A logical fallacy is an error in logical reasoning. While the common usage of the word fallacy would include any error in reasoning, in logic a fallacy is defined as a particularly deceptive argument which seems correct, but upon further examination is found to be incorrect. The maker of such an argument, however, need not be aware of its fallacious nature.
Logical fallacies fall into two general categories: formal fallacies and informal fallacies. Formal fallacies apply to deductive arguments, and are those which relate to an improper application of a rule, whereas informal fallacies apply to inductive arguments, and are those which involve the improper use of the content of an argument.
There are four categories of informal fallacies: fallacies of relevance, fallacies of defective or weak induction, fallacies of presumption, and fallacies of ambiguity.
A logical fallacy is not the same as lying, although it is still an error if you commit one (and dishonest if you know you are committing one). A lie in logic is a premise that one offers while knowing that it is false.
- 1 Fallacies of Relevance
- 1.1 Appeal to force
- 1.2 Appeal to pity
- 1.3 Appeal to Consequences
- 1.4 Argumentum ad hominem
- 1.5 Genetic fallacy
- 1.6 Proof by numbers
- 1.7 Special pleading
- 1.8 Fallacies of relevance based on the age of an idea
- 2 Fallacies of Defective or Weak Induction
- 3 Fallacies of Presumption
- 4 Fallacies of Ambiguity
- 5 Atheism and logical fallacies
- 6 References
- 7 See also
- 8 External links
Fallacies of Relevance
Appeal to force
- If person A does not accept P, then Q
- Q is a threat of force
- Therefore, P is true
For example: "If you do not pay me $30 I will break your leg. Therefore you owe me $30." Another example: "Might makes right." Or, the threat of persecution, rebellion, revolt or war.
This appeal is fallacious because no amount of force can change the truth or falsity of the initial proposition.
See Trial by combat.
Appeal to pity
- Person A argues P
- Person B agrees P, but adds X, where X is an emotional argument unconnected to P
For example: "Yes, officer, I realize I was speeding, but you shouldn't give me a ticket because I was racing to see my wife who is in the hospital." While this argument uses an emotional appeal to convince the officer not to hand out a citation, there is no logical connection between the conclusion ("you shouldn't give me a ticket") and the premise ("I was racing to see my wife").
Appeals to pity are very commonly seen in business. A factory manager may make the following argument: "our factory's overheads are too high, and we cannot maintain our business if we continue here. Therefore we should relocate to an area where labor is cheaper." An appeal to pity would be of the following type: "but our workers have bills to pay, families to support, we cannot fire them." That statement may be true, but is fallacious because it is not relevant to the manager's argument.
Appeal to Consequences
An appeal to consequences, or, more fully, appeal to adverse consequences or appeal to consequences of a belief, is an attempt to motivate belief with an appeal either to the good consequences of believing or the bad consequences of disbelieving. This may or may not involve an appeal to force. Such arguments are fallacious because the consequences of believing or disbelieving have no bearing on the truth or falsity of a belief. The following is an example:
- If you believe in evolution, then you'll be miserable, thinking that life is meaningless
- Therefore, evolution is false
This argument commits the appeal to consequences fallacy because it provides no evidence for its conclusion; all it does is appeal to the consequences of believing in evolution. Evolution is not disproven because it leads to bad consequences for those who believe in it. The following is a similar example:
- If you believe in evolution, then you'll be more respected in academic circles
- Therefore, evolution is true
This makes an appeal to the positive consequences of believing in evolution, without actually providing any proof of evolution itself. Just because belief in evolution makes you more respected in academic circles, this does not mean that evolution is correct.
To use another example often encountered in the real world, adherents of belief systems such as Islam tout the benefits of converting to such belief systems. However, such benefits, even if real, do not prove that those belief systems are true; instead, they could arise from the conversion experience itself.
A particular form of the appeal to consequences is the appeal to personal interest, which is fallacy of appealing to the personal likes and interests (preferences, prejudices, predispositions, fears, etc.) of others in order to have an argument accepted, when those personal likes and interests are irrelevant to the truth or falsity of the argument.
Argumentum ad hominem
- Main Article: Ad hominem
Ad hominem arguments (Lat: "argument directed toward the man") fall into two forms: ad hominem abusive and ad hominem tu quoque (circumstantial).
