Circular logic

Tuesday, April 24, 2007

Formal fallacy

In philosophy, a formal fallacy or a logical fallacy is a pattern of reasoning which is always or at least most commonly wrong. This is due to a flaw in the structure of the argument which renders the argument invalid. A formal fallacy is contrasted with an informal fallacy, which has a valid logical form, but is false due to one or more of its premises being false.

The term fallacy is often used more generally to mean an argument which is problematic for any reason, whether it be a formal or an informal fallacy.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion. Both may actually be true, or even more probable as a result of the argument (e.g. appeal to authority), but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. By extension, an argument can contain a formal fallacy even if the argument is not a deductive one; for instance an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

Recognizing fallacies in everyday arguments may be difficult since arguments are often embedded in rhetorical patterns that obscure the logical connections between statements. Informal fallacies may also exploit the emotions or intellectual or psychological weaknesses of the audience. Having the capability to recognize fallacies in arguments is one way to reduce the likelihood of such occurrences.

A different approach to understanding and classifying fallacies is provided by argumentation theory; see for instance the van Eemeren, Grootendorst reference below. In this approach, an argument is regarded as an interactive protocol between individuals which attempts to resolve a disagreement. The protocol is regulated by certain rules of interaction and violations of these rules are fallacies. Many of the fallacies in the list below are best understood as being fallacies in this sense.

These fallacies are used in many forms of modern communication where the intention is to influence behavior and change beliefs. Examples in the mass media today include but are not limited to propaganda, advertisements, politics, and opinion news shows.

Friday, February 23, 2007

Fallacy of many questions

Many questions, also known as complex question, presupposition, loaded question, or plurium interrogationum (Latin, "of many questions"), is a logical fallacy. It is committed when someone asks a question that presupposes something that has not been proven or accepted by all the people involved. This fallacy is often used rhetorically, so that the question limits direct replies to those that serve the questioner's agenda. An example of this is the question "Are you still beating your wife?" Whether the respondent answers yes or no, he will admit to having a wife, and having beaten her at some time in the past. Thus, these facts are presupposed by the question, and if it has not been agreed upon by the speakers before, the question is improper, and the fallacy of many questions has been committed.

The fallacy relies upon context for its effect: the fact that a question presupposes something does not in itself make the question fallacious. Only when some of these presuppositions are not necessarily agreed to by the person who is asked the question does the argument containing them become fallacious.

A related fallacy is begging the question, in which a premise is included that is likely to be at least as unacceptable to an opponent as the proposed conclusion.

Implied form
One form of misleading discourse is where something is implied without being said explicitly, by phrasing it as a question. For example, the question "Does Mr. Jones have a brother in the army?" does not claim that he does, but implies that there must be at least some indication that he does, or the question would not need to be asked. The person asking the question is thus protected from accusations of making false claims, but still manages to make the implication in the form of a hidden compound question. The fallacy isn't in the question itself, but rather in the listener's assumption that the question would not have been asked without some evidence to support the supposition.

In order to have the desired effect, the question must imply something uncommon enough not to be asked without some evidence to the fact. For example, the question "Does Mr. Jones have a brother?" would not cause the listener to think there must be some evidence that he does, since this form of general question is frequently asked with no foreknowledge of the answer.

In a September, 2006 New York Times column, David Leonhardt queried readers whether they would "prefer spending an extra $5,500 on health care every year — or losing 10 years off" their lifespan.
In doing so, Leonhardt — who earlier in the same column dismissed health-care cost-cutting as "wrong" — forced readers to make a choice that was, in essence, based on a fallacious presupposition that precluded medical cost-cutting.
Alternatively, those who saw value in medical cost-cutting might have arrived at a less loaded question, or, at least, at a less expensive loaded question. (E.g., "Would you prefer: (a) spending an extra $5,500 on health care every year as a couch potato, (b) spending an extra $3,000 on health care every year as a fitness enthusiast, or (c) losing 10 years off your lifespan?")
In 1952, US Senator Joe McCarthy said:
"This is a document which shows that Alger Hiss and Frank Coe recommended Adlai Stevenson to the Mount Tremblant Conference which was called for the purpose of establishing foreign policy (postwar foreign policy) in Asia. And, as you know, Alger Hiss is a convicted traitor. Frank Coe has been named under oath before Congressional committees seven times as a member of the Communist Party. Why? Why do Hiss and Coe find that Adlai Stevenson is the man they want representing them at this conference? I don't know. Perhaps Adlai knows."
On an October, 2006 The Daily Show monologue, Jon Stewart noted two common news-channel examples of this:
On CNN, Fox News, and MSNBC: the frequent use of television "crawl" (lines of text at the bottom of the screen) to ask questions that were fallaciously presuppositive, like "End Times?", "Apocalypse Now?", "Have Democrats forgotten the lessons of 9/11?", "Why do Democrats hate America?"
Asserting that two sides of an argument have equal weight, where one side is libelous, as in: "Is your mother a whore? What? I'm not saying she's a whore. I'm just wondering out loud if she is a whore."
The common schoolyard question — "Does your mom know you're gay?". In most cases the kid being asked this will say no as a reflex, only to fall into the trap set by the asker: either way, he admits to being gay. Another common form of this question is, "Have you stopped beating your wife?"
Note that in these cases, no accusation was actually made. However, there are clear presuppositions in the questions.

