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falsifiability

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Falsifiability is an important notion in science (WP) and the philosophy of science. For an assertion to be falsifiable it must be logically possible to make an observation or do a physical experiment that would show the assertion to be false. It is important to note that "falsifiable" does not mean false.

Some philosophers and scientists, most notably Wikipedia:Karl Popper, have asserted that no empirical Wikipedia:hypothesis, Wikipedia:proposition, or Wikipedia:theory can be considered scientific if no observation could be made which might contradict it.

Falsifiability and scientific propositions are distinguished from the practical, psychological, or rhetorical task of convincing an individual person that a proposition may have counterexamples.

Naïve falsification[edit]

Two types of statements: observational and categorical[edit]

In work beginning in the 1930s, Karl Popper gave falsifiability a renewed emphasis as a criterion of empirical statements in science.

Popper noticed that two types of statements are of particular value to Wikipedia:scientists:

  • Statements of observations, such as 'this is a white swan'. Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x which is a swan, and x is white.
    • Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a non-white swan that has somehow avoided observation. Yet some philosophers of science claim that science is based on such an inductive method.
  • Statements of interest to scientists which categorize all instances of something, for example 'all swans are white'. Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white.
    • Scientific laws are commonly supposed to be of the second type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements?

Inductive categorical inference[edit]

[[Wikipedia:Image:Mute.swan.slimb.750pix.jpg|thumb|right|250px|A white Wikipedia:mute swan, common to Wikipedia:Eurasia and Wikipedia:North America.]] [[Wikipedia:Image:Black.swans.slimb.750pix.jpg|thumb|right|250px|Two Wikipedia:black swans, native to Wikipedia:Australia.]] Popper held that science could not be grounded on such an invalid inference. He proposed falsification as a solution to the Wikipedia:problem of induction. Popper noticed that although a singular existential statement such as 'there is a white swan' cannot be used to affirm a universal statement, it can be used to show that one is false: the singular existential observation of a black swan serves to show that the universal statement 'all swans are white' is false - in logic this is called Wikipedia:modus tollens. 'There is a black swan' implies 'there is a non-white swan' which in turn implies 'there is something which is a swan and which is not white', hence 'all swans are white' is false, because that is the same as 'there is nothing which is a swan and which is not white'.

One notices a white swan. From this one can conclude:

At least one swan is white.

From this, one may wish to infer that:

All swans are white.

It may be impossible to observe all the swans in the world to verify that they are all white.

Even so, the statement all swans are white is testable by being falsifiable. For, if in testing many swans, the researcher finds a single Wikipedia:black swan, then the statement all swans are white would not be true; it would be falsified by the counterexample of the single black swan.

Deductive falsification[edit]

The falsification of statements occurs through Wikipedia:modus tollens, via some observation. Suppose some universal statement U forbids some Wikipedia:observation O:

<math>U \rightarrow \neg O</math>

Observation O, however, is made:

<math>\ \ O</math>

So by modus tollens,

<math>\neg U</math>

Although the logic of naïve falsification is valid, it is rather limited. Nearly any statement can be made to fit the data, so long as one makes the requisite 'compensatory adjustments'. Popper drew attention to these limitations in Wikipedia:The Logic of Scientific Discovery in response to criticism from Duhem. W. V. Quine expounded this argument in detail, calling it Wikipedia:confirmation holism. In order to logically falsify a universal, one must find a true falsifying singular statement. But Popper pointed out that it is always possible to change the universal statement or the existential statement so that falsification does not occur. On hearing that a black swan has been observed in Australia, one might introduce the Wikipedia:ad hoc hypothesis, 'all swans are white except those found in Australia'; or one might adopt another, more cynical view about some observers, 'the bird watchers are incompetent'. For example suppose that some existential statement V (such as those expressed in media) implies observation O, rather than having observation O supported on its own merits:

<math>V \rightarrow O</math>

Therefore:

<math>V \rightarrow \neg U</math>
<math>U \rightarrow \neg V</math>

V and other existential statements are the basis for many subject controversies, including Wikipedia:conspiracy theories, Wikipedia:urban legends, and other Wikipedia:myths. People arguing that there is no support for such an observation may argue that there is nothing to see, that all is normal, or that the differences or appearances are too small so as to be statistically insignificant. On the other side are those who concede that an observation has occurred and that a universal statement has been falsified as a consequence. Therefore, naïve falsification does not enable scientists, who rely on objective criteria, to present a definitive falsification of universal statements.

