Induction (philosophy)

from Wikipedia, the free encyclopedia
Schematic representation of the relationship between theory, empiricism, induction and deduction as it is classically represented

Induction ( Latin: inducere , “bring about”, “cause”, “introduce”) has meant, since Aristotle, the abstracting conclusion from observed phenomena to a more general knowledge , such as a general concept or a law of nature.

The term is used as the opposite of deduction . A deduction concludes from given conditions on a special case, induction, however, is the opposite way. How this is to be determined has been the subject of controversy, especially since the middle of the 20th century; likewise the question of whether induction and deduction correspond to actual cognitive processes in everyday life or in science, or whether they are artifacts of philosophy.

David Hume took the position that there can be no induction in the sense of a conclusion to general and necessary laws that is mandatory and expands experience. In the 20th century, theorists such as Hans Reichenbach and Rudolf Carnap tried to develop formally exact theories of inductive reasoning. Karl Popper tried vehemently to show that induction is an illusion, that in reality only deduction is used and that it is sufficient. Until his death he made the controversial claim that his deductive methodological approach had actually and finally solved the induction problem.

Various attempts have been made in the course of the 20th century to defend the concept of induction against criticism from, for example, Hume, Nelson Goodman and Popper. In this context, various theories of inductive reasoning and more general inductive methodologies were worked out (in particular with recourse to Bayesian probability theory) and empirical studies were carried out. Questions related to the concept of induction today fall into sub-areas of philosophy of mind , philosophy of science , logic , epistemology , rationality, argumentation and decision theory , psychology , cognitive science and artificial intelligence research .

From a logical point of view, the mathematical procedure of complete induction is not an inductive conclusion; on the contrary, it is a deductive method of proof .

Induction logic

Induction logic deals with the question of whether there is a valid scheme that allows conclusions to be drawn about general statements from individual observations and facts. In valid deductive arguments, the conclusion necessarily follows from the premises. Inductive arguments, on the other hand, are plausible and well confirmed at best. Like deductive arguments, they are not compelling and logically necessary .

Examples
All people are mortal.
Socrates is a human.
Deduction Socrates is mortal.
Socrates is mortal.
Socrates is a human.
induction All people are mortal.

The examples show deduction and induction in the traditional form of syllogistics . In the deductive argument (a singular mode Barbara ) it is concluded from the general statement “All people are mortal” and the existence of a case of this rule “Socrates is a person” that the rule applies in this case. In the inductive argument, however, an observation (“Socrates is mortal”) is regarded as a case, “Socrates is a person” and a general statement is derived from this. In the example above, both deduction and induction come to a true conclusion. In this case, induction does not represent a compelling conclusion, which is shown by the following example, which is logically identical:

Bodo is a dachshund.
Bodo is a dog.
induction All dogs are dachshunds.

Induction can therefore incorrectly evaluate the relationships between concepts. As soon as a dog that is not a Dachshund is found, the conclusion is refuted despite the true premises.

Most important forms of induction closure

Inductive generalization

It is concluded from a partial class on the overall class. The premises of this conclusion are that, on the one hand, a sub-class is contained in an overall class and, on the other hand, all elements of the sub-class have the same property . From these premises it is concluded that all elements of the overall class have this property. Example: I watch a lot of sheep and they are all black. The total class is called “sheep”, the subclass it contains is called “sheep I have observed”, and the “same quality” is called “being black”. Inductive conclusion: all sheep are black. Here are many sheep as a reference made to close the fact that all sheep are black, which does not have to agree, because not all sheep, but many were observed. In addition to the process of inductive closing, this example also illustrates its shortcomings. Although this inference is commonplace - it is, according to Hume, a property of human nature - it can lead to wrong conclusions.

There is a strong tradition of a probabilistic approach in the logical study of induction reasoning . Carnap distinguishes five main types of inductive generalization in his work Inductive Logic and Probability :

Proponents of the truth discussion like Popper (1989) or Hume doubt the possibility of being able to substantiate the truth of scientific hypotheses through inductive generalization. Hume was the first to deal with the induction problem. He was able to show that every attempt at an inductive generalization must succumb to a circular reasoning , because according to Hume one ultimately encounters illegal logical operations with every inductive generalization. That does not mean that Popper would deny the admissibility of generalizations, but he denies the possibility of putting them into a context of justification with individual statements. Ultimately, Popper tries to circumvent this apparent contradiction by rejecting the reasoning as a whole. According to Popper, generalization looks as if it were inductive, but in truth it functions purely deductively, with the establishment of unfounded, speculative generalizations (Popper's view, deductively permissible) as the starting point. Popper therefore uses the term “quasi-induction”.

