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Nature of Fallacy:
Formal and Informal Fallacies in Argumentation

Abstract: A fallacy is a mistake in reasoning: an argument which either does not prove, or does not provide evidence for, its conclusion. The history, nature, and classification of informal and formal fallacies is defined, characterized, and discussed.

1. Main Approaches to Argumentation Studies
2. The Standard Treatment of Informal Fallacies
3. Some Difficulties with the Standard Treatment of Informal Fallacies
4. What is a Fallacy?
5. Paralogisms, Sophisms, and Paradoxes
6. Three Basic Types of Fallacies: Informal, Deductive, and Inductive:
7. Chart of Fallacies
8. Final Comments and Cautions on Fallacies
9. Footnotes
10. Readings on Fallacies

1. Main Approaches to Argumentation Studies

   Apart from formal deductive logic and inductive logic, the main approaches for the study of argumentation include these overlapping fields which are perspectives by which arguments can be viewed: (1) informal logic (including critical thinking), (2) dialectical logic (including pragma-dialectical discourse analysis and pragmatic argumentation theory), and (3) rhetoric (including debate and persuasion).
   
   
   1. Informal Logic is the normative study of natural language arguments (as opposed to the formal or abstract methods of deductive logic) which seeks to develop standards of use and methods of evaluation of ordinary language argumentation.[1] Some informal arguments can be properly translated into formal logic. Formal logic uses symbolism and formal methods to evaluate arguments as valid or not; whereas, informal arguments not translatable into formal deductive or inductive arguments can be evaluated as evidentially relevant and sufficient if they are “good” arguments. Researchers disagree on the place of informal logic with respect to formal logic and argumentation theory. The Canadian school of informal logic, for example, holds that the study emphasizes arguments in everyday discourse not analyzable by formal logic. Informal logic is seen in these notes as the examination of the justification of arguments in context rather examination of the persuasiveness of arguments.[2]
      
      Critical thinking differs from informal logic in that this educational reform movement emphasizes the study of various intellectual activities for problem solving in accordance with rational criteria, whereas informal logic is narrower in focus and emphasizes traditional argument interpretation and evaluation of argumentative everyday language, dialogue, and discourse.[3] As J. Anthony Blair and Ralph H. Johnson point out, informal logic aspires to be a theory-based subject; whereas, critical thinking is an activity utilizing informal logic and other methods of problem solving.[4] These other methods include creative thinking, inquiry, information processing, and reasoning within different subject matters.[5]
      
      
   2. Dialectical Logic approaches argumentation as shared argumentative discourse between or among participants with opposing points of view. Pragma-dialectical discourse sets rules for rational critical discussion, and the speech acts which violate these rules are viewed as fallacies. In this manner, fallacies are viewed as statements that impair the progress of the dialogue.[6] Pragmatic logical argumentation evaluates defeasible normative reasoning within a dialectical context by means of argumentation schemes, mappings, and appropriate contextual standards of proof.[7] Often dialectical arguments are responses to oppositional counter-arguments. Dialectical logic is viewed here as a study of the persuasiveness of arguments rather that a study of the justification of arguments. Dialectical logic intends consensus as a surrogate for truth.
      
      
   3. Rhetoric emphasizes the effectiveness of emotive significance and argument used for the persuasion of changing attitudes toward a standpoint or point of view. Often the arguments are shaped to appeal to the attitudinal outlook of a specific audience such that truth per se is not specifically sought. Rhetoric can still be evaluated in terms of formal logic, but, for example, Chaïm Perelman and Lucie Olbrecht-Tyteca, emphasize rhetoric's purpose in terms of the effects of audience value preferences. Although rhetoric is eschewed by some formal logicians, the cornerstone of the rhetorical approach is that emotively neutral logical arguments, by themselves, rarely influence audience opinion. As a form of nonanalytic thinking, value-judgment hierarchies replace reason and empiricism.[8]
      
      
   4. These lecture notes emphasize informal and formal logic. Ordinary language arguments will often be translated with the principle of charity into conventional deductive and inductive arguments. Currently, most researchers in the argumentation field seem to agree with F. H. van Eemeren's appraisal:

      “[T]he label informal logic covers a collection of normative approaches to the study of reasoning in ordinary language that remain closer to the practice of argumentation than formal logic.”[9]

      1. Some researchers maintain accurate translation of many natural language arguments into formal logic is not possible given their vagueness, ambiguity, and incompleteness. Thus, it is thought, on this view, formal logic is not useful for these kinds of argumentation since a neutral observer's objective point of view is not possible. However, if adequate clarification of what is stated is not possible, then it is doubtful that reliable understanding of what is stated in argumentation is possible outside of interpretation or translation either.
         
