What is the conclusion? This is a certain form of thinking and the only correctly drawn conclusion. The specifics are as follows: in the process of cognition, it becomes clear that statements prompted by evidence are not all true, but only a certain part of them.
To establish the complete truth, a thorough investigation is usually carried out: clearly identify the issues, relate the already established truths to each other, add the necessary facts, make experiments, check all the conjectures that arise along the way and derive the final result. So it will be - inference.
In logic, the form of thinking does not look different: from true judgments - one or more - subject to certain rules for deriving the result, one obtains the following, a new proposition that directly follows from the previous ones.
Structure
So, what is the conclusion and what does it consist of? From judgments (premises), conclusion (new judgment) and the logical connection between judgments and conclusion. The logical rules by which the conclusion appears indicate a logical connection. In other words, the conclusion (any) consists of simple or complex judgments that equip the mind with new knowledge. These same judgments, if recognized as true and were able to give birth to a new, generalizing one, are called premises of inference.
The judgment obtained by processing the premises where the methods of inference have worked is called inference (as well as inference or logical consequence). Let us see how judgment and inference are related. Formal logic sets the rules for true inference. How is the conclusion drawn? We give examples of several premises.
- A student at the conservatory Natalya plays the piano wonderfully.
- For the second year, Elizabeth has been participating in competitions in piano ensembles in a duet with Natalya.
- Conclusion: Elizabeth successfully studies at the conservatory.
By example, one can easily learn what is the conclusion, and what is its relationship with the premise (judgment). The main thing is that the premises are true, otherwise a false conclusion will be obtained. Another condition: the connection between judgments must be correctly built in logic, in order to gradually and accurately build the path further - from premises to conclusions.
Three groups of inferences
The division into groups is carried out after reconciling the degree of generality of judgments.
- A deductive conclusion, where thought moves from the general to the particular, from large to small.
- Inductive, where thought goes from one knowledge to another, increasing the degree of generality.
- Inference by analogy, where both premises and conclusions have knowledge of one degree of generality.
The first group of inferences is constructed to the particular and from the singular, if it is equated to the general. That is, in any case, the method is one: from general to particular. A deductive inference is called deductio - “derivation” (from general rules, the investigation moves to a particular case). Logical judgments of any unions work for deduction: categorical inference, dividing-categorical and conditionally dividing. All of them are obtained in a deductive way.
They begin to study deduction from the most typical forms, and this categorical conclusion is syllogism, which in Greek means "counting." Here begins the analysis of reasoning, which consists of judgments and concepts.
Simple structure analysis
The study of complex mental constructions always begins with the simplest elements. All human reasoning in everyday life or in a professional environment - also conclusions, even arbitrarily long chains of conclusions - each extracts new knowledge from existing knowledge.
The environment - nature - gave mankind a little more than animals, but on this foundation a magnificent colossal building grew up, where a person recognizes space, and elementary particles, and alpine formations, and the depths of ocean depressions, and extinct languages, and ancient civilizations . None of the available knowledge would have been gained if humanity had not been given the ability to draw conclusions.
Output Retrieval Examples
To draw conclusions from the incoming information is not the whole mind in its entirety, but without this a person cannot live a day. The most important aspect of the human mind is the ability to understand what is inference and the ability to build it. Even the simplest phenomena and objects require the application of the mind: when you wake up, look at the thermometer outside the window, and if the column of mercury on it drops to -30, dress accordingly. It would seem that we are doing this without thinking. However, the only information that appeared was air temperature. Hence the conclusion: there is frost on the street, although it is not authentically confirmed by anything other than a thermometer. Maybe we won’t be cold in the summer sundress? Where does the knowledge come from? Naturally, such a chain of mind effort does not require. And additional packages too. These are direct conclusions. An intelligent person can have a maximum of information from a minimum of knowledge and anticipate 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 component judgments. There are simple and complex, abbreviated and complex abbreviated syllogisms.
Direct conclusions
As shown above, direct conclusions are conclusions that can be deduced from a single premise. By transformation, conversion, opposition, an inference is created by logic. Transformation - a change in the quality of the parcel without changing the quantity. A judgment in a connective changes to the opposite, and a statement (predicate) to a concept that completely contradicts the conclusion. Examples:
- All wolves are predators (affirmative). None of the wolves is a predator (general negative judgment).
- None of the polyhedra is flat (general negative proposition). All polyhedrons are non-planar (affirmative).
- Some mushrooms are edible (private affirmative judgment). Some mushrooms are inedible (private negative judgment).
- Partly the crimes are not intentional (private-negative judgment). Partly unintentional crimes (private affirmative judgment).
In appeals, the subject and the predicate change places with full submission to the rule of distribution of terms of judgment. The treatment is clean (simple) and with restriction.
Contrasts are direct conclusions, where the subject becomes a predicate, and a concept that completely contradicts the original judgment takes its place. Thus, the ligament is reversed. We can consider the 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 categorical deductive conclusion is one where a conclusion follows from two true judgments. The concepts that are part of the syllogism are denoted by terms. Simple categorical syllogism has three terms:
- conclusion predicate (P) is a larger term;
- subject of conclusion (S) is a smaller term;
- a bundle of packages P and S that is absent in the conclusion (M) is an average term.
Forms of syllogism, which differ in the average term (M) in the premises, are called figures in the categorical syllogism. There are four such figures, each with its own rules.
