What are the laws of deductive thinking

Deductive thinking

Syllogism (Greek: adding up), a statement and form of argument, especially in traditional logic, in which a conclusion is drawn from two assertions or judgments (premises). The first requirement is called the major premise or major premise (Proposia maior), the second minor premise or minor premise (Proposio minor).
The most famous example of a syllogism relates to the philosopher Socrates. It reads as follows: All people are mortal (Proposia maior), Socrates is a person (Proposia minor), so Socrates is also mortal.

Deduction is a procedure that allows to correctly derive more specific and complicated sentences from general, presupposed and elementary sentences, i.e. the deduction is the way from the theory (general) to the individual case.

Deduction (Latin for derogation) means in logicthat type of evidence in which a certain statement is derived from one or more other statements. In valid deductive reasoning, an inference must be true if all premises are true. Assuming that all human beings are fallible and that philosophers are human, then one can logically infer that philosophers are fallible. This is an example of a syllogism, a proof where two premises are given and a logical conclusion is drawn. Inference is always correct if all the steps in the derivation are justified by logical rules of inference. The formal logic determines which conclusions are permissible.

The deduction corresponds to the form of a syllogistic inference, i.e. the deduction is carried out with the help of the rules of inference, e.g. propositional logic. The simplest conclusion is this mode ponens.

The term "modus ponens" (also "splitting rule") denotes the following formalized logic: If X is a set of formulas, S1 and S2 formulas (with regard to a language L), then S2 is proven from X, if S1 and S1-> S2 from X can be proven. If one claims in an argument a knowledge regarding a proposition S2, which can be deduced in this way from a theory X, then one must use the modus Ponens as absolutely apply. Absoluteness In this context, means that if one can speak of knowledge at all, it can only be realized with the help of certain tools that are used in one's theories, because knowledge is always dependent on understanding, so when one speaks of knowledge or the elementary laws of logic speaks, these always have a public (linguistic) character, in which the general concept of truth can also be found, which is necessarily constituted from the common language. At this point in an argument, relativism ends, because without this absolute concept of truth, communication about knowledge, laws and conclusions is not possible. Only then can one justify the validity and thus the knowledge of S2, whereby these conclusive arguments also consist of this inference rule, because if S2 applies under the assumption of this inference rule, then one also applies logical laws, since one can then ask the question again how to come to this realization. The modus ponens must therefore be viewed as absolute within a binding argumentation, since otherwise no justifications would be possible for statements.

There are three types of deductive inference:

  • Conclusion from the general to the particular or the less general,
  • Conclusion from the general public to the same general public,
  • Conclusion from the individual to the particular.

Is there deductive thinking in children?

Two examples: The first is from Donaldson (1982), who has compiled compelling evidence to show that children in general (and Piaget in particular) are underestimated in their thinking skills. The second example is a much-cited study by Wason and Johnson-Laird (1972), which shows the low capacity of logically valid inference.

1st example

Using a variety of comments made by children on stories, Donaldson questions the claim that children cannot conclude deductively:

The presented picture shows a wedding in which the man looks more like a woman. The child takes it for a picture of two women and argues: "But how is that possible (that they get married)? There must be a man there too!"

Premises:

[1] A man must be present at a wedding.
[2] There is no man in the picture.

Enough: It can't be a wedding.

Formalized as an implication, this conclusive consideration reads:

"When there is a wedding, there is a man. There is no man. Therefore, there is no wedding."

If the statements are replaced by the symbols used in logic, the result is the following notation: "If p, then q. Not q. Hence no p."

Anyone who is familiar with propositional reasoning will recognize the "mode tollens": In the case of" negation of the consequence ", the logically valid conclusion is the" negation of the antecedent ".

2nd example

Wason Johnson-Laird gave their student test subjects the task of checking the following rule:

If there is a vowel on one side of the card, then there is an even number on the other. The material was four cards (visible side: E, K, 4, 7), of which only those were to be named that had to be turned over to check whether the rule applies.

The result of the investigation: Only approx. 8% of the test persons named the correct solution (E and 7). The error that almost half of the test subjects made (they chose solutions E and 4) will be discussed later.

If, on the one hand, children can already deductive conclusions, on the other hand, "educated" adults have difficulties logically checking the rules, the following questions arise: How does deductive thinking develop, and what does it depend on, even as an adult logically valid conclusions (or wrong conclusions) come?

Inferential reasoning in children
Deductive thinking
Inductive thinking
Analog closing

Another example

(A) All cats are black.
(B) Felix is ​​a cat.

(C) Felix is ​​black. (!)

That was a Deduction (Conclusion from the Praemissa maior and the Praemissa minor to the conclusion). (C) follows from (A) and (B). We often find this form of reasoning in mathematics and in classical theory logic. The inference is apodictic, this means necessary true. So it is truthful and conservative to that extent.

To deepen

A detailed discussion of the epistemological aspect of induction in connection with the foundation of a scientific psychology can be found in:

Stangl, Werner (1989). Psychology in the Discourse of Radical Constructivism.
Braunschweig: Friedr. Vieweg & Son.
Chapter: The Problem of Deductivism pp. 100-117.
WWW: https://www.stangl-taller.at/STANGL/WERNER/BERUF/PUBLIKATIONEN/PARADIGMA/100DEDUKTIVISMUS/

swell

Oerter, Rolf & Dreher, Michael (1995): Development of Problem Solving. In Oerter, Rolf & Montada, Leo (eds.), Developmental Psychology. Weinheim: PVU.
[stangl] test & experiment: logical empiricism / critical rationalism.
WWW: https://www.stangl-taller.at/
TEST EXPERIMENT / logischerempirismus.html (01-06-26)
Microsoft Encarta 1999.
Bauer Axel W. (2000). Deduction, induction, abduction, and the hypothetical-deductive method in the empirical sciences.
WWW: http://www.uni-heidelberg.de/institute/fak5/igm/g47/bauerabd.htm (01-06-26)
Image: http://med.uni-hd.de/igm/g47/bafelix.gif

  

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