Ad hominem abusive
An ad hominem is an argument which tries to disprove another argument by attacking the person who made it, rather than by focusing on the actual logical reasoning. The goal of an ad hominem argument is usually to take focus off of the actual argument by calling attention to a flaw of the person making it. This form of argument follows the form:
- Person A argues that P
- Person A is Q
- Q is some derogatory description not related to the argument at hand
- Therefore, P is false
Ad hominem tu quoque
A tu quoque argument (Lat: "you're another") is one which argues that, because someone does that which they are arguing against, that person must be wrong. This form of argument follows the form:
- Person A argues that P should not happen
- Person A does P
- Therefore, Person A's argument is incorrect
For example: "You can't tell me not to eat cheeseburgers, I just saw you eating one last week!" Another common example is often found in business: "why are you punishing me for dumping waste in the river? My rival does the exact same thing and you don't punish him!" In this case, dumping waste into the river is wrong (and illegal) regardless of how it is enforced for any other company.
A false causality fallacy is when a person argues that A caused B when there is little evidence to support the claim. Specifically, a false causality is committed when the basis for A causing B is based on some superficial coincidence.
- "Our house was robbed the day after that family moved in, they must have done it!"
In this example, it is only a coincidence that a new family has moved in at the same time another house has been robbed, and this is not grounds for evidence.
Poisoning the well
Poisoning the well is a particular type of ad hominem argument. It consists of attempts to discredit a speaker (and, by extension, their argument) by criticizing unrelated opinions that they hold or, alternatively, by presenting unfavorable information (be it true or false) about the person to discredit in advance any argument that that person may make. The first variant of the argument follows this form:
- Person A makes argument X.
- Person B counters that person A also believes Y, where Y is something unacceptable, foolish, or easily disprovable, but unrelated to X.
- Person A is wrong about Y.
- Therefore, person A must also be wrong about X.
The second variant follows this form:
- Person B, knowing that person A will make argument X, introduces unfavorable information about person A that is unrelated to X.
- Person A makes argument X.
- Therefore, person A must be wrong about X.
|“||You know, the hockey mom, you know, "I'm just a hockey mom from Alaska," and she's the president. And it's like she's facing down Vladimir Putin and you know, using the folksy stuff she learned at the hockey rink, you know, it's just absurd. It's totally absurd, and I don't understand why more people aren't talking about how absurd it is. I...it's a really terrifying possibility. The fact that we've gotten this far and we're that close to this being a reality is crazy. Crazy. I mean, did she really - I need to know if she really thinks dinosaurs were here 4000 years ago. That's an important - I want to know that. I really do. Because she's gonna have the nuclear codes. You know, I wanna know if she thinks dinosaurs were here 4000 years ago, or if she banned books or tried to ban books. I mean, you know, we can't have that.||”|
An example of the second variant is to introduce information (true or false) about a distateful or objectionable aspect of someone's personal life to persuade the listeners to reject out of hand whatever that person may say, when that aspect of the person's personal life may have nothing to do with the truth or falsity of the positions that that person will take.
When spelled out in the above form, the fallacy is easily seen, but it is used very frequently in political debate where skillful use of rhetoric can mask the underlying fallacy. The argument is fallacious because a person's opinions on one subject do not affect the truth or falsity of their statements on other subjects or because the asserted unfavorable information has no bearing on the truth or falsity of the position being attacked. There is some overlap between poisoning the well and ad hominem abusive, although poisoning the well in the second sense is used to mean introducing the irrelevant information preemptively.
For a more detailed treatment, see Affirming the consequent.
In general, this is the attempt to assert or reject a theory by citing its origins as either reputable or disreputable. The usual expression of this fallacy is "consider the source!" Thus it becomes a form either of argumentum ab auctoritate or of argumentum ad hominem, depending on whether one seeks to verify or disprove the theory by this method. This type of argument follows the form:
- If P then Q
- P is false
- Therefore, Q is false
Formally, the error arises in confusing "If P, then Q" with "If and only if P, then Q."
When the origin of evidence or of premises is relevant to the reliability of the same, then asking a hearer to "consider the source" is valid. Judges in courts of law, for example, routinely reject as unreliable the testimony of any witness who has demonstrably lied about a point that matters in the case at hand. The facts that such a witness is asserting might still be true, but they cannot stand without corroboration from another, more reliable witness.
