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The Amateur Logician Tutorial:
An Invitation | Arguments | Evaluating Arguments | Laws of Thought | Ontology & Logic | Concepts, Signs, & Names | Categorical Propositions | Negations & Complements | Distribution | Euler’s Circles & Venn Diagrams | Predicables | Categories | Definitions | Square of Opposition | Equivalent “Immediate Inference” | Traditional “Immediate Inference” | Informal “Immediate Inference” | Categorical Syllogism | Syllogisms & Venn Diagrams | Moods & Figures of Syllogisms | Polysyllogisms & the Sorites | Enthymemes | Compound Propositions | Conditional Propositions & Conditional Syllogisms | Conditional Contrapositions, Reductions, & Biconditionals | Conjunctions, Disjunctions, & Disjunctive Syllogisms | Dilemmas | Modal Propositions | Reductio ad Absurdum Arguments | Deduction & Induction | Inductive Abstraction | Inductive Syllogisms | Mill’s Inductive Methods | Science & Hypothesis | Formal Fallacies | Testimony & Unsound Authority | Informal Fallacies & Language | Diversion & Relevancy Fallacies | Presumption Fallacies | Causal & Inductive Fallacies
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Presumption Fallacies
Petitio Principii (a.k.a. Begging the Question)
– Begging the Question ≠ Raising the Question
– Circular Arguments
– Begging the Question & Immediate Inference
– Begging the Question & Categorical Syllogisms?
Persuasive Definition and Loaded Language
Complex Question
False Dichotomy
– Confusing Contrary with Contradictory Opposition
– Dilemma
Argumentum ad Ignorantiam (“appeal to ignorance”)
Good argumentation contains evidence.
Evidence comes from premises that are relevant to the conclusion and, at the same time, independent of the conclusion in such a way that none of those premises presuppose the conclusion from the outset.
Presumption fallacies contain premises that already presume what they are meant to prove. Such arguments thereby don’t actually prove their conclusions.
Petitio Principii (a.k.a. Begging the Question)
Warning!
To “beg the question” doesn’t mean “to raise the question.” Please, please don’t confuse the two!
An elephant is found in my backyard. That raises the question: How the heck did it get there? It doesn’t beg the question, since to “beg the question” is to engage in a fallacious argument that assumes in the premises what that argument seeks to prove.
Don’t sound like a journalist!
Stop using the colloquial sense of “begging the question” for “raising the question.”
Petitio principii translates into something like “request for the source.” The argument lacks a source of support. If a premise and conclusion are identical, for example, it is obvious that the argument has not provided any evidence for that conclusion.
Example 1: “The Bible is the word of God because it is divinely inspired.”
Example 2: “A new study has shown that Americans are better cooks than Canadians. The reason provided is that Canadians cook worse.”
With Example 1, the premise states that the Bible is divinely inspired. The conclusion states that the Bible is the word of God. However, being “divinely inspired” is the same as being “the word of God.” Hence, because the premise and conclusion are identical, the argument begs the question – petitio principii.
Example 2 likewise engages in the petitio principii fallacy. The only reason provided here is that “Canadians cook worse,” but that’s the same as saying, in this context, that Americans cook better (via converse relation).
Notice that an argument of the following form is “formally valid.”
Premise: X
Conclusion: X
This preserves the law of identity!
At the same time, that argument is “informally invalid” insofar as the issue is proving X. It is then begging the question.
Circular arguments are a species of begging the question. X is said to be true because of Y, and Y is said to be true because of X. The argument “circles around” the propositions.
Example 3:
Captain Benjamin Sisko – “Now, so far, your case is based on circumstantial evidence and speculation.”
Deputy Director Sloan – “What other kind of case can I make against a man who covers his tracks so well?”
Sisko – “That’s a circular argument, and you know it!”
(From Star Trek: Deep Space Nine, “Inquisition.”)
Sloan is arguing that Dr. Julian Bashir is an agent of the Dominion. Sisko basically replies, “Where’s the evidence?” According to Sloan, there’s little because Bashir is a cunning spy. Hence, Sloan is begging the question or engaging in a circular argument.
Controversy surrounds the next example.
René Descartes (1596 – 1650) launched “modern philosophy.” His “methodological doubt” started an investigation to search for what cannot be doubted. Descartes noted that “sense perception” has fooled him in the past; ergo, sense perception can be doubted.
Later Descartes reasoned that if he can prove in God’s existence, then he can trust such things as sense perception because God is not a trickster. Essential to this argument is that Descartes could doubt “clear and distinct ideas.” But, if God exists, he can trust them.
