-planar (generally affirmative).
- Some mushrooms are edible (privately affirmative). Some mushrooms are inedible (partial negative).
- Partly the crimes are not intentional (private negative judgment). Partially unintentional crimes (private affirmative judgment).
In appeals, the subject and the predicate are reversed with full obedience to the rule of distribution of judgment terms. Conversion is pure (simple) and limited.
Contrapositions - direct inferences, where the subject becomes a predicate, and its place is taken by a concept that completely contradicts the original judgment. Thus, the link is reversed. One can consider opposition as the result after conversion and transformation.
Inference by logic is also a type of direct inference, where conclusions are based on a logical square.
Categorical syllogism
A deductive categorical inference is one where a conclusion follows from two true judgments. The concepts that are part of the syllogism are denoted by terms. A simple categorical syllogism has three terms:
- conclusion predicate (P) - larger term;
- subject of confinement (S) - lesser term;
- bundle of premises P and S missing from conclusion (M) - middle term.
Syllogism forms that differ in the middle term (M) in the premises are called figures in a categorical syllogism. There are four such figures, each with its own rules.
- 1 figure: common major premise, affirmative minor premise;
- 2 figure: common large premise, negative smaller one;
- 3 figure: affirmative minor premise, private conclusion;
- 4 figure: the conclusion is not a universally affirmative judgment.
Each figure can have several modes (these are different syllogisms according to the qualitative and quantitative characteristics of premises and conclusions). As a result, the figures of the syllogism have nineteen correct modes, each of which is assigned its own Latin name.
A simple categorical syllogism: general rules
To make the conclusion in a syllogism true, you need to use true premises, honor the rules of figures and a simple categorical syllogism. Inference methods require the following rules:
- Do not quadruple terms, there should be only three. For example, movement (M) - forever (P); going to university (S) - movement (M); the conclusion is false: going to university is eternal. The middle term is used here in different senses: one is philosophical, the other is everyday.
- Middle termmust be distributed in at least one of the parcels. For example, all fish (P) can swim (M); my sister (S) can swim (M); my sister is a fish. The conclusion is false.
- The conclusion term is distributed only after distribution in the parcel. For example, in all polar cities - white nights; St. Petersburg is not a polar city; there are no white nights in St. Petersburg. The conclusion is false. The term conclusion contains more than premises, the larger term has expanded.
There are rules for the use of parcels that the form of inference requires, they must also be observed.
- Two negative premises do not give any output. For example, whales are not fish; pike are not whales. So what?
- With one negative premise, a negative conclusion is obligatory.
- No conclusion possible from two private parcels.
- With one private parcel, a private conclusion is required.
Conditional Inference
When both premises are conditional propositions, a purely conditional syllogism is obtained. For example, if A, then B; if B, then C; if A, then B. Clearly: if you add two odd numbers, then the sum will be even; if the sum is even, then you can divide by two without a remainder; therefore, if you add two odd numbers, then you can divide the sum without a remainder. There is a formula for such a relation of judgments: the consequence of the consequence is the consequence of the foundation.
Conditionally categorical syllogism
What is a conditionally categorical inference? There is a conditional proposition in the first premise, and categorical propositions in the second premise and conclusion. modus herecan be either affirmative or negative. In the affirmative mode, if the second premise affirms the consequence of the first, the conclusion will only be probable. In the negative mode, if the basis of the conditional premise is denied, the conclusion is also only probable. These are conditional inferences.
Examples:
- If you don't know, shut up. Silent - probably don't know (if A, then B; if B, then probably A).
- If it snows, it's winter. Winter has come - it's probably snowing.
- When it's sunny, the trees provide shade. Trees give no shade - not sunny.
Divisive syllogism
An inference is called a disjunctive syllogism if it consists of purely divisive premises, and the conclusion is also obtained as a distributive judgment. This increases the number of alternatives.
Even more important is the dividing-categorical inference, where one premise is a divisive judgment, and the second is a simple categorical one. There are two modes here: affirmative-negative and negative-affirmative.
- Sick is either alive or dead (abc); the patient is still alive (ab); the patient did not die (ac). In this case, the categorical judgment denies the alternative.
- A wrong is a misdemeanor or a crime; in this case - not a crime; means misconduct.
Conditional separators
The concept of inference also includes conditionally dividing forms, in which one premise is two or more conditional propositions, and the second- disjunctive argument. Otherwise it is called a lemma. The task of the lemma is to choose from several solutions.
The number of alternatives divides conditional-separative inferences into dilemmas, trilemmas and polylemmas. The number of options (disjunction - the use of "or") affirmative judgments is a constructive lemma. If the disjunction of negations is a destructive lemma. If the conditional premise gives one consequence - the lemma is simple, if the consequences are different - the lemma is complex. This can be traced by building inferences according to the scheme.
Examples would be something like this:
- A simple constructive lemma: ab+cb+db=b; a+c+d=b. If the son goes to visit (a), he will do his homework later (b); if the son goes to the cinema (c), then before that he will do his homework (b); if the son stays at home (d), he will do his homework (b). The son will go to visit or to the cinema, or stay at home. He will do his homework anyway.
- Complex constructive: a+b; c+d. If the power is hereditary (a), then the state is monarchical (b); if the government is elected (c), the state is a republic (d). Power is inherited or elected. State - monarchy or republic.
Why do we need a conclusion, judgment, concept
Inferences don't live on their own. Experiments are not blind. They only make sense when combined. Plus, synthesis with theoretical analysis, where by means of comparisons, comparisons and generalizations, conclusions can be drawn. Moreover, it is possible to draw a conclusion by analogy not only about what is directly perceived, but also about what is impossible to “feel”. How can one directly perceive suchprocesses, like the formation of stars or the development of life on the planet? Here such a game of the mind as abstract thinking is needed.
Concept
Abstract thinking has three main forms: concepts, judgments and inferences. The concept reflects the most general, essential, necessary and decisive properties. It has all the signs of reality, although sometimes reality is devoid of visibility.
When a concept is formed, the mind does not take most of the individual or insignificant accidents in signs, it generalizes all perceptions and representations of as many similar objects as possible in terms of homogeneity and collects from this the inherent and specific.
Concepts are the results of summarizing the data of this or that experience. In scientific research, they play one of the main roles. The path of studying any subject is long: from simple and superficial to complex and deep. With the accumulation of knowledge about the individual properties and features of the subject, judgments about it also appear.
Judgment
With the deepening of knowledge, the concepts are improved, and judgments about the objects of the objective world appear. This is one of the main forms of thinking. Judgments reflect the objective connections of objects and phenomena, their inner content and all patterns of development. Any law and any position in the objective world can be expressed by a certain judgment. Inference plays a special role in the logic of this process.
The phenomenon of inference
A special mental act, where from the premises you canto draw a new judgment about events and objects - the ability to draw conclusions characteristic of mankind. Without this ability it would be impossible to know the world. For a long time it was impossible to see the globe from the side, but even then people were able to come to the conclusion that our Earth is round. The correct connection of true judgments helped: spherical objects cast a shadow in the form of a circle; The Earth casts a round shadow on the Moon during eclipses; The earth is spherical. Inference by analogy!
The correctness of conclusions depends on two conditions: the premises from which the conclusion is built must correspond to reality; the connections of the premises must be consistent with logic, which studies all the laws and forms of building judgments in the conclusion.
Thus, the concept, judgment and inference as the main form of abstract thinking allow a person to cognize the objective world, to reveal the most important, most essential aspects, patterns and connections of the surrounding reality.