A hacker jargon term originating in Asian philosophy, mu (meaning neither yes nor no), can be used to accurately respond to a question of this sort, saying that the question asked carries incorrect assumptions.

A common way out of this argument is to not respond with a simple 'yes' or 'no' answer, but with a full statement that also includes context. To use an earlier example, a good response to the question "Do you still beat your wife?" would be either "I have never beaten my wife" or "I do not have a wife." This removes the ambiguity of the expected response, therefore nullifying the tactic. However, the askers of said questions have learned to get around this tactic by accusing the one who answers with "dodging" the question. The best tactic when faced with this kind of opponent is to ignore the question entirely or to point out that the question is, indeed, a loaded question.

Sunday, November 19, 2006

Begging the question


The term was translated into English from the Latin in the 16th century. The Latin version, Petitio Principii (petitio: petition, request; principii, genitive of principium: beginning, basis, premise of an argument), literally means "a request for the beginning or premise." That is, the premise depends on the truth of the very matter in question.

The Latin phrase comes from the Greek en archei aiteisthai in Aristotle's Prior Analytics II xvi:

"Begging or assuming the point at issue consists (to take the expression in its widest sense) in failing to demonstrate the required proposition. But there are several other ways in which this may happen; for example, if the argument has not taken syllogistic form at all, he may argue from premises which are less known or equally unknown, or he may establish the antecedent by means of its consequents; for demonstration proceeds from what is more certain and is prior. Now begging the question is none of these. [...] If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue.... [B]egging the question is proving what is not self-evident by means of itself...either because predicates which are identical belong to the same subject, or because the same predicate belongs to subjects which are identical."
Fowler's Deductive Logic (1887) argues that the Latin origin is more properly Petitio Quæsiti which is literally "begging the question" as opposed to "petitioning the premise".

An example

"That begs the question" is an apt reply when a circular argument is used within one Syllogism. That is, when the deduction contains a proposition that assumes the very thing the argument aims to prove; in essence, the proposition is used to prove itself, a tactic which in its simplest form is not very persuasive. For example here is an attempt to prove that Paul is telling the truth:

Premise: Paul does not lie when he speaks.
Premise: Paul speaks.
Conclusion: Paul is speaking the truth.
These statements are logical, but they do nothing to convince one of the truthfulness of the speaker. The problem is that in seeking to prove Paul's truthfulness, the speaker asks his audience to assume that Paul is telling the truth, so this actually proves "If Paul is not lying, then Paul is telling the truth." which is nothing more than a tautology.

It is important to note that such arguments are logically valid. That is, the conclusion does in fact follow from the premises, since it is in some way identical to the premises. All self-circular arguments have this characteristic: that the proposition to be proved is assumed at some point in the argument. This is why begging the question was classified as a Material fallacy rather than a Logical fallacy by Aristotle.

Formally speaking, the simplest form of begging the question follows the following structure. For some proposition p:

p implies p
suppose p
therefore, p.
However, the following structure is more common:

p implies q
q implies r
r implies p
suppose p
therefore, q
therefore, r
therefore, p.
The syntactic presentation of the fallacy is rarely this transparent, as is shown for example in the above argument purportedly proving Paul is telling the truth.