Falsificationism[edit]

Naïve falsificationism is an unsuccessful attempt to prescribe a rationally unavoidable method for science. Sophisticated methodological falsification, on the other hand, is a prescription of a way in which scientists ought to behave as a matter of choice. The object of this is to arrive at an evolutionary process whereby theories become less bad.

Naïve falsification considers scientific statements individually:

  • But scientific theories are formed from groups of these sorts of statements, and it is these groups that must be accepted or rejected by scientists. Scientific theories can always be defended by the addition of ad hoc hypothesis.
    • As Popper put it, a decision is required on the part of the scientist to accept or reject the statements that go to make up a theory or that might falsify it. At some point, the weight of the ad hoc hypotheses and disregarded falsifying observations will become so great that it becomes unreasonable to support the base theory any longer, and a decision will be made to reject it.

In place of naïve falsification, Popper envisioned science as evolving by the successive rejection of falsified theories, rather than falsified statements. Falsified theories are to be replaced by theories which can account for the phenomena which falsified the prior theory, that is, with greater explanatory power:

At each stage, experimental observation made a theory untenable (i.e., falsified it) and a new theory was found which had greater explanatory power (i.e., could account for the previously unexplained phenomena), and as a result, provided greater opportunity for its own falsification.

The criterion of demarcation[edit]

Popper uses falsification as a criterion of demarcation to draw a sharp line between scientific and unscientific theories. It is useful to know if a statement or theory is falsifiable, if for no other reason than that it provides us with an understanding of the ways in which one might assess the theory. One might at the least be saved from attempting to falsify a non-falsifiable theory, or come to see an unfalsifiable theory as unsupportable.

  • If a theory is falsifiable, then it is scientific; if it is not falsifiable, then it is not open to falsification and requires Wikipedia:faith in it not being, in fact, false. Some well-substantiated explanation, serving as useful prose or verbosity to reflect nuances of a statement-supported observation, may be unfalsifiable in principle, in the case that there is no empirically testable event forbidden by the explanation, since its past applicability is no way shaped or threatened by current events, such as humanity's increasing domination over aspects of the natural world (see Wikipedia:Not even wrong).

The Popperian criterion, excludes from the domain of science not unfalsifiable statements but only whole theories which contain no falsifiable statements; thus it leaves us with the Duhemian problem of what constitutes a 'whole theory' as well as the problem of what makes a statement 'meaningful'. His own falsificationism, thus, is not only an alternative to verificationism, it is also an acknowledgement of the conceptual distinction that previous theories had ignored.

Verificationism[edit]

See also Abductive reasoning (WP)

In the Wikipedia:philosophy of science, verificationism (also known as the Wikipedia:verifiability theory of meaning) held that a statement must be in principle empirically verifiable in order to be both meaningful and scientific. This was an essential feature of the Wikipedia:logical positivism of the so-called Wikipedia:Vienna Circle that included such philosophers as Wikipedia:Moritz Schlick, Wikipedia:Rudolf Carnap, and Wikipedia:Otto Neurath, and the Berlin philosopher Wikipedia:Hans Reichenbach, and the Wikipedia:logical empiricism of Wikipedia:A.J. Ayer.

Verifiability came to be replaced by falsifiability as the criterion of demarcation, when Popper noticed that the philosophers of the Vienna Circle had mixed two different problems, and had accordingly given a single solution to both of them, namely verificationism.

In opposition to this view, Popper emphasized that a theory might well be meaningful without being scientific, and that, accordingly, a criterion of meaningfulness may not necessarily coincide with a criterion of demarcation.

  • Falsificationism is neutral with respect to the question of 'meaningfulness'.