- 1 figure: general large premise, affirmative less;
- 2 figure: general big premise, negative less;
- 3 figure: affirmative less premise, private imprisonment;
- 4 figure: the conclusion is not a general affirmative judgment.
Each figure can have several modes (these are different syllogisms for the qualitative and quantitative characteristics of premises and conclusions). As a result, the figures of syllogism have nineteen correct modes, each of which has its own Latin name.
Simple categorical syllogism: general rules
For the conclusion in the syllogism to be true, you need to use the true premises, to honor the rules of figures and simple categorical syllogism. Inference methods require compliance with the following rules:
- Do not allow quadrupling of terms; there should be only three of them. For example, movement (M) is forever (P); going to university (S) - movement (M); the conclusion is false: going to university is eternal. The middle term here is used in different senses: one is philosophical, the other is everyday.
- The average term is necessarily distributed in at least one of the premises. For example, all fish (P) can swim (M); my sister (S) can swim (M); my sister is a fish. The conclusion is false.
- The term conclusion is distributed only after distribution in the package. For example, in all the 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 premises, which requires a form of inference, they must also be observed.
- Two negative premises do not give an output. For example, whales are not fish; pikes are not whales. So what?
- With one negative premise, a negative conclusion is required.
- It is impossible to deduce from two private premises.
- With one private parcel, a private conclusion is mandatory.
Conditional inferences
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. Visually: if you add up two odd numbers, then the sum will be even; if the sum is even, then it can be divided into two without a remainder; therefore, if you add two odd numbers, you can divide the amount without a remainder. For such an attitude of judgments there is a formula: the consequence of the investigation is the consequence of the foundation.
Conditionally categorical syllogism
What is a conditionally categorical conclusion ? A conditional proposition occurs in the first premise, and categorical judgments in the second premise and conclusion. The modus here can either be affirming or denying. In an affirming mode, if the second premise asserts the corollary of the first, the conclusion is only probable. In the negative mode, if the basis of the conditional premise is denied, the conclusion is also only possible. These are conditional inferences.
Examples:
- Do not know - be silent. Silent - probably you don’t know (if A, then B; if B, then probably A).
- If it snows, winter has come. Winter has come - it is probably snowing.
- If sunny, trees give a shadow. Trees do not give a shadow - not sunny.
Dividing syllogism
The conclusion is called dividing syllogism if it consists of purely dividing premises, and the conclusion is also obtained by dividing judgment. Thus, the number of alternatives increases.
Even more important is the separation-categorical conclusion, where one premise is a separation judgment, and the second is a simple categorical one. There are two modes: affirmative-negative and negative-affirmative.
- The patient is either alive or dead (abc); the patient is still alive (ab); the patient is not dead (ac). In this case, categorical judgment denies the alternative.
- An offense is an offense or a crime; in this case, not a crime; it means misconduct.
Conditional dividing
The concept of inference also includes conditionally dividing forms, in which one premise is two or more conditional propositions, and the second is a dividing proposition. Otherwise, it is called a lemma. The problem of the lemma is the choice of several solutions.
The number of alternatives divides conditionally dividing conclusions into dilemmas, trilemmas, and multilemmas. The number of options (disjunction - using "or") affirmative judgments - 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, according to the scheme, building conclusions.
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), will do homework later (b); if the son goes to the cinema (c), then before that he will do the lessons (b); if the son stays at home (d), he will do homework (b). The son will go to visit a movie or stay at home. He will do the lessons anyway.
- Complex constructive: a + b; c + d. If the power is hereditary (a), then the state is monarchical (b); if power is elected (c), the state is a republic (d). Power is inherited or elected. The state is a monarchy or republic.
Why do we need inference, judgment, concept
Inferences do not live on their own. Experiments are not conducted blindly. They make sense only in combination. Plus synthesis with theoretical analysis, where by way of comparisons, comparisons and generalizations, conclusions can be drawn. Moreover, the conclusion can be drawn by analogy not only about directly perceived, but also that it is impossible to "touch". How can processes such as star formation or the development of life on the planet be directly perceived? This requires such a game of the mind as abstract thinking.
The concept
Abstract thinking has three main forms: concepts, judgments and conclusions. The concept reflects the most general, essential, necessary and decisive properties. All signs of reality are present in it, although sometimes reality is deprived of clarity.
When a concept is formed, the mind does not take most of the individual or insignificant accidents in the signs, it summarizes all the perceptions and representations of as many objects as possible similar in homogeneity and collects from it the inherent and specific.
Concepts are the results of a generalization of the data of a particular experience. In scientific research, they play one of the main roles. The way to study any subject is long: from simple and superficial to complex and deep. With the accumulation of knowledge about individual properties and characteristics of the subject, judgments about it also appear.
Judgment
With the deepening of knowledge, 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 internal content and all the laws of development. Any law and any position in the objective world can be expressed by a certain judgment. A special role is played by inference in the logic of this process.
The phenomenon of inference
A special act of thought, where a new proposition about events and objects can be inferred from the premises is the inherent ability to reason. 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 shape of a circle; The earth casts a round shadow on the moon during eclipses; The earth has the shape of a ball. Inference by analogy!
The correctness of the conclusions depends on two conditions: the premises from which the conclusion is based must correspond to reality; communication premises must be considered with logic, which studies all the laws and forms of building judgments in the conclusion.
Thus, the concept, judgment and conclusion as the main form of abstract thinking allow a person to cognize the objective world, to reveal the most important, most essential aspects, laws and relationships of the surrounding reality.