Thursday, August 17, 2006

Example #3: Issac Newton and the Speed of Sound

In the Principia Issac Newton presented examples of his mechanical system of the world. These examples acted as much to show the power of his system as they did to illustrate its uses. Through many editions of the text Newton worked with his editor to revise applications and maintain conformance with experimental findings. One body of experimental findings involved the speed of sound in air.
Newton understood very well the mechanical principles involved in sound propagation, but the specific details eluded him because of an incomplete understanding of heat transfer in a fast process. As a result Newton used the value of isothermal compressibility of air rather than isentropic compressibility, which left his estimates of sound speed wrong by 20% or so. However, to maintain the illusion that all was right with his mechanical system he engaged in a pattern of fudging the theory with ingenious, but unfounded and indefensible "corrections" to his calculations. Newton always knew what value for the speed of sound he needed to reproduce, which allowed him to fudge exact correction factors. This was circular reasoning, perhaps even outright dishonesty. Through the circular reasoning Newton managed to justify mechanical corrections that were non-existent. A well made circular argument can prove nearly anything.

Is this means of deriving climate history a subtle circular argument?

There is no means of explaining the nature of this circular argument without referring extensively to an earlier study (Study #1) which explains in detail how a particular inverse method behaves. Then in a later study, the method is applied in a way that is circular.

Study #1: The inverse method

The objective of this method is to use temperature measured in a borehole to figure what the ground surface temperature (GST) was like over the past 1000 years. To do this the authors make a model of temperatures in the subsurface, combined with a computer program that uses the observed temperatures to find the parameters of the model. The central idea is to begin with a initial set of parameters for the model, which I denote here symbolically as mo , and systematically adjust the parameters to minimize an objective function like the following...
S=misfit to observations + change from initial model
Or mathematically...
S=(d-do)tCd-1(d-do) +(m-mo)tCm-1(m-mo).
The reason for using this objective is as follows.
The penalty for misfit to data helps insure that whatever surface temperature history results from the analysis actually explains the observed borehole temperature. However, a common problem with obtaining the history of surface temperature from borehole temperatures is that heat conduction destroys information regarding long past temperature quite completely, and, therefore, many different different temperature histories explain the borehole data equally well. Quite a few of these histories oscillate in temperature wildly--far more, in fact, than the curve labelled "1" in Figure 1. By including a penalty for deviating from the initial model the objective function drives the final solution toward some unique result, and, if the initial model is smooth, the solution is also smooth.
Values in the matrices Cm and Cd provide an optimum balance between fitting the data (d) and adhering to an a priori model (mo). The matrix Cm deals with quantities in the a priori model; most specifically the initial estimate of ground surface temperature (GST) history while Cd deals with uncertainty in the temperature observations. Specifying small values for elements of these matrices implies that a person has great faith in the validity of the a priori model or the data. This is called a tight constraint. Specifying large values for these elements provides a loose constraint.
A presumption of the model is that there is a long-term steady state GST that may or may not equal the present day surface temperature, and a steady background thermal gradient which has to be removed before analysis. These are available from the data and the inverse method. The authors use loose constraints on these parameters, however; amounting to 100K and 500mW/m2, respectively. These are such loose constraints that they allow a background heat flow directed into the earth instead of out of it.
Constraining how far the final GST may stray from the initial temperature history also helps prevent an oscillating solution. The authors suggest a constraint that tightens more on older GST than on recent GST. Specifically, they allow recent GST history to stray about 4 times more from the initial model than they allow variation near 1000 years ago.
The tightening of constraint on GST implies that the authors have more faith in their initial ancient GST than they do in the recent GST. Certainly this is not consistent with the way borehole temperature behaves.
Three hypothetical GST histories. The dashed history shows no significant temperature variation until about 1600AD, exhibits a substantial cold period from then until 1800AD, vacillates over a few decades, and finally increases until the present time. By comparison, the dashed and dotted line is constant until approximately 1900AD and then begins the century-long temperature increase that we call "global-warming."

Three hypothetical GST histories. The dashed history shows no significant temperature variation until about 1600AD, exhibits a substantial cold period from then until 1800AD, vacillates over a few decades, and finally increases until the present time. By comparison, the dashed and dotted line is constant until approximately 1900AD and then begins the century-long temperature increase that we call "global-warming."

This analysis leads to unexpected results

Some of results of this first study are unexpected. For example, a figure in the original paper shows the analysis of actual borehole temperatures. The GST derived from these diverges from one borehole to another in the recent past, but converges toward a zero value near 1000 years ago. Certainly this is unexpected. The physics of the problem suggests that the results would diverge most near 1000 years ago.
Similar behavior occurs in the numerical simulations the authors used to illustrate how loose constraints on thermal conductivity of the soil at a borehole can suppress noise and oscillations. Random noise added to the simulations had its largest effect on GST in the time period 1600-1700 AD when constraints on conductivity were tight and 1800-1850 AD when the constraints were loose.