         
      2. G.C. Goddu has argued that informal logic cannot meaningfully be defined in terms of the logic of real arguments, i.e. the logic of natural or ordinary everyday arguments, since there is no clear demarcation between real arguments and other kinds of arguments.[10]
         
         In this regard, Gottlob Frege writes:

         ”Of course we have to be able to count on a meeting of minds, on others’ guessing what we have in mind. But all this precedes the construction of a system and does not belong within a system. In constructing a system it must be assumed that the words have precise meanings and that we know what they are.”[11]

         For communication to be possible for all statements, a regulative principle is implicitly adopted that a sentence which states something can be translated into a different statement or statements which recognizably express the same thought.[12]
         
         

2. The Standard Treatment of Fallacies

   The traditional or standard treatment of informal fallacies is currently developing along divergent lines of inquiry.
   
   
   1. In 1970 C.L. Hamlin pointed out that the standard treatment of fallacies remained much the same as the thirteen fallacies pointed out by Aristotle in his Sophistical Refutations. Hamlin decries the standard treatment:

      “[I]n most cases, I think it should be admitted, is as debased, worn-out and as dogmatic a treatment as could be imagined — incredibly tradition-bound, yet lacking in logic and historical sense alike, and almost without connection to anything else in modern logic at all.”[13]

      And Douglas Walton cautions:

      “Indeed, it has been shown that many of the so-called ‘fallacies’ are, in some instances, not incorrect arguments at all, but reasonable kinds of argument or reasonable kinds of criticisms of arguments.”[14]

      Currently, defeasible reasoning and informal fallacies are analyzed in accordance with argumentation schemes and pragmatic theories of dialogue. Moreover, on many occasions, some supposed “traditional informal fallacies” can be set out and explained as acceptable (inductive) arguments.[15]
      
      
   2. Many traditionally-defined informal fallacies such as ad hominem, ad verecundiam, tu quoque, ad ignorantiam, slippery slope, composition, division, and others can be contextually effective and legitimate arguments when the conclusion follows from the premises with some degree of probability.
      
      
      1. For example, the basis of ad hominem argument depends on the relevance of the relationship between what is said and the character of the person who said it. Reliable authorities are more likely to state good arguments concerning their field of expertise than are non-authorities in that field. The relevance of a disputant's personal information must be established on a case-by-case basis. Obvious specialized expertise provides inductive evidential relevance for rendering conclusions drawn in that field more reasonable. In general, weak arguments can be distinguished from a fallacious argument.[16]
         
         
      2. Decades ago, F.H. van Eemeren and R. Grootendorst pointed out:

         “Referring to mitigating circumstances which make a fallacy no fallacy after all, however, does not solve anything. … [T]he detection and identification of fallacies becomes very much ad hoc: Each case has to be examined on its own merits … an adequate theory of fallacies is then out of the question.[17]

         The claim that some informal fallacies are not fallacies on occasion appears to be simply a verbal statement rather than a factual statement. E.g. the “mitigating circumstance” distinguishing between a fallacious ad hominem argument and a credible ad hominem is the essential aspect of the definition of the fallacy: viz., the relevance or the irrelevance of the disputant's character with respect to what the disputant states.
         
         
   3. Mistakes in arguments present in monotonic logic disputes are not limited to the errors of invalidity and unsoundness, but, also errors can arise from improbability of the inference based on the meaning of, or semantic content in, the statements used.
      
      
      1. The legitimacy of informal logic as a separate discipline is grounded on the presupposition that not all instances of ordinary language reasoning can be accurately translated into the abstract formal structures of deductive or inductive logic. The conclusions of those arguments can be altered by new information.
         
         
      2. If this is the case, the possibility of informal logic as an independent logical theory may well be based on the rejection of Sir William Hamilton's logical postulate as he applied it to formal logic:

         “The only postulate of Logic which requires an articulate enouncement is the demand, that before dealing with a judgment or reasoning expressed in language, the import of its terms should be fully understood; in other words, Logic postulates to be allowed to state explicitly in language all that is implicitly contain in the thought.”[18]

         Some argumentation theorists today seem to disagree with this thesis. For them, the early Ludwig Wittgenstein's optimistic statement …

         “Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.”[19]

         does not take account of the tacit vagueness, ambiguity, and inexplicitness, as noted above.
         
         
      3. J. Anthony Blair summarizes the popular current view as to why informal logic is not reducible to formal logic:

         “The idea that arguments can be adequately analyzed and evaluated outside the contexts or situations of their use is more or less dead among all but the most isolated philosophers and logicians.”[20]

         Even so, there still remain logicians who see the need for formal-reconstruction in the interpretation of much or all of informal argumentation.
         
         
   4. Some logicians, e.g., Peter Ramus, [21], Francis Bacon,[22] and John Locke,[23] among others, did not assay the treatment of informal fallacies because they emphasized that logic is concerned with correct reasoning. Some current logic textbooks in do not cover the topic of informal fallacies.
      
      Yet, unless we are aware of some of the mistakes that are likely to be made, i.e., unless we know how to avoid typical mistakes in thinking, we are unlikely reason well.
      