Use in Courts of Law[edit]

Criticisms[edit]

Kuhn and Lakatos[edit]

Whereas Popper was concerned in the main with the logic of science, Thomas Kuhn’s influential book Wikipedia:The Structure of Scientific Revolutions examined in detail the Wikipedia:history of science. Kuhn argued that scientists work within a conceptual Wikipedia:paradigm that determines the way in which they view the world. Scientists will go to great length to defend their paradigm against falsification, by the addition of ad hoc hypotheses to existing theories. Changing one's 'paradigm' is not easy, and only through some pain and angst does science (at the level of the individual scientist) change paradigms.

Some falsificationists saw Kuhn’s work as a vindication, since it provided historical evidence that science progressed by rejecting inadequate theories, and that it is the decision, on the part of the scientist, to accept or reject a theory that is the crucial element of falsificationism. Foremost amongst these was Wikipedia:Imre Lakatos.

Lakatos attempted to explain Kuhn’s work by arguing that science progresses by the falsification of research programs rather than the more specific universal statements of naïve falsification. In Lakatos' approach, a scientist works within a research program that corresponds roughly with Kuhn's 'paradigm'. Whereas Popper rejected the use of ad hoc hypotheses as unscientific, Lakatos accepted their place in the development of new theories.

Kuhn's work has also been seen as showing that sociological factors, rather than adherence to a prescriptive rational method, play the determining role in deciding which scientific theory is accepted.

Feyerabend[edit]

Wikipedia:Paul Feyerabend examined the history of science with a more critical eye, and ultimately rejected any prescriptive methodology at all. He rejected Lakatos’ argument for ad hoc hypothesis, arguing that science would not have progressed without making use of any and all available methods to support new theories. He rejected any reliance on a scientific method, along with any special authority for science that might derive from such a method. Rather, he claimed, ironically, that if one is keen to have a universally valid methodological rule, anything goes would be the only candidate. For Feyerabend, any special status that science might have derives from the social and physical value of the results of science rather than its method.

Physicists[edit]

In their book Wikipedia:Fashionable Nonsense (published in the UK as Intellectual Impostures) the two physicists Wikipedia:Alan Sokal and Wikipedia:Jean Bricmont have criticized falsifiability on the grounds that it does not accurately describe the way science really works. They argue that theories are used because of their successes, not because of the failures of other theories. Their discussion of Popper, falsifiability and the philosophy of science comes in a chapter entitled "Intermezzo," which contains an attempt to make clear their own views of what constitutes truth, in contrast with the extreme epistemological relativism of postmodernism.

Sokal and Bricmont write, "When a theory successfully withstands an attempt at falsification, a scientist will, quite naturally, consider the theory to be partially confirmed and will accord it a greater likelihood or a higher subjective probability. ... But Popper will have none of this: throughout his life he was a stubborn opponent of any idea of 'confirmation' of a theory, or even of its 'probability'. ... [but] the history of science teaches us that scientific theories come to be accepted above all because of their successes." (Sokal and Bricmont 1997, 62f)

They further argue that falsifiability cannot distinguish between astrology and astronomy, as both make technical predictions which are sometimes incorrect.

Examples[edit]

Claims about verifiability and falsifiability have been used to criticize various controversial views. Examining these examples shows the usefulness of falsifiability by showing us where to look when attempting to criticise a theory.

Non-falsifiable theories can usually be reduced to a simple uncircumscribed existential statement, such as there exists a green swan. It is entirely possible to verify that the theory is true, simply by producing the green swan. But since this statement does not specify when or where the green swan exists, it is simply not possible to show that the swan does not exist, and so it is impossible to falsify the statement.

That such theories are unfalsifiable says nothing about either their validity or truth. But it does assist us in determining to what extent such statements might be evaluated. If evidence cannot be presented to support a case, and yet the case cannot be shown to be indeed false, not much credence can be given to such a statement. However, you can also look at this case from another perspective. Let's say that the statement is "all swans are not green". An attempt to verify this positively would require a search for non-green swans, which you are sure to find. However, having rounded up and examined every known swan, there is always the possibility that there is at least one more swan but we will never know for sure until we find it and if we do, there may be yet, one more swan, and it may be green. On the other hand we may say that "all swans are not green" but instead of attempting to positively verify this statement we attempt to falsify it by looking for a green swan. In that case we need only find one swan (a green one), in the absence of which we can accept the original statement as a working hypothesis until such a swan is discovered.