Summary of Study #1

The inverse method of this study suppresses large variations in GST for the most ancient time periods of an analysis in three ways.
There is no misfit penalty in the data because of thermal diffusion, there is only a penalty for deviating from the initial model.
Placing the largest penalty for deviation from initial model in the oldest time periods.
Absorbing very old climatic information into the temperature background.
As an example of the third point consider the figure below. The curve labelled "2" shows the difference between the dashed and dotted curves of GST in Figure 1 at depths between surface and 400m. The beginning of the little ice age is not well resolved in this T-Z curve. In fact, it is nearly a linear increase of temperature with depth. With a small amount of added measurement noise, the inverse method would remove this linear increase along with the background temperature field, leaving only the recent climb out of the little ice age for analysis. The so-called steady state GST would equal the temperature appropriate to the little ice age, and the only GST change remaining is an increase beginning about 1800AD.

The crux of the circular argument

No invalid argument is implied in Study #1. However, in a subsequent study the same authors use this inverse method to examine the following problem. Divide the past 500 years into century long segments. Analyze a set of borehole temperatures to determine what GST change occured in each century.
The approach to the problem involves the following three steps, which taken together form a circular argument.
First, the method suppresses ocillations in GST history for the three reasons cited above. The most extreme suppression will occur either as the effect of old climate is absorbed into the background temperature or as the penalty for deviating from the initial, smooth model takes effect.
Second, suppressing GST is exactly the same as suppressing past temperature change in each century long segment.
Third, the authors interpret the lack of temperature change for the oldest centuries in the analysis as having been derived, when it is possibly preordained by the method and its initial assumptions, almost independently of the observed data.
The authors interpret the zeroed GST as being characteristic of climate rather than being characteristic of assumptions and method. The conclusion may turn out to be perfectly correct for unrelated reasons, but the argument certainly appears circular and therefore invalid.

Tuesday, August 15, 2006

Example #1: Theresa Imanishi-Kari's Notebook

Teresa Imanishi-Kari was alleged to have falsified experiments, and data, in her laboratory notebooks. She was exonerated of all charges in 1996, but only after a Kafka-esque decade in which the charges against her continually metamorphosed, during which she could not actually examine the specific charges or evidence against her, and during which she was characterized as an example of corrupt science by government oversight committees. One of the principal charges against her was that she had cobbled together a laboratory notebook to bolster her claim of having performed experiments on immune response -- experiments which lead to an acclaimed paper in the journal Cell.
Imanishi-Kari's notebooks were apparently very messy and difficult to decipher. They contained paper strips of instrument readings that were taped to pages, and which were in varying colors and degrees of fadedness, printed with varying ribbons on a variety of printers. The pages themselves appeared out of order, dates were scratched through and corrected, there was white-out correction fluid used back-to-back on both sides of some sheets, and mechanical impressions suggested that pages were, in fact, dated out of the order they were written. The question naturally arose whether this messiness was the product of a clumsy, hurried attempt to deceive. Thus, the U. S. Secret Service was asked to perform forensic analysis on the notebooks. Part of the forensics was to compare Imanishi-Kari's notebooks against a sample of the notebooks of other scientists.
Secret Service investigators were unable to examine more than a tiny fraction (an estimate was perhaps 1%) of the notebooks produced by researchers in the same laboratory during the same time period. In the forum of the hearing, Imanishi-Kari's counsel cross examined one of the Secret Service investigators about why he had not included for examiniation the laboratory notebook of Moema Reis, at one time a research collaborator of Imanishi-Kari. The agent testified that they excluded this notebook because it looked a lot like that of Imanishi-Kari so they were "...unwilling to use that as an example of what a normal or a usual notebook would be."

Since an explicit goal of the comparison was to establish the normalcy of Imanishi-Kari's notebook, the decision to exclude other notebooks that looked like hers becomes an implicit definition of hers as being abnormal. The neat circular logic is...
Collect a sample of notebooks to establish a norm.
Exclude from the sample notebooks that appear similar to that of the subject.
Conclude that the subject notebook is unusual and abnormal.

Thursday, February 23, 2006

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