      

3. Some Difficulties with the Standard Treatment

   No one is particularly satisfied with the traditional treatments of fallacies — many fallacies cannot be categorically well-defined.
   
   
   1. Thus, it may well be impossible to give a systematic treatment of fallacies, in part because different methods of logic have been adopted and in part because the nature of errors in reasoning are not always due to grammatical structures and forms of language.[24]
      
      
      1. Augustus De Morgan writes in his Formal Logic:

         “There is no such thing as classification of the ways men arrive at an error: it is much to be doubted whether there ever can be.”[25]

      2. H.W.B. Joseph says in his Introduction to Logic:

         “Truth may have its norm, but error is infinite in its aberrations, and they cannot be digested in any classification. The same inconclusive argument may often be referred at will to this or that head of fallacies.”[26]

   2. As an example of a fallacy which may be identified in either of two ways, consider the fallacy of the ambiguous middle term in syllogistic logic, also termed the four term fallacy, and normally described as a formal fallacy. The same argument can also be identified as a fallacy of equivocation which is an informal fallacy. Augustus De Morgan provides this example of a four term fallacy with equivocation of the term “criminal action”:

      “All criminal actions ought to be punished by law.
      Prosecutions for theft are criminal actions.
      Therefore prosecutions for theft ought to be punished by law.”[27]

      The form of this fallacy is illustrated as:

      All CA is PL
      All PT are CA’
      All PT are PL

      Although the terms for CA and CA’ appear to be the same, they have different meanings. The first occurrence of the phrase “criminal action” refers to “the commission of a crime” and the second refers to a “legal proceeding.” Either fallacy, formal or informal, can be cited as the reason the argument is fallacious depending on whether the structure of the argument or the content of the argument is being examined.
      
      
   3. No unified theory of fallacy has been proposed, except in an exceedingly superficial manner by negative definition. I.e., a fallacy is said to be incorrect reasoning. This negative definition of course depends upon having a complete and consistent explication of the meaning of proper reasoning.
      
      
      1. However, most logicians do not consider just any error in reasoning a fallacy per se; the term “fallacy” is reserved by many logicians for recognizable errors of a specific kind. Even so, some accounts of informal fallacies are cluttered with countless minor variations of traditional fallacies.
         
         
      2. Specific informal fallacies often are not definable in terms of some specific or common trait but are instead characterized by various family resemblances. For this reason, the completion of the development of a standard taxonomy of informal fallacies is implausible.
         
         
      3. So, most likely, what we call ‘fallacy’ has no common single meaning, and the characterization of the uses of this word fits Ludwig Wittgenstein's notion of “family resemblance” — where “we see a complicated network of similarities overlapping and criss-crossing; sometimes overall similarities, sometimes similarities of detail.”[28]
         
         
   4. Francis Bacon wrote in a similar regard:

      But these small wares and petty points of cunning are infinite; and it were a good deed to make a list of them, for that nothing doth more hurt in a state than that cunning mean pass for wise.”[29]

      But most fallacies and related infelicities of persuasion occurring in everyday discourse overlap so much in their complexities that attempting to name as many as possible proves unprofitable.[30]
      
      
   5. Even though there exists no agreed upon theory of fallacy, informal fallacies in this course are more or less organized traditionally. An attempt is made to incorporate the standard treatment of fallacies with a practical view toward everyday reasoning.
      
      

4. What is a Fallacy?

   1. Historically, fallacies have been defined in many different ways, not all of which are consistent with the usages in contemporary logic. Following Richard Whately, the first English logician to base the subject of fallacies on logical principles by dividing fallacies into logical or formal and material, [31] many logicians define “fallacy” as some form of deceptive reasoning. Richard Whately writes:

      “By a ‘Fallacy’ is commonly meant ‘any deceptive argument or apparent-argument, whereby a man is himself convinced, — or endeavors to convince others — of something which is not really proved.’”[emphasis original][32]

      And Jeremy Bentham writes:

      By the name fallacy it is common to designate any argument employed, or topic suggested, for the purpose, or with a probability, of producing the effect of deception …[33]

      Indeed, the conventional definition of “fallacy” expressed in the Oxford English Dictionary is “A deceptive or misleading argument, a sophism.”[34]
      
      
      1. The traditional view of fallacy, closely related to this view, is the oft-used contemporary definition: “an argument which seems to be valid, but really is not.”[35] However, several serious problems with this definition for logic are evident.
         