Inductive partial circuit

An important case of the induction inference is that one part of a class leads to another part of this class. Suppose that two types of bacteria are found to belong to the same class of bacteria, and that the first type of these two classes is found to be responsive to a particular drug. In this case, it is concluded that the second type of bacteria also reacts accordingly to the same drug. A special case of this induction inference is when a subclass of a class implies another element of this class.

Induction conclusion as a statistical law

This form of the induction conclusion is present when a statistical law results as the result of the induction . The probability of the occurrence of a certain property in the elements of a partial class is inferred from the probability of this property occurring in the elements of the overall class. Example: When examining a random sample of students, it is found that 4 percent suffer from dyslexia . From this it can be concluded that probably 4 percent of all students suffer from dyslexia.

Inductive methods by John Stuart Mill

To this day, John Stuart Mill is regarded as one of the main exponents of empirically oriented thinking. Since Mill was a co-founder of utilitarianism , his statements were often criticized only in the light of an "all-inductionism". For Mill, induction was the methodological foundation of all knowledge, which he mainly tried to analyze using methods to investigate individual causal relationships. According to Mill, "induction [...] is that intellectual operation by which we conclude that what is true for a particular case or particular cases will also be true in all cases which are similar to that in any demonstrable relationship" ( Mill, 1980, p. 160). In the sense of “all-inductionism”, according to Mill, any induction can be represented in the form of a syllogism , the major proposition of which is suppressed and is itself an induction. Induction is based on the human tendency to generalize experiences. As a prerequisite for his assumptions, Mill names the axiom of induction, which is itself based on one of the most general inductions and according to which the course of nature is absolutely uniform.

John Stuart Mill describes the following methods for inductive knowledge acquisition ( System of Logic, Vol. I, Book 3, Chapter 8: "Of the Four Methods of Experimental Inquiry" ):

Method of compliance ( Method of Agreement )

"If all the cases in which the phenomenon under investigation occurs have only one circumstance in common, then that circumstance is a cause (or effect) of the phenomenon."

Example:
A patient gets panic attacks in elevators, but also in crowded movie theaters, airplane toilets, etc.
Inductive conclusion: It is the confinement of the rooms that causes the panic attacks.

Method of difference ( Method of Difference )

“If a situation in which the phenomenon under study occurs and another situation in which the phenomenon under study does not occur are exactly the same except for one difference, that difference is the effect, the cause, or a necessary part of the cause of the phenomenon . "

Example:
Scientific experiment with experimental and control group: The experimental group receives a treatment , the control group does not. An effect is observed in the experimental group.
Inductive conclusion: The independent variable causes the effect.
Indirect method of difference ( Indirect Method of Difference , or Joint Method of Agreement and Difference )

“If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance: the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon. "

“If two or more cases in which the phenomenon occurs have only one circumstance in common, while two or more cases in which it does not occur have nothing in common except the absence of that circumstance, then that is the circumstance in which the two meet Groups differentiate between the effect, the cause or a necessary component of the cause of the phenomenon. "

- John Stuart Mill : A System of Logic, Vol. 1, p. 463 in the Google book search
example
Four people have a picnic, two of them get sick.
flow pudding beer Sun healthy
Anne Yes Yes Yes Yes No
Bertie No No Yes No No
Cecil Yes Yes No Yes Yes
Dennis No No No No Yes

Anne (sick) swam in the river, ate pudding, drank beer and was in the sun all the time. Bertie (sick) didn't swim, didn't eat pudding and was often in the shade, but also drank beer. Cecil (healthy): acted like Anne, but did not drink any beer. Dennis (healthy): like Bertie, but didn't drink any beer.

The phenomenon here is Anne and Bertie's illness. What they have in common is that they drank beer. Cecil and Dennis are healthy, however, the phenomenon does not appear here. They differ from the first two in that they did not drink any beer. Again, this is a fact that only Cecil and Dennis have in common.

Inductive conclusion: Either the beer was consumed because of the disease (effect), or the beer caused the disease (cause), or the disease cannot occur without beer (necessary component).

