In fallacies of presumption, the arguer has made an epistemological, or ideological assumption that is in error. An epistemological error concerns beliefs towards how one learns about the world. For example, some people believe we can learn things "emotionally." There is no such thing as an "emotional truth" only things we cognitively hold as true concordant with strong emotional feeling.
An ideological assumption concerns beliefs towards how logic and reason work, and their value. For example, some theologians and mystics claim that science or logic or even reason itself is only illusion. This is simply incorrect. I repeat here the words of Ethan Allen, the revolutionary war hero, who states why:
Those who invalidate reason ought seriously to consider whether they argue against reason with or without reason; if with reason then they establish the principle that they are laboring to dethrone: but if they argue without reason (which, in order to be consistent with themselves they must do), they are out of reach of rational conviction, nor do they deserve a rational argument.
With this renewed acceptance of the validity of reason, and thereby logic, we proceed to the following section.
Fallacy of Magical ThinkingEdit
Also known as the Labeling Fallacy, and similar to reification, the fallacy of magical thinking occurs when a debater claims that by merely naming or providing a name for a phenomenon, he has in fact provided an argument in favor of his position.
- "There are, of course, many who regard the concept of God as an exceedingly simple explanation of everything, and who regard scientific elucidations as either incomplete or ponderous. However, that is a self-delusion. Such views are generally held by people who do not understand the scientific method. Indeed, to believe that the assertion that God is an explanation (of anything, let alone everything) is intellectually contemptible, for it amounts to an admission of ignorance packaged into the pretence of an explanation. To aver that 'God did it' is worse than an admission of ignorance, for it shrouds ignorance in deceit."
- "Religion - The Antithesis to Science", Oxford Chemistry Professor, Peter Atkins
Magical thinking is akin to the problem of "labeling" - the fallacious assumption that providing a name for an observed phenomenon provides us with information.
Special pleading is a fallacy in which a person applies standards, principles, rules to others while claiming special dispensation or exemption for themselves without providing adequate justification for the exemption.
In particular, special pleading occurs when when a person in logical discourse asserts that their claims lie outside of reason or logic itself.
Example: How can there be an equally godlike Father, Son and Holy Ghost in the same person? Answer: You don't grasp the ineffable mystery of the trinity.
You don't have to grasp the ineffable mystery, (and as stated, your opponent doesn't grasp it either!) If your opponent wants to maintain a belief in an argument, he must provide you with his evidence, not his own explicit admission that he has no evidence!
Remember that the basic premise of rational discourse is to present your reason for why you hold a belief. Stating that you don't know the reason is not a reason. And we cannot invalidate reason simply because reason doesn't give us what we want
From the Nikor Project (http://www.nizkor.org/features/fallacies/special-pleading.html):
From a philosophic standpoint, the fallacy of Special Pleading is violating a well accepted principle, namely the 'Principle of Relevant Difference'. According to this principle, two people can be treated differently if and only if there is a relevant difference between them.
There are cases which are similar to instances of Special Pleading in which a person is offering at least some reason why he should be exempt but the reason is not good enough to warrant the exemption. This could be called "Failed Pleading."
Warning signals: You've just asked your opponent for his reason for maintaining his proposition. He tells you the only problem is you - you just can't grasp, comprehend, or admire that the phenomena in question is a paradox that is (safely) beyond science or beyond reason. He is special pleading you.
The anthropomorphic fallacy or pathetic fallacy is the treatment of inanimate objects as if they had human feelings, thoughts, or sensations. The pathetic fallacy is a special case of the fallacy of reification. The word "pathetic" in this use is related to empathy (capability of feeling), and is not pejorative.
The pathetic fallacy is also related to the concept of personification. Personification is direct and explicit in the ascription of life and sentience to the thing in question, whereas the pathetic fallacy is much broader and more allusive.
Also known as the fallacy of questionable criteria. this is the application of irrelevant standards to the subject of the argument. It is a basic fallacy of assumption. Asking someone to 'weigh an idea' which presupposes or 'begs the question" that ideas are particular entities and not fluid, interconnective process involving numerous neurons, would be an example.
A particular type of False Criteria fallacy that argues something is inferior just because it doesn't do something it was never intended to do. An example would be to question the value of Social Security as a means of affording senior citizens with adequate funds to enjoy their 'golden years', when the program was actually instituted as a means to help aged people avoid indigency.