         
         1. The definition is psychological; it turns on whether an individual happens to be misled by an argument. William Spalding points out deception is not essential to the definition of fallacy:

            “The name is sometimes … used to deceive. But the intention is a point of secondary importance in the theory of fallacies … [36]

         2. What could count as something being unqualifiedly “deceptive”? E.g. consider this oft-used fallacy of equivocation in several 18th century books:

            Nothing is better than Heaven;
            But a Penny is better than nothing;
            ∴ A Penny is better than Heaven. [37]

            Since few persons would regard the argument as valid, on the above definition of “fallacy,” the syllogism would not be treated as fallacious because it is not deceptive. Nevertheless, the fallacy committed here is formally the syllogistic four term fallacy and informally the fallacy of equivocation. The middle term “nothing” is being used in two different senses of the word: a positive sense in the first premise and a negative sense in the second premise. [38]
            
            
         3. The notion of validity is normally applied to deductive arguments only. So the above proposed definition of “fallacy” would not address the incorrectness or unacceptibility of inductive, probabilistic, or informal arguments.
            
            
      2. Moreover, in the case of petitio principii (circular reasoning), its fallacious aspect is not its deductive invalidity, but instead its deceptiveness. This is one reason many argumentation theorists argue that some informal fallacies are not necessarily viewed as arguments per se but instead viewed as deceptive techniques or rule violations. Additionally, the fallacy of complex question (the fallacy of many questions) is not prima facie an argument — it couches an unwarranted presupposition within a question.
         
         
   2. Fallacy: an incorrect argument which reflects a mistake in reasoning describable as a rule violation of a logical system whereby either the conclusion of the argument does not logically follow from the premises or the conclusion is not provided evidential support due to a violation of some prior jointly-accepted conventional rule of inference.
      
      
      1. So a fallacy is simply a mistake in reasoning which is often misleading or deceptive. A useful short definition is provided by J. Weldon:

         “A Fallacy is a violation of logical principle disguised under a show of validity.”[39]

         A fallacious argument either does not prove, or does not provide sufficient evidence for, its conclusion.
         
         
      2. The definition of fallacy is assumed here as a working definition, even though the definition is inadequate insofar as it presupposes a set of known, agreed-upon rules for all forms of systematic reasoning.[40]
         
         
      3. Some logicians maintain that informal fallacies must occur with some frequency to count as fallacy. [41] The view taken here is any error in reasoning is a fallacy no matter how seldom it occurs, but such fallacies are not usefully designated with a stipulative definition.
         
         
      4. This definition is not consistent with the pragma-dialectical definition of “fallacy” as ”systematically connected with the rules for critical discussion.”[42] Pragma-dialectic stipulates rules of behavior rather than describes rules of what constitutes a logical mistake per se. [43]
         
         
   3. These notes follow the traditional logical practice of regarding fallacies as occurring in arguments but not occurring in statements, premises, or beliefs.[44]
      
      
      1. Single false or misleading statements are said to be fallacies in everyday discourse, but in these notes we will restrict the term, for the most part, to arguments. So, we will follow a precising definition of fallacy where a false, disparaging, or emotively significant statement or belief is not a fallacy.[45]
         
         
      2. For example, even in the U.S. electoral milieu of “insult politics,” name-calling per se, in an argumentative context, is not necessarily the commission of an ad hominem fallacy unless the proffered abusive attack on the opponent is cited as a reason or ground for the truth of some putative conclusion. Consider this abridged argument by presidential candidate Donald Trump in 2016:

         “This election is also about, so importantly to me, African-American and Hispanic-American people whose communities have been plunged into crime, poverty and failing schools by the policies of crooked Hillary Clinton. Believe me, she's crooked. … I say to the African-American community, what the hell do you have to lose? I will fix it. I will fix it. I will make it good. I'll bring back our jobs. We'll have good education. We'll have great safety in the inner city.”[46]

         In this argument, Mr. Trump is arguing that he will provide safety for the inner city because it is important to him. The personal attack on presidential candidate Hillary Clinton is assertive, but not argumentative, consequently not a fallacy.
         
         Even though the offensive and unsupported comment is rudely gratuitous and violates a norm of civility, it is not a fallacious argument with respect to the topic at issue of inequitable issues in inner city communities. It is rather plainly a contextually unsupported assertion. An ad hominem insult does not always function as an ad hominem fallacy.
         
         
      3. In the evaluation of arguments, logicians now recognize that each argument need be evaluated in terms of the statements in the argument together with the context of the dialogue in which it appears.[47] The evaluation of an argument apart from its context can often result in misinterpretation of the argument.
         
         
      4. The framework for various kinds of fallacies depends upon a theory of argument — e.g., what kinds of arguments are rule-based. No matter how logic in general is described, a fallacy can be thought of as a violation of a logical-rule in one or more of its kinds or divisions. Whether or not there is only one type of correct logic is a matter of some disagreement.[48]
         
         
         1. Different logics are such that what is fallacious in one logic might not be fallacious in different logic. This is not necessarily a problem since different logics are put to different purposes.[49] E.g. any correct inductive argument in science is analyzable as an invalid deductive argument in formal logic.
            