Logic and mathematics[edit]

The question may be raised as to whether the theorems of logic and Wikipedia:mathematics are falsifiable or not. After all, they appear on first encounter to be unexceptionally true. In considering this question it is helpful to introduce a classical distinction that is frequently emphasized in this connection by Charles Sanders Peirce. On the one hand, he defines a positive science as "an inquiry which seeks for positive knowledge", that is, for knowledge that can be expressed in a categorical proposition (Peirce, EP 2, 144). He goes on to say the following of the Wikipedia:normative sciences, namely, Wikipedia:logic, Wikipedia:ethics, and Wikipedia:aesthetics:

Logic and the other normative sciences, although they ask, not what is but what ought to be, nevertheless are positive sciences since it is by asserting positive, categorical truth that they are able show that what they call good really is so; and the right reason, right effort, and right being of which they treat derive that character from positive categorical fact. (Peirce, EP 2, 144).

On the other hand, Peirce distinguishes mathematics proper from all positive sciences, and reckons it more fundamental than any of them, saying that any positive science "must, if it is to be properly grounded, be made to depend upon the Conditional or Hypothetical Science of Pure Mathematics, whose only aim is to discover not how things actually are, but how they might be supposed to be, if not in our universe, then in some other" (Peirce, EP 2, 144).

In this way of looking at things, logic is a science that seeks after knowledge of how we ought to conduct our reasoning if we want to achieve the goals of reasoning. As such, the logical knowledge that we have at any given time can easily fall short of perfection. Thus rules of logical procedure, as normative claims about the fitness of this or that form of inference, are falsifiable according to whether their actual consequences are successful or not.

Pure mathematics, on the contrary, contains no propositions that are not contingent on prior assumptions. Its apparent certainty is but a relative certainty, relative to the axioms and definitions that are taken as the basic descriptions of one or another hypothetical universe. One can say that its theorems are tautologies, so long as one remembers the original meaning of tautology, which is a repetition of something previously asserted. Mathematical theorems merely say more acutely what the axioms more obtusely already say.

Applied mathematics, in particular, mathematics as applied in empirical science, is still another thing. The application of mathematical abstractions to a domain of experiential phenomena involves a critical comparison of many different mathematical models, not all of them consistent with each other, and it normally leads to a judgment that some of the hypothetical models are better analogues or more likely icons than others of the empirical domain in question. This is, of course, an extremely fallible business, and each judgment call is subject to revision as more empirical data comes in.

How well a mathematical formula applies to the physical world is a physical question, and thus testable, within certain limits. For example, the proposition that all objects follow a parabolic path when thrown into the air is falsifiable; indeed, it is false. To see this, one has but to think of a feather. A slightly better proposition is that all objects follow a parabolic path when thrown in a Wikipedia:vacuum and acted upon by gravity, which is itself falsified in regard to paths whose lengths are not negligible in proportion to a given planet's radius.

What is the conclusion then? Are mathematical theorems falsifiable or not? The most that can be said of them is that they are true of what they are true of, but what they are true of may not be the object of a given experience, and thus there can be things of which they are false.

The above discussion addressed the nature of mathematical theorems in and of themselves, and then took up their application to empirical phenomena. But the actual practice of mathematics involves yet another level of consideration, and it may yet involve activities that are very similar to empirical science. Many working mathematicians, from Peirce in his day to Wikipedia:Stephen Wolfram in ours, have remarked on the active, observational, and even experimental character of mathematical work. Wikipedia:Imre Lakatos brings the concept of falsifiability to bear on the discipline of mathematics in his Wikipedia:Proofs and Refutations. The question of whether mathematical practice is a quasi-experimental science depends in part on whether proofs are fundamentally different from experiments. Lakatos argues that axioms, definitions, and proofs evolve through criticism and counterexample in a manner not unlike the way that a scientific theory evolves in response to experiments.

Ethics[edit]

Ethical statements such as "murder is evil" or "John was wrong to steal that money" are not usually considered to be falsifiable. The meta-ethical thesis that ethical statements have no truth-value is called Wikipedia:non-cognitivism.