Feelings are cues - they alert us to certain facts. Feelings may enhance belief. Feelings may lead us to a sense of conviction that a belief is true. But feelings, on their own, are not an argument, and in some cases, strong emotions may cloud reason.
NOTE: This fallacy is also listed in the Rhetorical Appeals section the Appeal to Faith.
Universal skepticism is the claim that all epistemological positions - and reason itself, ultimately relies on faith - i.e we must have faith in first foundations in order to know anything.
By Nathaniel Branden:
- One of the most grotesque instances of the stolen concept fallacy may be observed in the prevalent claims made by neo-mystics and old-fashioned mystics alike that the acceptance of reason rests ultimately on "an act of faith." Reason is the faculty that identifies and integrates the material provided by the senses. Faith is the acceptance of ideas or allegations without sensory evidence or rational demonstration. "Faith in reason" is a contradiction in terms. "Faith" is a concept that possesses meaning only in contradistinction to reason. The concept of "faith" cannot antecede reason, it cannot provide the grounds for the acceptance of reason, it is the revolt against reason. One will search in vain for a single instance of an attack on reason, on the senses, on the ontological status of the laws of logic, on the cognitive efficacy of man's mind, that does not rest on the fallacy of the stolen concept. The fallacy consists of the act of using a concept while ignoring, contradicting or denying the validity of the concepts on which it logically and genetically depends. This fallacy must be recognized and repudiated by all thinkers, if truth and reality are their goal.
The claim that all beliefs ultimately rest upon an unsubstantiated, unjustified, desire driven beliefs (what we will properly defined as 'non contingent faith') is self refuting - If we cannot know anything with certainty, then we cannot be ascertained of the value of faith.
The Appeal to Faith is often used by fundamentalists to undermine classical logic (which they often confuse for all logic) or reason itself. Classical logic rests on axioms, not faith. Axioms do not need to be proven because there is nothing to prove: they are prescriptive statements concerning a method, and not descriptive statements about the world to be classified as true or false. If you accept these axioms, then you must accept the conclusions that follow from arguments built upon them. In other words, they are the foundation upon which we'd form any proof. They are self evident, atomic statements, that all other statements rely upon, which are defended through retortion. As held by defenders of classical logic, any attempt to refute an axiom leads to a self refutation. As Ayn Rand notes, axioms are supported by the fact that we cannot know anything,or make any claims, without illustrating their veracity. For these reasons, accepting axioms is not equitable with holding to a belief through non contingent faith.
Non-contingent or theological faith is simply the maintenance of a belief despite the lack of evidence, or even in the face of negating evidence. To confuse faith for a reasoned assumption is a gross error.
Faith is not a means to gain knowledge. Faith is an assertion that one can accept a belief without justification. It's an end to rational thought, not a beginning. Faith has never been shown to be anything more than believing what you want to believe no matter the reality. Faith depends on irrational thought and produces intransigence. Historically, people "of faith" have used the very next appeal that follows "to alter the opinions" of their opponents.
Naked Assertions and Related FallaciesEditI am truly stunned that I have to even list these as logical fallacies, but my experiences arguing with others shows this is clearly necessary.
Naked or "Bare" AssertionsEdit
A "naked" assertion is simply an assertion without any evidence, proof, or other support. It is usually based on the false presumption that since we all have "a right to an opinion", that this implies that our opinions must be automatically accepted as valid. What invariably proceeds the blunder of a "naked" assertion is the logical fallacy of "shifting the burden of proof" which further illustrates that the arguer has no concept of logic.
A common example of a Naked Assertion masquerading as a logical argument is found in Christian Presuppositionalism:
- Archer says, "Without a good and holy God in heaven above, however, there is no solution to be found in freethinking or any other kind of thinking." Again no proof or justification is provided. Just another assertion that is supposed to be sufficient unto itself. Too bad I didn't think of that approach! Instead of devoting so much time and effort to reading and research, I could have just forgotten about all my studies, thrown away my notes, discarded my citations, and told it like it is. That certainly would have been easier. - Dennis McKinsey from Bible Errancy (http://mywebpages.comcast.net/errancy/issues/iss160.htm)
Archer's statement also includes the fallacy of arguing to dire consequences and "correct by default"
Fallacy of Belief as ProofEdit
Closely related to the fallacy of a naked assertion is the fallacy of belief as proof. In fact, this fallacy is often used to support a naked assertion!