            
         2. Stephen Toulmin, Richard Rieke, and Allan Janik state:

            “[A]rguments that are fallacious in one context may turn out to be sound in another context.”[50]

            (The notion of “sound” for Toulmin, et al. has to do with differing standards of evidence for different fields of inquiry not (necessarily) with validity and truth of premises.)[51]
            
            
   4. In current practice, the notion of fallacy in argumentation is interpreted in several different ways:
      
      
      1. In formal logic, language syntax is formulated into argument structures with logical validity defined in terms of rules for those structures. Validity is a necessary condition for normative logical correctness. In semantical, formal deductive logical theories, “fallacy” is defined in terms of a violation of formal logical rules; for instance, the fallacy of the undistributed middle term occurring in Aristotelian syllogistic logic can be interpreted as the fallacy of affirming the consequent in symbolic or mathematical logic.
         
         
      2. However, it is essential to point out that not all violations of formal logical rules are fallacies, since an argument might be valid on other grounds — viz., its semantic content. An argument might not be formally valid but its validity might be due to an analytical relationship in the meanings of the statements in the argument (i.e., the what is said). Consider the following argument:

         Some raptors are birds.
         Some hawks are raptors.
         ∴ Some hawks are birds.

         Formally, this argument commits the fallacy of the undistributed middle term (as described above). Nevertheless, the meaning of the word “hawk” includes the notion of being a bird, so if someone understands what the premises mean, then the conclusion of this argument necessarily follows from reasons other than its form. It's to be wondered if such semantic interpretations are to be termed “arguments” at all.
         
         
      3. Rolf George points out that understanding an argument involves more than just understanding its statements:

         “[T]here is a further act of understanding, viz. ‘understanding the argument.’”[52]

         And understanding the argument includes understanding its structure, formal or informal.
         
         
      4. In pragmatic and dialogical argumentation theory, a fallacy is defined as the violation of a normative rule or conversational maxim occurring in a dialogue or critical conversation. For instance, evading the burden of proof in an argument or providing irrelevant arguments both count as incorrect moves in a critical discussion.
         
         
         1. Presently, several significant accounts of pragmatic dialogical norms or rules have been proposed, and in general in those accounts a fallacy is defined as a violation of the variously determined norms, rules, or procedures.
            
            
         2. Nevertheless, as these rules are not universalizable, the notion of fallacy comes to mean different dialogue rule infractions in different dialogue games: “[W]hat constitutes a fallacy in one game of dialogue does not need to constitute a fallacy in another (it could be just a blunder, or even be entirely all right).”[53]
            
            
      5. In other critical reasoning contexts, an informal fallacy is been defined in terms of a false premise or dubious statement or presupposition in an argument (often as an intentional deception). Richard Whately, who revived Aristotelian logic in the nineteenth century explains his fallacy of unduly assumed premise as a material “nonlogical fallacy.”[54] For instance, consider the following “put-up” argument:

         All U.S. persons should have the right to vote.
         All U.S. criminals are U.S. persons.
         So all U.S. criminals should have the right to vote.

         The argument is valid — it has a correct logical structure. However, since the first premise is not true (as of year 2019), the argument is not sound.
         
         
         1. Whately and some current informal logic academics consider this argument fallacious as well because the first premise is an unsupported statement. E.g., Ralph Johnson and Anthony Blair explain their “problematic premise fallacy” as follows:

            “[A] premise is problematic if it is introduced into the argument without defense and is unacceptable without this defense.” [emphasis original][55]

            This approach has many advantages; however, in these logic notes, this usage of “fallacious” is not followed. First, there is no clear method for resolving all disputes as to what is unacceptable if there is no generally acceptable criterion of acceptability. Second the notion of fallacy acquires an additional meaning, and in contentious disputes there may well be no clear way to agree on generally acceptable premises. Finally, working with low probability problematic premises is sometimes essential in anticipating conclusions which reveal extraordinary risk exposure.
            
            
         2. Instead, often arguments can be analyzed with reformulated or revised true premises.

            Some U.S. persons should have the right to vote.
            All U.S. criminals are U.S. persons.
            All U.S. criminals should have the right to vote.

            In this case the argument is invalid since the “persons” referred to in the first premise are not necessarily the same persons referred to in the second premise. Thus, since the middle term does not refer to each an every person in either premise, no logical connection can be made between the other two terms. This method of the formal translation of informal fallacies is further discussed below in Section VI, A, 1-2.
            
            
         3. The choice between the acceptability of the fallacy of a false or problematic premise and an unsound argument in such cases is ultimately dependent upon how “fallacy” is to be defined.
            
            
      6. Another use of the term “fallacy” not followed here includes the shift from one dialogue model to a different one.[56] These kinds of errors are not emphasized in these notes even though examples of these uses are occasionally provided in the discussions of various informal fallacies.

