Argumentation and Logic

What is an Argument?

An argument is a connected series of statements or propositions, some of which are intended to provide support, justification or evidence for the truth of another statement or proposition.

In philosophy, “arguments” are those statements a person makes in the attempt to convince someone of something, or present reasons for accepting a given conclusion. Internet Encyclopedia of Philosophy

Claims are made all the time. In science, especially medical science, claims are made in support of practices, treatments and products. We learned in previous sections that the scientific method is the best way to discover reliable knowledge. Knowledge is then used to make practical decisions. Ideally, claims should stem from the scientific method. We learned that in pseudoscience, claims are made directly to the public with little regard to the scientific method.

People are persuaded to accept claims through arguments. Some arguments sound very convincing. However, it follows that bogus claims require bogus arguments. While legitimate arguments follow formal rules of logic, bogus arguments show little regard to logic. Proponents of pseudoscience stealthily use both formal and informal logical fallacies to bamboozle the listener and, often, themselves.

Skeptical doctors should become familiar with the formal rules of argumentation and the fallacies of bogus arguments. First, let's make sure we understand how a good argument stays on the subject, while a bogus argument may subtly change the subject. In logic, an argument revolves around "stasis points".

Stasis Points (Are We Arguing About the Same Thing?)

Stasis ("stah-sis") Identifies what is actually in dispute. It is the "angle" of an argument. All too often, debates get heated because one debater begins arguing from a stasis point that is different from the original point of the argument. Responders should counter argue toward the same stasis point.

Changing stasis points in the course of an argument may be referred to as "Moving the Goalpost" (see Logical Fallacies) and is a hallmark of a bogus argument.


Conjecture concerns whether an act actually occurred. There is little point in arguing over the effects of a phenomenon without establishing if the phenomenon actually exists.


Definition concerns what an act actually is. An argument cannot proceed if the topic is not clearly defined.


Quality concerns if an act is justified. For instance, a disease may be treated, but the treatment may not have an acceptable risk/benefit ratio. To argue from Quality, one assumes that the disease exists, has a treatment and both are well defined.


Place concerns if the argument is occurring in an appropriate forum ("This is not the time, nor the place to discuss this.")

Note - An argument from "place" concedes that the argument may have "quality"; an argument from "quality" concedes "definition"; and "definition" concedes "conjecture".

If one starts an argument from Definition or Quality, the arguer assumes that the thing actually exists (assumes Conjecture). For unlikely claims, such a strategy can be deceiving.

“Before we try to explain something, we should be sure it actually happened.”-- Ray Hyman

The Forms of an Argument

Now, let's look at the structure of basic arguments. Verbal arguments may not be presented with such formal structure, but good arguments, when analyzed, can be broken down into premises, followed by logic (inferences and warrants) and then conclusions.

Syllogism - Simple formal argument, usually with 2 or more stated premises and a logical conclusion. We often use the word "conclusion" synonymously with "claim". It uses 2 or more terms (objects of discussion). Simple syllogisms generally have 2 relational statements about the terms which are to be taken at face value (premises), and a statement that is derived from the premises (conclusion).

Conditional Syllogisms

The first premise is a conditional ("If, then") statement.

Inclusive Conditional

This form of a syllogism has 2 terms: the antecedent and the consequent. Term A is the Antecedent and Term B is the Consequent

One term is included in the other.

If A is present, then B is present.

A is present.

Therefore, B is present.

eg. If I am a man, then I am a mammal.

I am a man.

Therefore, I am a mammal.

Exclusive Conditional

One of the terms is excluded from the other (this is called a negative premise).

If A, then not B.


Therefore not B.


A or B


Therefore, not A.

eg. If I am a man, then I am not a reptile.

I am a man.

Therefore, I am not a reptile.

** Rules of the Conditional Syllogisms

1. The second premise may "affirm the antecedent". The second premise may state that the "If" term is actually true.

2. The second premise may "deny the consequent". The second premise may state that the "then" term is actually false.

3. No conclusion can absolutely follow if the second premise "denies the antecedent" (states that the "If" term is actually false).

4. No conclusion can necessarily follow if the second premise "affirms the consequent" (states that the "then" term is actually true).

(See Logical Fallacies for Denying the Antecedent and Affirming the Consequent formal logical fallacies.)