Method of residuals ( Method of Residues )

“ Deduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. "(German:" Remove from a phenomenon that part of which it is already known through previous inductions that it is the effect of certain causes; the rest of the phenomenon is then the effect of the remaining causes. ")

Example:
A patient has three pathological abnormalities in the blood count and three symptoms.
It is already known that two of the symptoms are caused by two of the abnormalities.
Inductive conclusion: the third abnormality causes the third symptom.

Method of simultaneous changes ( Method of Concomitant Variations )

“Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.” (German: “Wenn two phenomena covariate , if also one phenomenon changes whenever another phenomenon changes, there is a causal relationship between the two . ”) This is the method of scientific experimentation ; here one speaks of dependent and independent variables .

Example:
Hillary is given a small dose of medication and feels slightly better.
Hillary is on a medium dose and gets medium improvement.
Hillary was given a large dose and felt greatly improved.
Inductive inference The drug brings about improvement.

Induction problem

It is not immediately clear why and whether an induction circuit is permitted. David Hume discussed this question very clearly . Hume argues as follows: An induction conclusion cannot be analytical , since otherwise a (deductive) logical conclusion would exist here. However, logical conclusions cannot increase wages. An induction inference cannot be synthetically a priori true either , because otherwise propositions inferred with its help would have to be just as true. They could then no longer prove to be wrong a posteriori . But this is an essential characteristic of experience-based sentences. One could argue that one knows from experience that the induction closure works. For this, either a higher-order induction principle is required, the reasoning is broken off or a circular argument is used.

psychology

Without the discourses in philosophy and psychology always having to be sharply separated, the focus of thought psychology is on which inductive conclusions people actually draw, regardless of whether these conclusions are rationally justified. Philip Johnson-Laird's definition is widely accepted: induction is “any thought process that produces a statement that increases the semantic information content of the original (the thought process triggering) observations or premises”. According to this, induction is the production of knowledge from information. According to Johnson-Laird's definition, an important function of induction is the formation of hypotheses : The thinker reduces his uncertainty by assuming a cause for a phenomenon or a general rule. An additional meaning is assigned to the object of thought, which is not necessary, just more or less plausible.

The most important job of induction, however, is to reduce the huge amount of data that the brain has to process. Instead of presenting every single experience with every single object (which is impossible - the so-called tractability - or complexity problem), simplifying categories are constantly being created and projected (see step 3 ); this is the only way to make meaningful behavior possible. Example: “Heavy things” on “feet” - “to drop” - “causes” - “pain”.

If only one rule is postulated without asking about the cause (“The sun rises every morning”, “The rat pushes a lever more often if it is rewarded for it”), one speaks of “descriptive induction”, and then there is also a cause postulated, one speaks of “explanatory induction” or abduction .

“General induction” denotes the conclusion from several observations to a rule (e.g. if one believes to recognize a pattern), “special induction” denotes the conclusion from an individual case to the cause or a general rule.

The induction problem is presented differently in psychology, since the question of what an individual finds convincing (cf. subjective probability ) is an emotional and not a formal one. While one person makes no further attempts after a single experience (e.g. with self-picked mushrooms), another will only come to the inductive conclusion after several failures that the idea was not as good as it initially appeared.

Examples of inductive thinking

Manktelow describes inductive thinking as "what you do when you come to a conclusion based on circumstantial evidence ." He cites typical examples:

  1. the work of the criminal investigation department and the criminal courts (Manktelow: "If induction guaranteed truth, we could replace the judges with logicians.")
  2. the estimation of frequencies and probabilities, such as "looks like it will rain tomorrow"; the discussions about whether there is global warming or whether (youth) crime is increasing
  3. the evolution of heuristics .

For problem solving , S. Marshall cites the example of scheme induction : By repeatedly dealing with a problem type (for example recursion tasks) one can induce a solution scheme and apply it to new problems of the same type.

A special case of inductive thinking is inductive reasoning. For this call Eysenck and Keane as an important purpose, the prediction : If one encounters an object, "dog" that one as classified , one can infer inductively "could bite." So our ancestors didn't have to know every single bear in the forest: Anyone who had a term “bear” that included the attribute “dangerous” could behave in a species-preserving manner.

Induction process

An induction consists of the following work steps:

  1. Pattern recognition (prerequisite for induction): Noticing regularities in the stream of perceptions or in other data pools. Example 1 (for a term): I find an emerald, it is green. I find another emerald, it is also green, etc. Example 2 (for a rule): Yesterday morning the sun rose, the day before yesterday morning the sun rose ...
  2. Categorization or concept formation (the actual induction): Summarize the recognized pattern in one statement. Example 1: Emeralds are green. Example 2: The sun rises every morning.
  3. Projection (useful application of induction, optional): extend the proposition thus found to unobserved objects (in remote places or in the past or future). Example 1: All emeralds found in the future and in other places will be green. Example 2: The sun will rise again tomorrow too.