5. Paralogisms, Sophisms, and Paradoxes:

   1. A formal fallacy is termed a paralogism when its conclusion does not follow from its premises, and the illogical reasoning is believed valid by the proponent of that argument. The argument is presented with no intention of deception. In addition, a paralogism can be advanced as a topic for disputation in the examination of the question why specific premises an an argument seem to warrant its conclusion but do not actually do so. Usually and etymologically, a paralogism is more or less synonymous with a definition of formal fallacy as the violation of a rule of inference.
      
      
   2. When a proponent's illogical reasoning is intentionally advanced in order to deceive other persons, the fallacy is called a sophism. In sum, as Immanuel Kant writes, a fallacious argument, “when one deceives himself with it, is a paralogism; and when he endeavours to deceive others with it, a sophism.” [Kant, Logic trans. Richardson ¶ 90.]
      
      
   3. A paradox is an apparently good argument based on apparently true premises which reach a contradictory conclusion.
      
      
      1. A paradox is resolved by discovery of the faulty assumptions or by an emendation or change of a rule of logic. Traditionally, faulty assumptions were termed fallacies of a false premise. In these notes paradoxes of this kind are viewed as unsound arguments.
         
         
      2. The study of paradoxes is often useful for revealing mistaken ordinary presuppositions in our thinking.
         
         

6. Three Basic Types of Fallacies: Informal, Deductive, and Inductive:

   Since most fallacies arise from either the lack of premises or a confusion of premises, their identification is dependent upon what must be supplied in order to support the conclusion. And as Whately points out:

   ”[I]t must be often a matter of doubt, or, rather of arbitrary choice, not only to which genus each kind of fallacy should be referred, but even to which kind to refer any one individual fallacy …” [emphasis original][57]

   Fallacies cannot be as clearly classified as the types of arguments can be classified. Fallacy classifications overlap. Some informal fallacies can be formally explained; many inductive fallacies can be explained informally.
   
   Thus, arguments can be assessed by different standards depending upon their semantic content and purpose. (Other schemes of classification of fallacies are also used in the literature but are not reviewed here.) In these notes, all fallacies will be classified as either deductive and inductive. Informal fallacies are considered one type of inductive argument rather that a separate category differing from deductive and inductive arguments.
   
   Nevertheless, we will study informal fallacies as if it were a separate subject from that of inductive arguments.
   
   
   1. Informal Fallacy: those dependent upon language — i.e., a fallacy that arises from the content or the subject of an argument (the what is said), not the logical form, the grammatical structure per se, or how it is said). These notes include informal fallacies as a type of nonformal inductive arguments.
      
      Historically, from Aristotle, most informal fallacies are classified as material fallacies, “non-logical,” or extra dictionem fallacies since such fallacies are not due to the violation of formal (in dictione) rules for valid structure of arguments but rather due to the consistency of the semantic matter, meaning, or information expressed.[58]
      
      Informal fallacies, in general, usually arise in ordinary language contexts from mistakes in written and oral argumentation, persuasion and debate.
      
      In other words, traditional informal fallacies are not usually considered breaches of the rules of formal logic; instead, informal fallacies occur in disputes over specific questions at issue which are more clearly understood by other methods of analysis than those of formal logic.
      
      
      1. When an argument is valid with at least one premise false, the truth of the conclusion does logically follow from the premises, but historically, such arguments were considered to be a type of material (informal) fallacy since the conclusion wasn't proved to be true even though the argument was valid. (If you are not clear on the meaning of these terms, review the explanations offered on the truth, validity, and soundness webpage.)
         
         Some logicians today want to restrict the term “fallacy” only to a mistake in reasoning. Thus, these logicians consider a valid argument with at least one false premise good reasoning even though the truth of the conclusion has not been proved. So rather than identifying such an argument as a fallacy, they state that the argument is valid but not sound, and the claim the conclusion has not been proved true. The phrase “follows logically” here can be described by means of the counterfactual statement:

         “If the premises were true in the argument, then the conclusion would necessarily be true.”

         Consider, for example, the following argument presented by Rousseau:

         “Let us consider, therefore, the arts and sciences in themselves. Let us see what must result from their advancement … Their evil origin is, indeed, but too plainly reproduced in their objects. … [T]he labours of the most enlightened of our learned men and the best of our citizens are of so little utility … [their] waste of time is certainly a great evil; but still greater evils attend upon literature and the arts. One is luxury … can it be denied that rectitude of morals is essential to the duration of empires, and that luxury is diametrically opposed to such rectitude?”[59]

         Rousseau argues here that since the evil origin and nature of the arts and science lead to luxury, and luxury is opposed to morality, the arts and sciences are immoral.
         
         This valid argument rests on false premises and so is unsound. Some researchers simply see the argument as valid based on false assumptions and others classify it as also a case of the fallacy of false cause or even the genetic fallacy.
         
         
      2. Formal Translation of Informal Fallacies: When some informal fallacies are viewed as (formal) enthymenatic arguments, these arguments can be found valid when the missing premise is charitably found. But the argument is not sound because the missing premise must of necessity be false in order to reconstruct the enthymeme into a valid argument.
         