This fallacy occurs when one maintains that one's strong conviction is itself a proof, without any other evidence. As Sigmund Freud wrote in Future of an Illusion:
Your own convictions can not serve as proofs for me.
This fallacy stems from the confusion of that the intensity of one's beliefs indicates the veracity of one's beliefs. Try to remember that intensity of a belief in no way correlates with the veracity of a belief. Billions of people are sure and wrong. Every christian who knows that the christian god is real also "knows" that there are a billion Muslim fools.
Shifting the Burden of ProofEdit
The burden of proof is always on the person asserting something. Shifting the burden of proof, a special case of Argumentum ad Ignorantiam, is the fallacy of putting the burden of proof on the person who denies or questions the assertion. The source of the fallacy is the assumption that something is true unless proven otherwise. This is not the case. You can't assume the truth of a proposition without proof. If we could assume truth until disproven, we would be stuck with the ridiculous conclusion that anything we said to be true, must be true, and would only become false when proven false. Reread the ignorantiam law if you are still confused.
This error, above nearly all others, indicates a lack of knowledge of the tenets of logic.
Arguments from IgnoranceEdit
An Argument from Ignorance occurs when one makes a positive claim based on a lack of information. Basically, the claimant assumes that since something has not been proven false, it is therefore true. But you can't make claims without reason or evidence. All a lack of information can tell you is that you do not know. A claim's truth or falsity depends upon supporting or refuting evidence for the claim, not the lack of support for a contrary or contradictory claim.
- The weakness of my argument does not imply the strength of yours - Sigmund Freud
An argument from ignorance often is merely an expression of one's desires and little more. The Skeptic's dictionary calls it "Wishful thinking".
See also Special plead, Shifting the Burdon of Proof, Correct by Default, Centipede Fallacy, Platonic Fallacy and Argument from Uncertainty.
God of the GapsEdit
God of the Gaps may also be referred to as a Correct by Default Fallacy. It is a compound fallacy, a combination of the False Dichotomy fallacy and Arguing from Ignorance. The reasoning here goes as follows: One person in a debate puts forth a naked assertion that their position is true and demands that the the opponent provide a satisfactory argument for his position. He then holds that the opponent cannot provide an alternative explanation. Therefore, the first arguer claims that his position MUST be true, since there is no alternative explanation. However, the arguer has not put forth any reason why his explanation is true, he merely assumes it is correct by default. The absence of other proposed explanations does not imply validity for his assertion. If this were true, and we followed this logic to its conclusion, we end up with this absurdity: ANY first explanation for a new phenomena must be true, since at that time no alternative exists!.
Here is a nice example of a response to this fallacy, by Brooks from the Bogus Beyond Belief website:
- You keep saying that I am reading too much into your questions, implying that you are merely asking them out of idle curiosity. Hardly. You are attempting to use the so-called moral "argument" for God. You apparently hope that I will be unable to explain the basis for human morality, and that you then will be able to insert "God" as an explanation, sort of a round-about way of promoting Christianity. It is a great ploy to use, because it doesn't require you to provide those troublesome things known as real arguments and evidence. It relies on a lack of an explanation from the other side. There is a problem, however. You say that you "believe" that morality comes from "God." This is your *opinion*-you have not supported it with any evidence yet. Until you provide me with some evidence or arguments for this statement, it remains your opinion and nothing else, and this is true "whether it is acknowledged or not."
The Centipede FallacyEdit
The Centipede Fallacy is closely related to the God of the Gaps Fallacy and the Argument From Ignorance. It occurs when an arguer implies that your inability to explain how some concept or phenomena works implies that the phenomena therefore cannot work, or does not even exist. The name comes from fact that a centipede has no idea how to move hundreds of legs in unison, but he does so anyway.
Example: Since science cannot provide a complete explanation of phenomenon x, we have reason to question whether it really knows anything about X
This fallacy does not apply when a debater points out that the phenomena in question cannot work because it violates an observable law of physics, or that the precepts it is based on are in contradiction. In this case, he is not committing a fallacy... and in fact, if his premises are true, he is right - the phenomena is untrue.
Sorry, but that is now logic goes. Also see the Reification Error.
The Platonic FallacyEdit
The Platonic fallacy is a specific form of Centipede Fallacy, which in turn is a form of an Argument from Ignorance. It is based on the notorious difficulty in defining a concept, such as 'chair', in a way that gives both necessary and sufficient conditions for chairs, rules in only things that we consider chairs, and rules out anything that is not a chair.