This so-called "enumerating" method of induction has been known since Aristotle and is based on a generalization of individual cases. In the English-language literature it is therefore called instance based .

It should be noted that the induction of terms (e.g. categories) and rules is not worked out independently by individuals, but is massively influenced by the social context, in particular by education. In one experiment, two groups of toddlers who were younger than a year old and could not speak were given five stuffed cats each. One group was told repeatedly that these were "cats", the other group was not told anything. After a while, both groups were given a stuffed cat and a stuffed bear and it was found that the children in the first group were much more involved with the bear, while the children in the second group played with the two new dolls equally often. This result was interpreted as follows: The children in the first group were given a name for all five objects by the adults, which encouraged them to look for common properties. The bear, which did not share these common characteristics, was recognized as something new.

Special induction closings

Multiple occurrences of a phenomenon are not always required in order to draw conclusions. In everyday life it is often necessary to draw conclusions from a single observation:

The car will not start. Induction: The battery is probably dead.
My toe hurts after putting the shoe on. Induction: There is a stone in the shoe.

As in these examples, these are mostly abductions : From the knowledge I have brought with me that a car does not start when the battery is empty (and that empty batteries are more common than defective starters or the like), I draw the most plausible conclusion that that the battery will probably be empty.

Once you've got your stomach upset, you may never eat mussels again. And those who have the same experience more often will find their conclusions confirmed and increasingly solidified. The motivation and the experience thus play a major role in the induction closing. If such conclusions are inadmissibly generalized and adopted by others, prejudices can arise.

The result of an induction need not be a category, term, or rule. New information can also lead to old rules being relaxed. This rule-based induction method has been studied in particular in AI research . The classic example: For centuries it was believed in Europe that swans were large waterfowl from the duck family, with long necks etc. and white plumage. The new information from Australia that there are also black swans led to the induction conclusion that the well-known rule should be relaxed and now read that swans are large waterfowl from the duck family, with long necks, etc.

credibility

How convincing an induction circuit works depends on several factors. In the case of induction by generalization, the number of summarized individual cases (also called sample size ) has a significant influence: the more examples support a hypothesis, the more trust I can place in it. Example: I meet an Angolan who is extremely polite. I get to know a second Angolan who is also very polite, etc. The (preliminary) judgment is formed in me: Angolans are polite. Counterexamples (I also get to know rude Angolans) can lead me to weaken my judgment ("Almost all / most / many Angolans are polite", so-called subjective probability ) or to reject it completely ("Angolans are not more polite than other people") .

Another criterion for the credibility of an induction conclusion is the variability of the reference class . Reference class is the smallest common generic term for the individual cases in question. If someone is convinced that the members of a reference class are very similar to one another (low variability), a few observations are sufficient to generalize them. However, if the reference class includes very diverse individuals (high variability), many individual observations are necessary before a general judgment is justified. In statistics, this property is called representativeness . For example, a new species of plant was discovered, and the first specimens found all bore sweet-tasting red berries. The inductive conclusion that other specimens will not reproduce differently becomes highly probable after just a few individual observations. However, it is different with the size of the plants: even if the first specimens were all smaller than 20 cm, there is still the possibility that the plant will grow larger in different light and soil conditions. Significantly more finds would be necessary here, in as many different locations as possible, until the induction “This plant species does not grow larger than 20 cm” is convincing.

This last example shows that the observed individual phenomena should cover the entire field of the induced term as far as possible. Example: The information that Ms. A. does not eat redfish, herring, pikeperch, perch, trout, plaice, halibut etc. does not allow the conclusion that Ms. A. is a vegetarian. Despite the many different individual cases, there is a lack of coverage . Only when it becomes known that she does not eat beef, pork, poultry, game, etc., is the term “vegetarian” sufficiently covered and the induction credible.

Induction in the Social Sciences

The general scheme of induction is as follows: Premises: “Z percent of the F are G” and “x is F”, conclusion: “x is G - but only with Z percent probability”.

If the value of Z is close to 100% or 0%, then you are dealing with strong arguments. In the first case: "x is G", in the second case: "x is not G". If the z-score is close to 50%, the conclusion is weak because both arguments are equally supported.