         David M. Godden cogently argues that the interpretation of informal arguments as deductive must be based on the context in which the argument is given and evidence that the arguer intends or ought to intend the argument to be deductive.[60]
         
         E.g., consider the following ad hominem fallacy stated by Voltaire:

         “Excessive pride and envy have destroyed Jean-Jacques [Rousseau], my illustrious philosopher. That monster dares speak of education! A man who refused to raise any of his sons and put them all in founding homes! He abandoned his children and the tramp with whom he made them.”[61]

         So, the ad hominem part of the sorites can be roughly translated as follows:

         Rousseau is an abandoner of his children and their mother.
         Rousseau is not an educational authority.

         On the one hand, since in this passage from Voltaire, Voltaire seems to express no doubt that anyone who abandons his children and their mother does not have the wisdom required to speak meaningfully about education, the context of the argument indicates his conclusion is intended to follow with certainty. Supplying the missing premise to produce a valid argument yields the following:

         Argument 1 :
         
         [No educational authority is an abandoner of his children and their mother.] F
         Rousseau is an abandoner of his children and their mother.
         ∴ Rousseau is not an educational authority.

         The quotation is an informal fallacy; the completed enthymeme is a valid but unsound argument with a false major premise.
         
         On the other hand, the recognition of Voltaire's keen wit in other contexts might suggest that he would be well aware of the tenuousness of the argument. So, perhaps we should supply a more conservative premise:

         Argument 2:
         
         Some abandoners of their children and their mothers are not educational authorities.
         Rousseau is an abandoner of his children and their mother.
         ∴ Rousseau is not an educational authority.

         This translation results in the fallacy of the undistributed middle. Moreover, if the major premise is converted to “ Some educational authorities are not abandoners of their children and their mother,” the resultant syllogism would commit fallacy of the illicit major.
         
         
         1. The first formal analysis of this informal argument above suggests a reason why one definition of “fallacy” in the nineteenth century was “A false belief, whether due to correct reasoning from untrue premises … or to incorrect reasoning from true ones.”[62] And this analysis would also be consistent with Richard Whately's fallacy of unduly assumed premise discussed above.
            
            
         2. The second and third formal analyses reinforces H.W.B. Joseph's observation that “The same inconclusive argument may often be referred at will to this or that head of fallacies.”[63]
            
            
         3. Voltaire's argument and the subsequent analyses also clearly illustrate why Richard Whately writes that the same argument can be analyzed in different ways:

            “Since in any Argument one Premiss is usually suppressed it frequently happens, in the case of a Fallacy, that the hearers are left to the alternative of supplying either a Premiss which is not true, or else, one which does not prove the Conclusion.”[64]

            In other words, often, to avoid a problematic premise in a valid argument, the argument can only be interpreted with a true premise at the price of an invalid argument. Or, as J.S. Mill writes about arguments such as these:

            “[S]ome might assent to the false premise; others allow the unsound syllogism.”[65]

      3. The pragma-dialectical theory of fallacy developed by the Amsterdam School (Frans H. van Eemeren and Rob Grootendorst) defines fallacies as violations of rules for critical discussion.[66] Douglas Walton enumerates six conditions or characteristics for fallacy in his earlier pragmatic theory.[67] Both accounts depend upon an interpretation of multiple conditions with considerable open texture involving judgments involving criteria of reasonableness, acceptableness, relevance, and sufficiency.
         
         
      4. Logic and critical reasoning textbooks (and, unfortunately these lecture notes!) usually explain informal fallacies as specific exhibits with slight attempt to analyze them in the general context in which they occur. Informal fallacies, however, are contextually dependent and require analysis in terms of their circumstances of use. A particular fallacy or argument is presumed to occur within a particular context of a dialogue, conversation, or extended argument even though the context and content usually develops and evolves as the discourse progresses. The context is, so to speak, the common ground or common knowledge of the participants.
         
         
   2. Formal Fallacy: those not dependent on the content of language. Formal fallacies arise from an error in the logical form or structural grammar of an argument; they are analyzed independently from their informational content.
      
      
      1. Formal fallacies often arise from errors arising in poorly formed deductive systems of logic. In deductive arguments, the conclusion is claimed to logically follow from the premises with certainty.
         
         
      2. The ideal of formal logic is based on (1) the belief that validity in arguments is independent of, yet abstracted from, the relationships of material or informational content of statements, and (2) the belief that the formal logical relations are independent of the psychology and context of intention and circumstances of the assertions.[68]
         
         
      3. Currently, as noted above, fallacies can be studied from different viewpoints. An argument can be found fallacious by a formal standard of validity and yet be seen as valid from a semantic point of view. Or an argument can appear to be valid from a formal point of view and yet be seen as invalid from ambiguity.
         
         Additionally, some invalid formal arguments are correct or strong inductive arguments. The usefulness of an argument depends upon its purpose and context.
         