Theism[edit]

Wikipedia:Theism may not be falsifiable, if the existence of Wikipedia:God is asserted without sufficient conditions to allow a falsifying observation. If God is an unobservable transcendental being then one cannot disprove his existence by observation. It remains quite consistent for a theist to agree that the existence of God is unfalsifiable, and even that the proposition 'God exists' is not scientific, but is a matter of faith alone. Theists may also claim to have presentable evidence that verifies the existence of God. This is, of course, a matter of interest for anyone who places stock in witnesses who claim to have seen God or ideas like Wikipedia:natural theology—the argument from design (WP) and other a posteriori arguments for the Wikipedia:existence of God. (See Wikipedia:non-cognitivism.) However, arguments relating to alleged actions and eye-witness accounts, rather than to the existence of God, may be falsifiable. See Wikipedia:nontheism for further information.

Conspiracy theories[edit]

Conspiracy theories are often essentially unfalsifiable because of their logical structure. Specifically, they may take the form of uncircumscribed existential statements, alleging the existence of some action or object without specifying the place or time at which it can be observed. So, for instance, one might claim that there are Wikipedia:little green men without saying when or where, and furthermore that their existence is kept secret by a conspiracy. In this case, failure to find any little green men does not falsify the conspiracy theory, but rather is claimed as verification of the conspiracy to hide their existence. Such a conspiracy theory cannot be shown to be false.

Economics[edit]

Aspects of Wikipedia:economics have been accused of not being falsifiable, mainly by sociologists (WP) and other social scientists in general.

The most common argument is made against Wikipedia:rational expectations theories, which work under the assumption that people act to maximize their Wikipedia:utility. However, under this viewpoint, it is impossible to disprove the fundamental theory that people are utility-maximizers. The political scientist(WP) Wikipedia:Graham T. Allison, in his book Wikipedia:Essence of Decision, attempted to both quash this theory and substitute other possible models of behavior.

Historicism[edit]

Theories of Wikipedia:history or politics which allegedly predict the future course of history have a logical form that renders them neither falsifiable nor verifiable. They claim that for every historically significant event, there exists an historical or economic law that determines the way in which events proceeded. Failure to identify the law does not mean that it does not exist, yet an event that satisfies the law does not prove the general case. Evaluation of such claims is at best difficult. On this basis, Popper himself argued that neither Marxism (WP) nor Wikipedia:psychoanalysis were science, although both made such claims. Again, this does not mean that any of these types of theories are necessarily incorrect. Popper considered falsifiability a test of whether theories are scientific, not of whether propositions they contain or support are true.

Memetics[edit]

The model of cultural evolution known as Wikipedia:memetics is as of yet unfalsifiable, as its practitioners have been unable to determine what constitutes a single meme, and more importantly, what determines the survival of a meme. For the theory to be falsifiable, more exact accounts of this are needed, as currently every outcome of cultural evolution can be explained memetically by suitable choice of competing memes. This does not, however, mean that all epidemological theories of social and cultural spread are unscientific, as some of them have (mostly due to smaller scope) more exact terms of transmission and survival.

Solipsism[edit]

Wikipedia:Metaphysical solipsism is the view that the individual self of the solipsistic philosopher is the whole of reality and that the external world and other persons are representations of that self having no independent existence (Wood, p. 295). Metaphysical solipsism is not falsifiable because once one has taken the solipsistic position, any evidence that might establish an external world is already viewed as being within (or produced by) the self. Anti-solipsism--the position that an external world does exist--is also non-falsifiable because regardless of what evidence is produced, it is always possible that one's experiences of an external world are mere illusions.

Physics[edit]

The laws of Wikipedia:physics are an interesting case. Occasionally it is suggested that the most fundamental laws of physics, such as "force equals mass multiplied by acceleration" (F=ma), are not falsifiable because they are definitions of basic physical concepts. More usually, such formulas are regarded as falsifiable laws. As summarized in the introduction of this article, it must only be logically possible to falsify a basic law of physics for it to qualify as falsifiable. That is, the proposition (in this case a law of physics) must define what is forbidden, and it must be logically possible to observe what is forbidden by the proposition even if the ability to observe possible minor discrepancies is not currently available to establish such a falsification.