In the social sciences, the latter is often the case. In the social sciences, one often has to be content with "part-part statements". The goal of deriving generally applicable laws of social behavior is abandoned in favor of a "quantifying" representation.

Example:
In electoral research, surveys are carried out with the results of CDU / CSU 39%, SPD 32%, FDP 9%, Linke.PDS 8%, Greens 8% and others 4% (ZDF Politbarometer from June 16, 2006).

The question that the social sciences also have to deal with: "How are inductive universal propositions possible?" Or "How can general laws (" universal propositions ") be derived from individual observations?" Cannot be answered satisfactorily.

The way out of the dilemma is sought in two ways in the social sciences. The deductive nomological scientists of the analytical philosophy of science refer to the “Popper turn” of falsificationism : deduction instead of induction. The scientists of the phenomenological / hermeneutic method largely forego the formulation of universal sentences that are unlimited in space and time, in favor of a subjective interpretative-historical method and are content with spatially and temporally limited statements ( theory of medium range ).

Inductive inference has a heuristic value. A valid induction scheme, which allows one to infer true conclusions from true premises, is logically excluded and only possible with metaphysical assumptions.

Induction in Artificial Intelligence

In Artificial Intelligence , u. a. the PI model ( Processes of Induction , 1986) by Holland, Holyoak and co-workers with induction. In this model, the rules found by induction are divided into static, timeless rules that describe states ( synchronic rules ) and those that describe changes ( diachronic rules ). The synchronous rules can in turn be subdivided into class-forming rules ( categorical rules ) and memory-activating rules ( associative rules ). The diachronic rules are either predictive ( predictor rules ) or determine the reaction to a stimulus ( effector rules ). All of these rules are arranged hierarchically, there are superordinate general and subordinate special rules.

Examples:
categorical, general: "If an object has four legs, it is an animal."
categorical, special: "If an object is a mammal and lays eggs, it is a platypus."
associative: "When the traffic light shows red, activate the meaning of this signal."
predictive: "If I stroke my cat, it will purr."
action activating: "When the phone rings, answer it."

See also

literature

General

  • SA Gelman, JR Star, JE Flukes: Children's use of generics in inductive inference. In: Journal of Cognition and Development 3 (2002), 179-199.
  • SA Gelman, EM Markman: Categories and induction in young children. In: Cognition, 23 (1986), 183-209.
  • SA Gelman: The development of induction within natural kind and artifact categories. In: Cognitive Psychology 20: 65-95 (1988).
  • ML Gick, KJ Holyoak: Schema induction and analogical transfer. In: Cognitive Psychology 15: 1-38 (1983)
  • E. Heit, J. Rubinstein: Similarity and property effects in inductive reasoning. In: Journal of Experimental Psychology: Learning. Memory, and Cognition, 20: 411-422 (1994).
  • JH Holland, KJ Holyoak, RE Nisbett , PR Thagard (eds.): Induction: Processes of inference, learning, and discovery. Cambridge, MA: Bradford Books / MIT Press 1986.
  • Kayoko Inagaki, Giyoo Hatano: Conceptual and Linguistic Factors in Inductive Projection: How Do Young Children Recognize Commonalities between Animals and Plants? in: Dedre Gentner, Susan Goldin-Meadow (eds.): Language in Mind , Advances in the Study of Language and Thought, MIT Press 2003, 313–334
  • Keith J. Holyoak , Robert G. Morrison (eds.): The Cambridge Handbook of Thinking and Reasoning , CUP 2005, various chapters, v. a. 13-36 and 117-242
  • PN Johnson-Laird: Human and machine thinking. Hove, 1993
  • TK Landauer, ST Dumais: A solution to Plato's problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge. In: Psychological Review 104 (1997), 211-240.
  • Ken Manktelow: Reasoning and Thinking. Psychology Press: Hove (GB) 1999
  • Gregory L. Murphy: The Big Book of Concepts. MIT Press 2002, v. a. Cape. 8: Induction, 243-270
  • N. Ross, D. Medin, JD Coley, S. Atran: Cultural and experimental differences in the development of folkbiological induction. In: Cognitive Development 18 (2003), 25-47.
  • SA Sloman: Feature-based induction. In: Cognitive Psychology 25 (1993), 231-280.
  • EE Smith: Concepts and Induction. In: M. Posner (Ed.): Foundations of Cognitive Science. Cambridge: MIT Press 1989

History of philosophy

  • JR Milton: Induction before Hume. British Journal for the Philosophy of Science, 38: 49-74 (1987).
  • Jaakko Hintikka : On the Development of Aristotle's Ideas of Scientific Method and the Structure of Science. In: William Wians (ed.): Aristotle's Philosophical Development: Problems and Prospects , Rowman and Littlefield, Lanham, Maryland 1996, 83-104.
  • Ders .: The Concept of Induction in the Light of the Interrogative Approach to Inquiry. In: John Earman (Ed.): Inference, Explanation, and Other Frustrations , University of California Press, Berkeley 1993, 23-43.