Example 4:
Proposition A – “Clear and distinct ideas are trustworthy because God guarantees them.”
Proposition B – “God exists because I have a clear and distinct idea of His existence.”
[Read Descartes’ Third Meditation.]
Under this standard interpretation of Descartes’ argument, he has it that God’s existence ensures him that “clear and distinct ideas” are reliable and argues for God’s existence based on “clear and distinct ideas.”
Circularity is present because Descartes “proves” God’s existence based on “clear and distinct” ideas, and justifies “clear and distinct” ideas as being reliable by God’s existence. However, he can’t prove God’s existence without first proving that “clear and distinct” ideas are reliable! He seems to “get around” this by (fallaciously) arguing in a circle.
What about the next example?
Example 5?
“Cogito, ergo sum.”
(“I think, therefore I am.”)
[Read Descartes’ Discourse on Method.]
On first glance, it looks alright. Look again. . .
The premise is “I think.” It seems as if that already presupposes an “I am” that exists; however, if that is the case, then the argument begs the question.
To be fair, I believe it’s better to interpret Descartes as expressing a self-evident truth. I can immediately recognize, as self-evident to myself, that I exist. (You can do the same: it is obvious to you that you exist.) It is not supposed to be an inference from “I think” to “I am.”
On this interpretation, Descartes is not begging the question.
Another interpretation, which can supplement the last interpretation, is to think about what a denial will do to the self-evident truth. Deny, to yourself, that you exist. Doing so is incoherent. That act of denial itself presupposes that you exist, and so there is a performative contradiction. You must exist to presently say to yourself, “I am.”
Begging the Question & Immediate Inference
Immediate inference can sometimes help us detect an argument that begs the question. That’s because “immediate inference” allows us to see if two propositions are logically equivalent to each other.
With immediate inference, we can take a single proposition to immediately derive another. For example, “all men are mortal” is equivalent to the proposition “no men are immortal” (by obversion). That’s formally valid!
Yet, when the argument is something like “all men are mortal because no men are immortal” that’s informally invalid by begging the question.
Begging the Question & Categorical Syllogisms?
John Stuart Mill (1806 – 1873) attacked all categorical syllogisms as “begging the question.”
Consider the example:
“All men are mortal.”
“Socrates is a man.”
“Ergo, Socrates is mortal.”
How do we know the major premise is true?
(Namely, “all men are mortal”?)
Mill thought we would have to count up individuals. Moreover, if this is the case, a syllogism’s conclusion couldn’t reveal new information because the prior enumeration already revealed what the conclusion says. Hence, we learn nothing from syllogisms. Petitio principii!
However, Mill failed to understand the de omni et nullo.
The major premise is not based on enumeration. It’s not about “counting up” individuals. We didn’t go out and find Socrates in a counting survey. A process of enumeration does not arrive at a new truth, which is what a syllogism’s objective is. Mill failed to understand that we can think about concepts and universals. Necessary features of the middle term can be analyzed.
In the proposition “All men are mortal,” we’re not supposed to be thinking about the predicate in its extension, but in its intention or comprehension.
Man has the power of abstraction. As logician George Joyce writes, “The Empiricist school deny that we possess this power… By doing so they cut away the foundations of Logic” (p. 198).
Review Joyce’s arguments against Mill in his Principles of Logic textbook.
(1) Universal propositions are not “a mere record of individual facts.”
— Predicates can state a necessary property, reached via abstraction.
(2) The major premise alone is not enough.
— It takes two premises, and we can be ignorant of one or both of them.
— Only together can a mediate inference occur from the two premises.
(3) Categorical syllogisms involve the application of a universal proposition.
— Universality allows applicability to every relevant case.
Persuasive Definition
and Loaded Language
Terms or phrases can be defined in question-begging ways. A propagandist can slant language in a way in which he uses words that are both descriptive and normative at once. Words that perhaps should be purely descriptive can be twisted to carry emotive charge with a value judgement.
Example 1:
Neutral Example: Governorship will change hands after the reelection failed.
Loaded Example: Voting for Linda will bring a voice of change.
“Change” as a word can be purely descriptive (i.e., factual) or it can carry additional connotation that’s normative (i.e., a value judgment). The neutral example states a matter of fact. The loaded example adds a positive judgment to the word “change.”
Things become fallacious when someone starts using loaded words or phrases to beg the question. Rather than proving something, things are just assumed to be true. Things are defined to be such-and-such, not argued to be such-and-such.
Example 2: A “liberal” is one who has wrong ideas about economic freedom.
Example 3: A “conservative” is for old-fashioned, out-of-date ideas.
Slogans are not arguments. People often talk as if they are adequate substitutes.