But when corroboration is established, the origins of a conclusion, however tainted, become irrelevant.
As an example, Gregor Mendel established the genetic theory that remains current today, even though Mendel's experimental technique was badly flawed, and he even stands accused of falsifying key data. But succeeding scientists, using accepted methods of verification and statistical assessment, have achieved results consistent with this theory. Thus the theory remains valid even though Mendel's original presentation was fraudulent. Any attempt today to discredit Mendel's theory on account of Mendel's sloppy methods would be an example of a genetic fallacy.
Proof by numbers
For a more detailed treatment, see Argumentum ad populum.
Also known as "appeal to the people" (Lat: ad populum), this is an argument that a person bases on the numbers of people holding to its conclusion, rather than on the premises that might support that conclusion. An appeal to the people follows the form:
- Most people believe P
- Therefore P is true
"Ninety nine point nine percent of all respondents can't be wrong" is the classic phraseology of this fallacy One does not effectively disprove such an argument by challenging the numbers. Instead, one reminds the other person that the numbers of people holding to any given conclusion are irrelevant to establishing the truth or falsehood of that conclusion. History is in fact replete with multiple examples of conclusions that memorable scientists and other great discoverers have shown to be false even though large numbers of people believed them. Antoine Lavoisier, who disproved "phlogiston" as the principle of fire, was one such person. Christopher Columbus and Ferdinand Magellan are two others. After all, millions of people believed in the roman gods, but they were proven wrong.
The converse argument holds that because a position is unpopular and controversial, even ridiculed, denounced and persecuted by the majority, and has been proven by the majority to be in error, that that position is ipso facto (by the fact) proven to be correct and true. For example: Elitism, Racism, Sects, Cults, International Flat Earth Society, LGBTQIAPK supporters.
- Main Article: Special pleading
Special pleading means applying to other people a set of standards that one is not willing to apply to oneself, without offering sufficient grounds, called the relevant difference, to support such exemption. Special pleading follows the form:
- If Person X is in set P then Q happens to person X
- Person A is in set P
- Person A cites R circumstance, unrelated to P or Q
- Therefore, Person A is not subject to Q
For example: a political or military leader who urges his subjects (or those under his command) to observe "iron rations" without similarly depriving himself leaves himself open to a charge of special pleading.
Fallacies of relevance based on the age of an idea
The appeal to antiquity, also known as the appeal to tradition, holds that an idea must be right just because it is old. Its opposite is the appeal to novelty, which holds that an idea must be right just because it is new. Both are fallacies of relevance because the mere age of an idea does not tell us whether it is true. For example, an old idea could be a time-tested and sound concept, or it could be an ancient superstition like astrology. Similarly, a new idea could be the result of new information or an intellectual fad like postmodernism.
Fallacies of Defective or Weak Induction
Fallacies of defective or weak induction are fallacies which are due to a lack of understanding for how well premises lead to a conclusion.
Argument from silence
Argument from silence (in Latin, argumentum ab silencio) or argument from ignorance (Lat: ad ignorantiam) is an assertion which states that, because there is no evidence to support a given argument, the opposite must be true. The fallacy follows the form:
- If P then Q
- P cannot be shown true
- Therefore, Q is false
For example: "Nobody has ever seen God, so clearly he doesn't exist".
This fallacy is often associated with and best remembered by the phrase: "the absence of evidence does not constitute evidence of absence." However, sometimes, absence of evidence can be so overwhelming that it constitutes strong evidence of absence. Such a situation arises when we have good reason to believe that the absent evidence would have been uncovered by now if it existed. For example, since evidence of the existence of the Loch Ness Monster would surely have come to light by now, but has not done so, it is reasonable to assume that the Loch Ness Monster does not exist, i.e., that the null hypothesis is true. In such cases, absence of evidence, while perhaps not conclusive, is strong evidence of absence.
Another example from history. Assertions of evidence of corruption of Christian doctrine and apostasy from the faith is seen by Protestant and Fundamentalist apologists in the evident contrast of the 16th century doctrines of the Protestant Reformation, which the Reformers assert was original Christianity, against the clearly "Catholic doctrines" in the Ante-Nicene Fathers which refute them. The utter historical silence about any fundamental paradigm shift in doctrine after the first century is due to a total lack of any supporting extant evidence of Protestant or Mormon theology in any of the writings of the first four centuries of Christianity by any of the known heretics and sects. This very fact is argued by Protestants and Mormons as sure and certain evidence that a monstrous apostasy must have occurred, because there is no evidence that it ever did, and no evidence of their unmistakable doctrines can be found, leading them to the conclusion that there was a massive cover up. (This is also a form of circular reasoning. Compare Memory hole and Revisionism.)