Categorical Syllogisms

These generally have 3 terms that are related by categories.

All B's are C's.

All A's are B's.

Therefore, all A's are C's.

A is the Minor term (the subject of the conclusion; has the smallest extension)

B is the Middle term (in the premises but not in the conclusion)

C is the Major term (the predicate of the conclusion; has the largest extension)


In a categorical syllogism, a term is "distributed' if it refers to all members of the set denoted by the term. This is an important concept as it is used to establish the rules of logic to determine if an argument is valid.

** Rules of the Categorical Syllogism

Violations of these rules constitute formal logical fallacies (see the Logical Fallacies section

1. The middle term must be distributed at least once.

2. A term that is not distributed in the premises, must not be distributed in the conclusion.

3. At least one premise must be inclusive (positive). A conclusion cannot follow from two negative premises.

4. If one premise is exclusive (negative), then the conclusion must be negative.

5. If both premises are inclusive (positive), the conclusion must be positive.

Types of Arguments Based on Knowledge

The syllogism describes the rules for an argument's structure. The truth of the premises is irrelevant to the validity of the argument's form.

Now we must consider how sure we can be of the conclusion.

Deductive Arguments

Premises lead to a definite conclusion. However, no new information is actually produced in the conclusion. The argument proceeds from generalized statements to a specific conclusion. If the premises are true, the conclusion is necessarily true.

In deductive arguments, if the conclusion is supported by the premises, then the argument is said to be sound. If the premises are true statements, and the argument is sound, then the argument is valid. These often take the form of categorical syllogisms.

Inductive Arguments

Premises lead to a probable conclusion. Specific statements lead to a generalized conclusion. It the premises are true, the conclusion is likely to be true. Remember from the What is Science section, ideas in science are formed through induction. They are tested with deduction. These often take the form of conditional syllogisms (If, then statements).

In inductive arguments, logical conclusions are said to be strong. If the premises are true, and the argument strong, then it is cogent.

General Structure of Inductive Arguments

(adapted from Argumentation: The Study of Effective Reasoning (The Teaching Company))

Syllogisms are logical structures that are useful if the arguers accept the claims in the premises to be true. However, unless we have a priori knowledge of a claim's truth (such as in statements of math or trivial statements of definition), then we must establish the truth value of a claim by considering evidence and warrants.

Evidence is linked to a Claim by an Inference. An inference is supported by a Warrant(s).

What is Evidence?

This question must be agreed upon and accepted by the arguing parties for an argument to proceed. In argumentation, evidence can take many forms. In science, evidence must be coherent with the scientific method.

**** Extraordinary claims require extraordinary evidence! ****

In everyday arguments, evidence usually comes in the form of the following:

- Examples

Examples must be commonly understood by the listener. In scientific arguments, examples may be considered anecdotal and therefore have little value.

- Statistics

Statistics can be notoriously misused and spun to support most claims. They must be compiled properly and explained well to avoid bias.

- Tangible Objects

These are actual objects, facts, laws, hypotheses, theories, etc.

- Testimony

The strength of personal testimonies depends on the relevance and reliability of the witness. In science, testimony is usually a weak form of evidence.

- Consensus

In common arguments, consensus refers to previously established and accepted conclusions within the culture of the arguers.

It refers to generally accepted values and the "Basic Beliefs" common to the arguers and the audience (see Foundationalism).

In scientific matters, there is a definite hierarchy of evidence that is quite different from the list above (see Scientific Studies in Medicine and Statistics and Risk). Scientific evidence focuses on statistics, tangible objects and consensus (of relevant experts).

In medicine, evidence can be divided into basic science and clinical science. Ideally, a medical claim should have support from both.

Evidence from the accepted cannon of scientific knowledge in biology, chemistry, physics and others (akin to 'Tangible Objects' above).

The U.S. Preventive Service Task Force defined a hierarchy of reliability for clinical studies and evidence. Of the types of study designs listed above, the rank levels from most to least reliable have been classified as follows:

I Randomized controlled trials (double blinded > single blinded)

II-1 Controlled trials without randomization

II-2 Cohort and Case Control studies

III Expert opinion, and case reports (anecdotes)

What are Warrants?

Warrants give licence to make the inference/claim; a warrant must be generally accepted or previously established for an argument to proceed. One must be careful when claiming a warrant. It is very easy to mistake a logical fallacy for a legitimate warrant.