The reason we find the application of categories to the real world so daunting is because categories are themselves artificial: we create them. The universe is a continuum, not a set of static categories, and as such, is under no obligation to fit into our categories. We struggle to find an absolute separation point between things like chairs and couches, or tables, or even a fallen tree log because there is, in fact, no real, obvious and absolute demarcation between such entities in the first place. The fallacy, therefore, occurs when one attempts to rely on this notorious difficulty in applying categories to the real world entities, as a grounds for holding to incoherent or contradictory terms, since they, too, are 'difficult to define'.
Also known as compound proposition. This fallacy occurs when an argument includes more than one claim in the proposition and treats proof for one claim as proof for all the claims.
Argument from UncertaintyEdit
This is a bit different from Arguing from Ignorance. Arguing from uncertainty occurs when one attempts to use the tentative nature of inductive claims as a reason in of itself to reject an inductive claim. Inductive claims are accepted or rejected on a probabilistic basis, as per their evidence.
Consider the following table:
|Absolute truth||Most likely true||Maybe true||Probably false||Defintely False|
|Tautologies||Theory of Gravity||Kant's Categories||"Big Foot"||Contradictions|
ere we can see that whereas mountains of evidence exist to support the notion of gravity, there is but a dearth of evidence to support "Big Foot' Therefore, while both ideas lie along the continuum, they are hardly equitable in truth value. We can reasonably reject Big foot claims, while we can reasonably accept claims about gravity.
"Quite frequently I encounter people who equate lack of certitude with giant inferential leaps. Science deals with probabilities, often quite high probabilities, but not certitudes. It is one of the strengths of the scientific method as it acknowledges a chance of error(while maintaining rigorous standards to establish provisional acceptance of propositions). Therefore, to reject a claim such as "smoking is bad for your heatlh" based on the tentative nature of scientfic claims in of itself, is equitable with questioning whether there is gravity (as the concept of gravity is an inductive claim as well.)
It is a mistake to believe that a science consists in nothing but conclusively proved propositions, and it is unjust to demand that it should. It is a demand only made by those who feel a craving for authority in some form and a need to replace the religious catechism by something else, even if it be a scientific one. Science in its catechism has but few apodictic precepts; it consists mainly of statements which it has developed to varying degrees of probability. The capacity to be content with these approximations to certainty and the ability to carry on constructive work despite the lack of final confirmation are actually a mark of the scientific habit of mind." -- Sigmund Freud
On the other hand, it is also a fallacy to argue that because something is possible, that it will happen.
Fallacy of the Golden Mean
This fallacy assumes that to be correct, one must be 'balanced'. Like most errors in thinking, this idea originates in a good idea: keeping oneself open minded by considering 'all sides' of a question. But once one has sufficient data to hold to an answer rationally, simply 'avoiding a side' no longer makes sense. Avoiding extremes does not guarantee correctness.
"He's a Capitalist, she's a Communist. I'm smack dab in the middle, so I must be right."
Fallacy of the Law of Averages
Author A. K. Dewdney, from his book "200% of Nothing" speaks about a form of ignorance nearly as bad as illiteracy - innumeracy, or the ignorance of math. A particular form of innumeracy is citing the "law of averages" or the belief that if some statistically measured event has happened an inordinate amount of times, it must soon stop. A good example would be the roulette player who knows that black must now come up after a string of reds.
The contraposition is that if such a event has yet to occur, it must now be "due." This mentality is seen most in sports announcing, where an announcer might say "Jeter hit .320 on the season. He is currently in the middle of a slump, 1-11. He's due!"
The fact is, logically, every single event is separate from prior events. If Jeter's real average is .320, then at every at bat he has, approximately, a 30% chance of getting a hit. (This leaves out individual differences in pitchers, who may reduce or increase this percentage.)
The Conjunction Fallacy
This fallacy occurs when we presume the following equation to be true:
P(A + B) > P(A)
In order to understand this equation, use this key: P=probability, A, B = Propositions, and += AND, i.e. both A and B together. So the equation reads: the probability of a premise, in conjunction with another premise, being true is greater than the probability of just the one premise being true.
Stated abstractly, this seems a ridiculous error, and an easy fallacy to avoid. Assuming there is no causal connection between B and A, how can the possibility of both premises A AND B being true be more likely than just premise A , being true?! Yet, when we use specific premises, the conjunction fallacy seems a much more confusing issue:
Go ahead and try this one out:
Bill is a boring guy. Knowing this, which of the statements is more likely to be true?