More generally, assertion of a fact coupled with total absence of evidence does not prove there was a concerted effort involving total removal of the evidence supporting the assertion. The compelling weight of conclusive evidence supporting absence of any evidence of a removal of all evidence is strong evidence that no evidence was removed. Absence (silence) of evidence is not proof of evidence erased or made absent (silenced). Conclusive evidence of absence is absence of conclusive evidence. Compare Abductive reasoning and Confirmation bias.
A particular form of the argument from silence is the argument from personal incredulity, which takes the form "I cannot believe/understand/explain P; therefore, not-P." For example, someone who does not understand why God would condemn homosexuality or condemn sinners to eternal hell may commit this fallacy and conclude that the relevant Bible passages should be rejected. Another particular form is the black-swan fallacy.
False cause (Lat: non causa pro causa) is a fallacy which arises when a poor cause/effect link is used within an argument, especially if coincidence or chance are not taken into account. The fallacy follows the form:
- P is true.
- Q is true.
- Therefore, P causes Q.
For example: "I used to be a well paid teacher until I started being a tougher grader. When my students' grades went down, so did my salary. Therefore, I must have been paid based on my students' grades." While this sounds like a logical explanation, not all factors are taken into account. For example, the teacher's school could have been subject to budget cuts, or maybe the teacher was overpaid at first and now his salary corrects his true worth.
Post hoc ergo propter hoc
For a more detailed treatment, see Post hoc ergo propter hoc.
Post hoc ergo propter hoc (Lat: "after this; therefore, because of this") is a subcategory of false cause fallacies. In this type of argument, a close temporal proximity is used as a justification of a cause/effect relationship. Post hoc ergo propter hoc arguments follow the form:
- P happened, and then Q happened
- Therefore, P caused Q
For example: "Right around the time the sun goes up my alarm clock goes off, so the sun causes my alarm clock to go off." Clearly this is not the case.
Texas sharpshooter fallacy
- Main article: Sharpshooter fallacy
Another form of false cause is the Texas sharpshooter fallacy. The name comes from a failed marksman who shoots at a barn, draws a bullseye around the biggest cluster of bullet holes, and proclaims himself to be a skilled marksman. In the fallacy, a cluster of data points is assumed to be caused by an apparent cause at that location. The assumption is fallacious because the clustering could be random, or there could be some other cause. Other ways of explaining the fallacy are that the hypothesis is constructed after the fact to conform to the very data that are used to "test" the hypothesis and that the same data are used to formulate and test the hypothesis.
Equating correlation with causation
- Main article: Correlation is not causation
Yet another form of false cause is equating correlation with causation. An often cited example is "As sales of ice cream rise, so do reports of shark attacks." Neither one causes the other, whether or not there is a correlation; instead, they are both associated with summer.
- Main Article: Non sequitur
A non sequitur (Lat: "It does not follow") is an argument which moves from a premise to a conclusion without showing a valid connection, or sometimes any connection at all. This form of argument follows the form:
- Therefore, R is true
For example: "Crime rates are high, so we should increase the penalty for drug possession."
Overgeneralization (also called hasty generalization, converse accident, or painting with too broad a brush) is an error in reasoning which comes about by making a logical leap far greater than what the data allow. Overgeneralization follows the form:
- P is/does Q.
- P is a member of the set R.
- Therefore, everyone/everything in the set R is/does Q.
For example: "I just read that three kids were arrested yesterday for drug possession. Teens in this country are really going downhill!"
Overgeneralization the central problem in trying to conclude something about a population from a non-representative sample, or about a larger group from a non-representative subset of that group.
Proving too much
Proving too much is a form of overgeneralization in which one attempts to use a set of premises to sustain more conclusions than he can reasonably sustain using the argument presented. Proving too much includes reaching a conclusion that contradicts either things known to be true or the premises used to reach that conclusion. The term comes from the medieval saying, "What proves too much proves nothing."