Logic and philosophy of science

  • Alexander Bird : Philosophy of Science , London: UCL Press 1998, chap. 5 and 7, Easy to understand introduction
  • Rudolf Carnap : Logical Foundations of Probability , Chicago, IL: University of Chicago Press, 2nd A. 1962. Classical elaboration of a theory of the induction reasoning.
  • AF Chalmers: What is this Thing Called Science? Open University Press, 3rd A. 1999, chap. 4-6. Very easy to understand introduction
  • Martin Curd , John A. Cover (Ed.): Philosophy of Science: The Central Issues , WW Norton & Co. 1998, esp. 412-432, 495-508. Important classical essays or excerpts and more recent overview articles
  • Nelson Goodman : Fact, Fiction and Forecast , Indianapolis, IN: Hackett Publishing Company, 1955 (3rd A. 1979). Classic formulation of the so-called new induction problem
  • Jaakko Hintikka : Inquiry as Inquiry : A Logic of Scientific Discovery, Kluwer Academic, Dordrecht 1999. Idiosyncratic proposed solution.
  • PN Johnson-Laird: A model theory of induction. International Studies in the Philosophy of Science 8 (1994)
  • Mark Kaplan: Epistemic Issues in Induction. In: Routledge Encyclopedia of Philosophy
  • Philip Kitcher : The Naturalists Return. In: The Philosophical Review 101 (1992), 53-114. Naturalistic proposed solution.
  • Peter Lipton : Inference to the Best Explanation , Routledge, London 1991. Modern classic.
  • Patrick Maher: Inductive Inference. In: Routledge Encyclopedia of Philosophy
  • John D. Norton: A Material Theory of Induction (PDF; 161 kB), in: Philosophy of Science 70 (2003), 647-670.
  • Wesley C. Salmon : Inductive Inference. In: B. Baumrin (Ed.) Philosophy of Science: The Delaware Seminar. New York: Interscience Publishers, 353-70. Classic defense of the pragmatic solution
  • Steven A. Sloman, David A. Lagnado: The Problem of Induction. In: Keith J. Holyoak , Robert G. Morrison: The Cambridge Handbook of Thinking and Reasoning , CUP 2005, 95-116
  • Wolfgang Stegmüller : The Problem of Induction: Hume's Challenge and Modern Answers. In: H.Lenk (ed.) New aspects in the theory of science, Braunschweig 1971 Discussion of the positions of Hume, Carnap and Popper; Confirmation theory as a successor problem to the induction problem
  • Richard Swinburne (Ed.): The Justification of Induction , Oxford: Oxford University Press 1974.
  • Jonathan Vogel: Inference to the best explanation. In: Routledge Encyclopedia of Philosophy

Social sciences

  • Andreas Diekmann (Ed.): Methods of Social Research , Cologne Journal for Sociology and Social Psychology, special issue 44/2004

Web links

Individual evidence

  1. ↑ See for example: Karl R. Popper, David W. Miller: A proof of the impossibility of inductive probability. In: Nature, 302: 687-688 (1983)
  2. ↑ Logic of Research , Section 1
  3. ↑ in the original: "If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon."
  4. ↑ in the original: "If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occuring only in the former: the circumstance in which alone the two instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon. "
  5. ↑ in the original: "Induction is any process of thought yielding a conclusion that increases the semantic information in its initial observations or premises."
  6. ↑ Manktelow, s. Literature list; Originally: what you do when you arrive at a conclusion on the basis of some evidence
  7. ^ Sandra P. Marshall: Schemas in problem solving . Cambridge University Press 1995.
  8. ↑ Michael W. Eysenck , Mark T. Keane: Cognitive Psychology . Psychology Press, Hove (UK), 2000.
  9. ↑ DN Osherson and others (1990): Category-based induction . Psychological Review, 97