Complex Question (a.k.a. Fallacy of Many Questions)
A “complex question” is another form of “loaded language.” No question itself is a fallacy. Nonetheless, a question can be worded in a way that assumes something that is to be demonstrated. “Complex questions” place someone in a no-win position.
…It’s a trap!
(I needed some Star Wars reference!)
Example 1: “Have you stopped beating your wife?”
Answer “yes,” then that means I beat my wife in the past. Answer “no,” then that means I am still beating my wife.
The question “begs the question” in that it assumes I beat my wife.
“Fallacy of many questions” is another name for “complex question.” We can disentangle several questions from the single question. Answering the single question requires us to make finer distinctions than the question allows. “Have you stopped beating your wife?” should be disentangled into two questions: “Have you beat your wife in the past?” “If you have, have you stopped now?”
False Dichotomy
False dichotomies give us choices that are not exhaustive. Hence this fallacy is also called the “either-or fallacy.” It gives us what is called a “false bifurcation.”
Pretend we’re given the disjunction P or Q, told it’s exhaustive in the two choices; and that, therefore, because P is not the case, we’re told Q must in fact be true.
It is valid (as a modus tollendo ponens argument), but is it sound?
That is, is it a good argument that reaches a true conclusion from true premises? Determining that requires us to evaluate the truth or falsity of (1) the disjunctive premise P or Q and (2) the premise that denies P.
Alternative explanations might be possible!
Alternative choices might be possible!
It may be that the disjunctive premise is not exhaustive and, therefore, that the argument commits the false dichotomy fallacy.
Example 1: “You’re either for the War in Afghanistan or for the terrorists.”
“You’re against the war; ergo, etc.”
False dichotomy! Somebody can oppose both.
Such illogic is often encountered during war; it’s simplistic “black-and-white thinking.”
Example 2: “You’re either a theist or an atheist.”
Example 3: “You’re either a Democrat or Republican.”
Example 2 and Example 3 leave out other real choices.
Confusing contrary with contradictory opposition is the source of the next example.
Example 4: “You’re either rich or poor.”
One source of false dichotomies is thinking, or pretending, that contradictory opposition entails contrary opposition.
P versus non-P are contradictory, not necessarily contrary. The contradictory of being rich is being non-rich, but being non-rich doesn’t mean you’re necessarily poor. Rich and poor are contraries because they are opposite extremes.
Contraries cannot both be true, but both can be false. So, just because one is true, doesn’t mean the other must be false. This is unlike contradictories! Then, if one is true, the other must be false. (Review the Square of Opposition.)
Contrary opposition allows for a spectrum to exist.
E.g., between rich and poor is the middle class.
Contradictory opposition has no spectrum.
E.g., between having $1 million or more versus not having $1 million or more.
See the “Dilemmas” page for more. Review “escaping between the horns.”
Argumentum ad Ignorantiam (“appeal to ignorance”)
Here’s another type of presumption fallacy. It’s an argument that reasons that the lack of proof for X not being the case is proof that X is the case. Conversely, it’s an argument that reasons that the lack of proof for X being the case is proof that X is not the case.
What logically follows from not knowing? Nothing! Hence, we cannot infer that, since we don’t know X is false, it is therefore true or it is therefore false. We just don’t know.
Example 1: “Life doesn’t exist on another planet. Nobody has provided evidence that there is.”
Example 2: “Life exists on other planets. Nobody has provided evidence that there isn’t.”
Warning! Like any informal fallacy, there are contexts in which the argumentum ad ignorantiam is not necessarily fallacious. The lack of evidence for X can, in some cases, make probable that X is not true.
First, sometimes it’s reasonable to tentatively conclude something is probably not the case from a lack of evidence.
Second, our knowledge base might be sufficiently complete to rule out a proposition’s truth based on the lack of evidence.
Third, a presumption might place the “burden of proof” on those proving or disproving a proposition. A man is “innocent until proven guilty” in the courtroom, for example.
Douglas Walton, a scholar of informal logic, has given examples of when the argumentum ad ignorantiam is not fallacious in the American Philosophical Quarterly. Consider the following. . .
Example A: Experts might be testing a new drug on rats with no evidence that there’s any poisonous effect. It’s reasonable to infer the drug is likely not toxic, provided no new evidence has shown otherwise. This argument assumes (1) the experts are reliable and (2) that there’s a high probability that if the drugs were bad they would be discovered to be bad.
Example B: A posted train schedule states that train Ω that travels to location α stops at location β and location γ. Therefore, we infer, it doesn’t stop at location δ because the posted train schedule doesn’t list it.