Also known as argumentum ab auctoritate ("argument proceeding from clout") or argumentum ad verecundiam ("appeal to unqualified authority"), this is an argument that a person bases on authority, either his own or that of another person, rather than on the merits of the position. When the authority involved is a relevant source who has access to more information about the topic than the people discussing it, then the argument becomes a citation. However, a valid citation must be in an area of study, research, or mental discipline in which the authority being cited is a recognized expert.
- P says Q
- P is an authority in his field
- Therefore, Q is true
A classic example of argument from unqualified authority is a reference to a celebrity or religious leader for their opinion on a matter of science or public policy, when that celebrity or cleric has never adequately studied the subject. A standard argument from authority is often used by evolutionists. A notable scientist claims that evolution is true, and based on that the average person is expected to believe in it as well. This becomes fallacious if the "notable scientist" has never considered alternatives which also provide the answers to the asked questions.
Fallacies of Presumption
Fallacies of presumption are fallacies in which an unstated or shaky presumption is made.
The fallacy of accident occurs when a generalization is inappropriately applied to an individual. A fallacy of accident follows the form:
- Some P are Q
- R is in P
- Therefore, R is Q
For a more detailed treatment, see Fallacy of analogy.
The fallacy of analogy argues that because one thing resembles another in some aspects, they must resemble each other in another aspect. In its most extreme form, it argues that a superficial resemblance proves identity, that because they look like the same thing they are in fact the same. In general, an argument by analogy takes the following form:
- A is like B (they share properties X, Y, and Z).
- B also has property Q
- Therefore, A has property Q as well.
The strength of such an argument depends upon the strength of the analogy. If A and B have more differences than shared properties, the argument is weakened. It may also be true that A is like B in many ways, but still differs from B in terms of the specific property Q. If the analogy is too weak or irrelevant to the conclusion that is drawn, then a fallacy of weak analogy has been committed. An analogy itself is never true or false; it is only weak or strong.
For a more detailed treatment, see Contradiction.
A contradiction is a statement that contradicts its own terms. Aristotle famously stated that contradictions cannot exist. In any case of a contradiction, some of the premises must be false. A contradiction is an argument which includes in its reasoning:
- Not P
- Main Article: Loaded question
A loaded question is a question that assumes facts, usually unflattering, that are not in evidence, with the intent of trapping the other person into admitting those facts. The classic loaded-question example is "When did you stop beating your wife?" Another example is, "Do you disbelieve in global warming, which 99.9 percent of all reputable scientists now accept?"
Proof by assertion
Proof by assertion is an argument that states something as true without offering supporting evidence or attempting to construct a valid argument. This form of argument follows the form:
- P is true
Often the argument is simply repeated over and over, and no evidence for support is given. Statements beginning with expressions such as "It goes without saying that ..." or "Everyone knows ..." are commonly proofs by assertion.
Proof by assertion can also be broken down into several subcategories of fallacies: circular reasoning, infinite regression, manufacturing facts from a theory, and your theory does not work under my theory, so your theory must be wrong.
For a more detailed treatment, see Circular reasoning.
Circular reasoning, also called begging the question (Lat: petitio principii), is a form of proof by assertion in which one asserts a premise, then asserts a conclusion from that premise (directly or indirectly), and then tries to show that the last conclusion supports the original premise.
- Main Article: Infinite regression
An infinite regression results when one asserts that a given event caused another, and yet that first event requires another, identical event, to cause it. An infinite regression follows the form:
- P1 causes Q1
- Q2 causes P1
- P3 causes Q2
- Q4 causes P3
- And so on, forever
For example: Panspermia, an alternative to abiogenesis as a proposition about the origin of life, suffers from the infinite-regression flaw so long as it fails to state positively what conditions could have brought about an origin of life on a planet other than the earth, other than the alleged mechanism of the "seeding" of life on the earth itself.
Manufacturing facts from a theory
Manufacturing facts from a theory is the assertion as fact of an undemonstrated, unobserved idea for no better reason than that a given theory requires that fact. In law, it is called assuming facts not in evidence. It should not be confused with formulating a prediction to test a hypothesis. False Christians often engage in this fallacy by making baseless assertions as to what God wants that may have no basis in the Bible or even contradict it, but that conveniently support whatever those false Christians would have wanted to believe anyway.