In the example of acceleration just mentioned (Newton's Second Law), by definition it is not possible to directly observe a net force of any other magnitude than one Wikipedia:newton causing an acceleration other than one Wikipedia:metre per second squared on a one Wikipedia:kilogram mass, any more than it is possible to directly measure the acceleration of a car. As with many other aspects of nature, an intermediary formula must be used. In this case, F=ma is that intermediary formula. If instances were found in which force was shown to be equal to mass multiplied by something other than acceleration as defined by Newton's calculus (say, by the number of hairs on a sled dog, one of the things forbidden by this law), the formula F=ma would be falsified and in need of appropriate modification or qualification (here, say, "except above the Arctic Circle when using a sled dog"). The same principle applies to all three variables in this equation, and also to the definitions of force and acceleration as vectors (often presumed, but always attached as part of the technical definition). Indeed, the falsifiability of acceleration-related formulas is well illustrated by the famous modifications which the theory of relativity superimposed on the theory of gravity. Wikipedia:Newton's law of universal gravitation in its original form was thus falsified by experiments in the twentieth century (eg, the anomaly of the motion of Mercury, the slightly skewed behavior of light passing sufficiently close to a star, etc), and replaced by a theory which was consistent with those phenomena, general relativity. Further evidence of the falsifiability of relativity theory is, for instance, provided by its well-known use to accurately predict the necessary paths for space-shuttle rendezvous; relativity would be quickly falsified by errors in intended flight path that were not attributable to malfunction or human error--such errors between predicted flight path and observed flight path would easily be measured in kilometers. Newton's account of motion remains a precise enough approximation for the vast majority of human needs. It nonetheless remains a matter of some controversy in the philosophy of science what to regard as evidence for or against the assertion that the most fundamental laws of physics are falsifiable.

The range of available testing apparatus is also sometimes an issue - when Galileo showed Wikipedia:Roman Catholic Church scholars the moons of Jupiter, there was only one telescope on hand, and telescopes were a new technology, so there was some debate about whether the moons were real or possibly an artifact of the telescope or of the type of telescope. Fortunately, this type of problem can usually be resolved in a short time, as it was in Galileo's case, by the spread of technical improvements. Diversity of observing apparatus is quite important to concepts of falsifiability, because presumably any observer with any appropriate apparatus should be able to make the same observation and so prove a thesis false.

Quotes[edit]

  • No amount of experimentation can ever prove me right; a single experiment can prove me wrong. — Wikipedia:Albert Einstein
  • The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability. - Wikipedia:Karl Popper

References[edit]

  • Angeles, Peter A. (1992), Harper Collins Dictionary of Philosophy, 2nd edition, Harper Perennial, New York, NY. ISBN 0-06-461026-8.
  • Feyerabend, Paul K., Wikipedia:Against Method: Outline of an Anarchistic Theory of Knowledge, Humanities Press, London, UK, 1975. Reprinted, Verso, London, UK, 1978.
  • Kuhn, Thomas S., Wikipedia:The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL, 1962. 2nd edition 1970. 3rd edition 1996.
  • Peirce, C.S., "Lectures on Pragmatism", Cambridge, MA, March 26 – May 17, 1903. Reprinted in part, Collected Papers, CP 5.14–212. Reprinted with Introduction and Commentary, Patricia Ann Turisi (ed.), Pragmatism as a Principle and a Method of Right Thinking: The 1903 Harvard "Lectures on Pragmatism", State University of New York Press, Albany, NY, 1997. Reprinted, pp. 133–241, Peirce Edition Project (eds.), The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Indiana University Press, Bloomington, IN, 1998.
  • Popper, Karl, Wikipedia:The Logic of Scientific Discovery, Basic Books, New York, NY, 1959.
  • Runes, Dagobert D. (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ, 1962.
  • Sokal, Alan, and Bricmont, Jean, Wikipedia:Fashionable Nonsense, Picador, New York, NY, 1998.
  • Theobald, D.L. (2006). 29+ Evidences for Macroevolution: The Scientific Case for Common Descent. The Talk.Origins Archive. Version 2.87.
  • Wood, Ledger (1962), "Solipsism", p. 295 in Runes (ed.), Dictionary of Philosophy, Littlefield, Adams, and Company, Totowa, NJ.

See also[edit]

External links[edit]

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