- Example

Assumes "What is true for the part is true for the whole" or "what is true for the whole is true for the part". Risks the "Composition and Division Fallacies"

- Analogy

Assumes that a lesser-known thing will be like a commonly known thing.

- Literal Analogy compares directly a known and an unknown.

- Figurative Analogy compares the relationship of two knowns and two lesser knowns (A is to B, as C is to D). Risks the "False Analogy Fallacy"

- Sign

Assumes a correlation between two things.

"When A is present, so is B". In other words, 'A' is a sign of 'B'.

Risks confusing coincidence with correlation and the "Cum Hoc Fallacy".

- Cause

Assumes a causal relationship between two things.

"A causes B. A is present, therefore B."

- See the Bradford-Hill Criteria for causation.

- Risks the "Post Hoc Ergo Propter Hoc" fallacy, multiple causes, and confusing effect for cause

- Commonplaces

Assumes that a belief is commonly held to be true. Assumes it is a generally accepted value.

Often begins with the phrase, "Everybody knows that....".

- "Basic Beliefs" (See Foundationalism)

Risks the "False Premise Fallacy"

- Form

Attempts to make an inherently inductive argument seem as if it is deductive by limiting its options.

Takes the form of a syllogism and attempts to prove with certainty.

Risks the "Slippery Slope Fallacy" as the premises are likely to be probabilistic rather than deterministic.

- Hybrids

Combinations of the above inference patterns

Complex Arguments

Once a claim has been inferred from evidence with support of a proper warrant, the claim may be used in conjunction with other claims to support a larger resolution. For instance, a foundational theory in science may be supported by multiple lines of evidence. When arguing in support of such a theory, one may choose to make (and support) a series of claims that, if accepted by the other party, lead to the acceptance of the larger concept (the 'Resolution'). A resolution may also take the form of a policy; it may be a statement of what we ought to do. We learned in the Philosophy and Science section that Science is our best source of knowledge (what 'is'). We use Philosophy to determine how we act (what 'ought' to be done). Philosophy should be informed by science. Argument resolutions should be supported by logical and justified claims. For skeptical doctors, the art of medicine is informed by the science of medicine.

In the public realm, these issues are hashed out in complex arguments, either in debates, presentations, editorials or other forums. Complex arguments utilize two or more claims in series, convergence, parallel or combined arrangements.

Claims in Series

One of the weakest ways of utilizing multiple claims in an argument is to arrange the claims in a dependent series such that each claim depends on the strength of the claim before it. Like a lamp suspended by a chain, the resolution is only as strong as the weakest claim in the series.

Example: Homeopathy advocates may support their belief system by making a series of claims. The resolution being that Homeopathy works as a health care device. The first claim is that of the "Law of Similars" (literally meaning that the substance which causes illness can be used to cure). The second claim is the "Law of Infinitesimals" (literally meaning that the more dilute a substance is, the more potent its healing power). A third claim may be that Homeopathic treatment works beyond the placebo effect. Each claim is necessary for the resolution. If any one of these claims can be falsified, a reasonable thinker would have to reject the resolution.

Claims in Convergence

In this type of argument, the claims are independent. An individual claim's validity does not depend on the other claims. Each individual claim may not completely support the resolution. However, like legs of a tripod, they converge to support the resolution.

Example: It is generally accepted that the world is (more or less) spherical. At one time, this was not widely accepted. However, the idea of a spherical Earth can be induced by pointing out the curvature of the horizon observed at great heights. One could also quote the observations and calculations of Eratosthenes of ancient Greece, in which he calculated the radius of the Earth with remarkable accuracy. One could point out that boats and planes can reach the west side of a continent by traveling east (albeit in a roundabout way). One could point out the experience of the astronauts and the photography from space flights. Each of these claims are independent and sufficient to support the resolution.

Claims in Parallel

This arrangement may be used to demonstrate the validity of our strongest, foundational theories. The validity of each claim is independent of the other claims, and each claim is independently capable of supporting the resolution. Such a resolution would be very difficult to falsify because even if an individual claim is called into question, the remaining claims support the resolution.

Example: In medicine, a patient may have a condition for which a definitive treatment plan may not be obvious. The first claim may be that a certain drug may help cure the disease. Another claim may involve the patient's ability to physically tolerate the treatment. Yet another claim may involve the patient's quality of life if the treatment is given. A proper resolution should be decided on only after considering all of the claims together in convergence.