         
   3. Inductive Fallacies arise from mistakes in inductive arguments where the conclusion is claimed to follow from the premises with some degree of probability. Inductive arguments vary in strength. The assignment of probabilities to statements is often arbitrary and subjective.
      
      It's important to realize that the semantic content of many formal and informal fallacies provide evidence for the truth of their conclusions.
      
      So, a correct or an acceptable inductive argument can also be analyzed as an invalid formal argument depending on the context of the analysis.
      
      
      1. Inductive fallacies have no clear historical standard of classification. Many traditional inductive arguments depend upon semantic content rather than argument forms so many inductive fallacies are informal fallacies: e.g. converse accident (hasty generalization), accident, causal fallacies, false or faulty analogy, genetic fallacy, and ad ignorantiam.
         
         
      2. J.S. Mill points out that induction proceeds from facts; when these facts are mistaken, fallacies based on poor observations or mistaken inferences result.[69] Examples of these types of fallacies include confirmation bias, preconceived opinion, faulty generalization, suppressed evidence, and so forth.[70]
         
         
      3. These and other presumptive fallacies are common in inductive logic, especially in the use of formal scientific methods, including probability and statistics.
         
         
      4. Inductive methods used in causal reasoning, probability, and statistics are based on formal rules, and consequent fallacies in these areas of inductive logic are violations of formal rules. Analyses of informal fallacies using these methods is promising. [71]

7. Chart of Formal, Informal, and Inductive Fallacies

   The following chart of fallacies, with some suggestive examples, is an indication of some of the terrain to be discussed in this course:

The following Google Ngram of the frequency of usage of the main divisions of logic suggest the historical periods of active interest in these fields of inquiry:



FIG. 1. Historical Frequency of Use of formal logic, inductive logic, and informal logic in Google Books 1800-2008

8. Final Comments and Cautions on Fallacies

   The classification of fallacies used in these notes is, to some degree, an oversimplification.
   
   
   1. Since errors in reasoning depend upon the type of mistakes made in different evolving logical systems, ideally fallacies should be described in terms of the different kinds of logic in which they occur. However, to present adequately these topics at the beginning of our study would not only be impractical but also would result in a disorganized treatment. [72]
      
      
      1. Since logic is normative, logical pluralism most likely gives rise to different epistemic norms. In a recent influential paper, Hartry Field concludes:

         The upshot of this is a kind of normative pluralism: there are lots of possible norms, and we can rate them as better or worse (relative to our epistemic goals), but there's no reason to think there's a uniquely best one. And talk of correctness of epistemic norm just doesn't seem to make sense.”[73]

         And, as well, different logical systems continue to evolve.
         
         
      2. John Woods and others cogently argue no clear distinction can be drawn in general between fallacies and non-fallacies since many times arguments containing traditional fallacies perform useful functions of abductive and inductive reasoning which are often correct. When evaluating such arguments as these, it is often more reasonable to “commit the error” than to jettison the argument altogether.[74]
         
         
   2. Consequently, the assumption taken in these notes is that, even given these difficulties, a somewhat less than comprehensive organization of fallacy topics is still useful in beginning preparation for studying reasoning in all areas of human inquiry.
      
      It's important to be aware that in debate and in other forms of persuasive discourse, the skillful use of fallacies often proves effective in argumentation — even though no proof or proper justification is provided in the argumentative discourse presented.
      
      
      1. Many of the difficulties in studying informal fallacies stem from the fact that in ordinary language discourse, fallacies often occur with implicitly assumed premises. Consequently, whether or not arguments are intentionally being advanced is sometimes a question open to interpretation. In such cases, in beginning a reconstruction of a presumed argument, the principle of charity ought be followed in so far as possible, whereby misinterpretation or misconstruction of an opponent's discourse is minimized.
         
         
      2. In our discussion of informal fallacies, an effort will be made not to assume a passage is argumentative unless its context and language indicates that this is the author's intention. If a passage is argumentative, frequently, but not always, premise and conclusion indicator words will be present.
         
         
         1. A brief caution here is important: When studying fallacies for the first time, many persons have the tendency to see fallacies in merely emotive, persuasive, and rhetorical non-argumentative passages. It's important to remember that unless an argument is present, no fallacy can occur.
            
            
         2. Thus, the prerequisite for finding a fallacy in a reading is the presence of a logical argument. (An argument is composed of at least two statements: a premise and a conclusion.)
            
            
      3. Some textbooks refer to passages to be analyzed as appeals rather than referring these passages as arguments. The topic of rhetorical appeal, where no argument is present, is properly treated in terms of “disagreements in belief and attitude” as discussed in Logic and Language. An important related topic of the distinction between “arguments and nonarguments” is explained in The Nature of Arguments. Normally, arguments in rhetorical discourse should be evaluated by translating those passages into emotively neutral language prior to analysis.
         

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