In the early stages of formulating a model, this sort of behavior is acceptable. But when repeated efforts to demonstrate such a new fact have failed, the proper logical response is to discard or revise the theory, and not merely to assume that the "fact" still exists and someone hasn't tried hard enough to find it. This is especially true when someone develops evidence that the inferred "fact" could not possibly exist.
Your theory does not work under my theory, so your theory must be wrong
This fallacy occurs when one theory is judged by the premises and assumptions of another theory, rather than against its own premises and assumptions. This form of fallacy follows the form:
- Theory A says that if P then Q
- Theory B says that if P then R
- Q and R are mutually exclusive
- Therefore, theory A is wrong
For example: "Dinosaurs died 65,000,000 years ago, so the earth couldn't have been created 6,000 years ago." It should be noted that although the above argument by itself is a fallacy, strong evidence supporting the death of dinosaurs 65 million years ago, as well as other evidence, would result in the argument being a proof by contradiction, not necessarily a fallacy.
A similar fallacy is No true Scotsman, which in effect says, "Your facts do not work under my theory, so your facts must be wrong."
For a more detailed treatment, see Straw man fallacy.
A straw man fallacy occurs by first incorrectly attributing an argument to someone, disproving this argument, then claiming that the person was wrong. Typically, the fallacy involves distorting what a person actually said to make it superficially similar but easier to disprove. A straw man argument follows the form:
- Person A says P.
- Person B says that person A says P', which is not the same as P.
- Not P'.
- Therefore, not P.
Straw man arguments can sometimes be hard to detect, because a valid statement may be used in a distorted fashion. For example:
- Person A believes that a military program should be cut
- Person B argues that since Person A wants to cut military funding, he wants to leave the country defenseless to attack
This is fallacious reasoning, because there is no way to know why person A believes what he does, and Person B has used one reason which suits his own purpose. For example, it's quite possible that Person A wants to cut the program because he wants to change the funding to something which he thinks does a better job at defending the country.
For a more detailed treatment, see tautology.
A tautology (Greek ταυτο- tauto-, "the same") is an argument that becomes a repetition of a definition. Literally it means "the study of the same." Such an argument, or statement, can prove nothing beyond itself and is useless as a premise.
Fallacies of Ambiguity
Fallacies of ambiguity are fallacies which arise from ambiguity in language used.
Amphiboly is an ambiguity which arises though loose or awkward phrasing:
For example: "Save soap and waste paper".
The fallacy of composition occurs when the parts of a whole are incorrectly used to describe the whole.
For example: "Since one of the battleships is ready to deploy, the whole fleet is ready to deploy".
Conflation is the treatment of two different concepts as one.
For example: "Comparing apples to oranges".
The fallacy of division occurs when it is argued that what is true for the whole must be true for its parts.
For example: "That company is very important. Since Joe works at that company, he must be very important."
Equivocation is the use of word with multiple meanings, and then using a different meaning in the conclusion than in the premise.
For example: "The coach said we should eat light, so take your heavy coat off."
Unequivocal means leaving no doubt about the exact meaning of what is said, being completely clear, allowing no misunderstanding.
Moving the Goalposts
Moving the goalposts is jargon used almost exclusively by evolutionists to decline to answer a question that is the logical next step in their argument. This next step is avoided by evolutionists by claiming that their critics are "moving the goalposts."
For example, Darwinists claim that asking how the theory of evolution explains the origin of life is "moving the goalposts," even though it is a logical question to ask.
Atheism and logical fallacies
- Copi, Irving M. and Carl Cohen. "Introduction to Logic, 12e". Pearson Education: 2005
- Fallacy: Appeal to Consequences
- Fallacy: Poisoning the Well
- Page F30. Matt Damon on Sarah Palin with transcript (2008)
- Genetic Fallacy on The Fallacy Files
- Appeal to Antiquity / Tradition
- Appeal to Novelty
- Fallacy: Burden of proof
- The Texas Sharpshooter Fallacy
- Severe Testing
- Precognition paper to be published in mainstream journal
- Debate:Is infinite regression ever valid as a form of reasoning, or acceptable as a way the universe works, or came to be?
- Logical fallacy by CreationWiki
- The Baloney Detector
- SGU-Top 20 Fallacies
- Sagan, Carl. "The Fine Art of Baloney Detection" in The Demon-Haunted World, Science As a Candle in the Dark';' Ballantine: New York, pp. 201–218 (1996)