A more specific example would be the resolution that vaccines and vaccination programs are effective and beneficial. Such a resolution is supported and warranted by a convergence of claims from microbiology, immunology, epidemiology, and even economics.


Many arguments take a combined form. Some claims are stringed in series and are dependent, some are independent but convergent, while some are independent, sufficient and parallel.

** Mistaking Complex Arguments

Opponents of scientific theories frequently mistake convergent and parallel arguments for series arguments. Those opposed to vaccinations may point to anomalies in epidemiology data to support the idea that certain diseases decreased due to factors other than vaccines. However, the validity of vaccines is supported by multiple lines of evidence (immunology, epidemiology, microbiology, public records, history books, etc). Even if the opponent were able to falsify one claim (not the case in our example), there would still be numerous claims that independently support the efficacy and safety of vaccines.

Rules for a critical discussion (Pragma-dialectics)

In real-life, public arguments, such as debates, the formal components of the arguments are not obvious. However, rules of conduct have been described that help to maintain legitimacy. Van Eemeren, Grootendorst and Henkemans listed ten rules as part of their Pragma-dialectical theory (Argumentation, 2002). Violations of these rules are considered fallacies.

They are spelled out on the Wikipedia page as:

Freedom rule

Parties must not prevent each other from advancing standpoints or from casting doubt on standpoints.

Burden of proof rule

A party that advances a standpoint is obliged to defend it if asked by the other party to do so.

Standpoint rule

A party’s attack on a standpoint must relate to the standpoint that has indeed been advanced by the other party.

Relevance rule

A party may defend a standpoint only by advancing argumentation relating to that standpoint.

Unexpressed premise rule

A party may not deny premise that he or she has left implicit or falsely present something as a premise that has been left unexpressed by the other party.

Starting point rule

A party may not falsely present a premise as an accepted starting point nor deny a premise representing an accepted starting point.

Argument scheme rule

A party may not regard a standpoint as conclusively defended if the defense does not take place by means of an appropriate argumentation scheme that is correctly applied.

Validity rule

A party may only use arguments in its argumentation that are logically valid or capable of being made logically valid by making explicit one or more unexpressed premises.

Closure rule

A failed defense of a standpoint must result in the party that put forward the standpoint retracting it and a conclusive defense of the standpoint must result in the other party retracting its doubt about the standpoint.

Usage rule

A party must not use formulations that are insufficiently clear or confusingly ambiguous and a party must interpret the other party’s formulations as carefully and accurately as possible.

Rapoport's Rules

Psychologist and game theorist Anatol Rapoport (1911-2007) wanted to use argumentation to promote truth rather than to elevate the social status of one arguer over another. Philosopher Daniel Dennet summarized Rapoport's advice for arguing in his book Intuition Pumps and Other Tools for Thinking:

1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says,

“Thanks, I wish I’d thought of putting it that way".

2. You should list any points of agreement (especially if they are not matters of general or widespread agreement).

3. You should mention anything you have learned from your target.

Only then are you permitted to say so much as a word of rebuttal or criticism.


Many arguments would be over quickly if each party starts with the same understanding of the process and the rules. The purpose in scientific argumentation is to come to a conclusion that is coherent with the rules of logic, the scientific method and the body of accepted scientific knowledge. However, we do not live in such an ideal world. It is not enough to just know and adhere to these rules ourselves, but to spot and to correct deviations from these rules. To do this, we must also learn about logical fallacies. That is the topic of the next section.

John Byrne, M.D.

Reference Links

"Argument [Internet Encyclopedia of Philosophy]." 2009.


"Argumentation: The Study of Effective Reasoning, 2nd Edition." 2010.


"Nonsense: A Handbook of Logical Fallacies: Robert J. Gula ..." 2009.


"Pragma-dialectics - Wikipedia, the free encyclopedia." 2005.


"Argumentation: Analysis,Evaluation: Frans H. van Eemeren,Rob ..."


"Purdue OWL: Stasis Theory." 2010.


"Foundationalism - Wikipedia, the free encyclopedia." 2003.


"Intuition Pumps and Other Tools for Thinking", Daniel Dennet.

W. W. Norton & Company, May 6, 2013