Bill plays Jazz trumpet Bill plays jazz trumpet, and is an accountant
Are you tempted to say the second answer is more likely? Of course you are. This occurs because we never look at facts without using prior knowledge. We use schemas or stereotypes based on experience, to evaluate any facts. We "know" that boring people are often not jazz musicians, so in order to accept that a boring guy named Bill would play Jazz trumpet, we need to ground this incongruous knowledge with something that appears to be more likely to be true - i.e. that a boring guy is an accountant.
But the truth is, unless there is some strong causal relationship between being boring, playing the Jazz trumpet, and being an accountant, this is fallacious thinking. In lieu of any other information, it is more logical to state that the first response, "Bill plays Jazz trumpet", is correct, because it only makes one assumption, not two!
My apologies to all accountants, everywhere, as well as any boring guys named Bill.
Also known as Hypostatization, Reification error occurs when we treat a sign as a signifier - i.e. when we treat abstract concept as having an existence independent of the brain. This error also occurs when one makes the claim that since one can imagine some phenomenon, then this phenomenon must exist. This argument was used by Saint Anselm. See my entry on Anselm on my "Christian philosophers of the middle ages" page. Briefly, Anselm's argument was that since he could imagine a perfect being, then he must exist, since its "more perfect" for him to actually exist "extra-mentally".
The argument was so silly that it was refuted in his own time. Yet, 1000 years later, it still pops up. Here are the obvious refutations:
You can't imagine a perfect being. When you try, you usually come up with a contradiction - i.e. an all good, all powerful god who is restrained for some reason against stopping evil (I.e. he will allow a child to be repeatedly gang-raped, before going to hell for non belief, so that you and I have free will.)
You imagine plenty of things that don't exist: unicorns, pink elephants, well adjusted mature women... (ok, that last one strains credulity), so why is it that only this one imagination, god, must be true, while no one maintains that there are in fact unicorns?
This fallacy can be much like the centipede fallacy (See centipede fallacy) when it is then used to make the claim that the abstract concept that you cannot define, therefore cannot exist. See also 'category error'
Confusing Abstractions for Immateriality
The fallacy occurs in this form: "There is no materialistic account of abstractions/numbers/colors/universals, ergo abstractions/colors/numbers/universals are immaterial and this proves that immateriality is coherent, since 'abstractions/colors/numbers/universals are coherent existents."
This is the fallacy of confusing an abstraction for immateriality - it is a compound fallacy, containing three more basic informal fallacies. Let me first point out the logical fallacies contained in this error.
"There is no materialistic account of "X"
This is an argument from ignorance. Your inability to perform a task does not prove the task impossible. In addition, we have a parsimonious materialistic account for these entities: Neuroscience provides a rational, albeit incomplete basis for holding that abstractions exist within material brains. Any failure of neuroscience in giving a satisfactory materialist account for abstractions is not a basis for holding that abstractions are immaterial.
"...X is immaterial"
This is the fallacy of begging the question. One is simply assuming that "X" is immaterial, based on the previous argument from ignorance, and not for any positive reason.
"...and this proves that immateriality is coherent"
This is the fallacy of non sequitur. You are merely begging the question that "X" is immaterial and then asserting it as evidence of immateriality. Nothing in this claim actually addresses the ontological problems outlined in this brief essay. Nothing in this claim demonstrates how immateriality is coherent, it merely assumes that immaterial things exist, ergo the claim doesn't even address the challenge.
A category error occurs when one attempts to use an invalid sensory modality, or manner of knowing a particular phenomena, such as trying to hear light, or feel an idea, and then holds that the failure of this modality or manner of knowing to detect the phenomena proves that the phenomena either does not exist, or that it exists in some 'immaterial form'.
An example would be the claim put forward by immaterialists that colors or numbers must be immaterial, since we cannot locate 'color' or "numbers" as physical objects within a brain. Yet the same arguer would not expect to find tiny actors and musicians inside his television set, he would expect to find electronics that interpret electrically transmitted data as audio-visual entities. So clearly there is some error here!
And there is. This error occurs because of a fallacy of composition - one presumes that the electro chemical impulses in neurons that make up ideas can be observed as if it were the number 2, rather than representative of the number 2, data points, which are inferred by the brain as the number 2.
See also: the fallacies of composition and division.
Begging the Question
In Latin: Petito principii - Any argument that relies on its own conclusion (often implied) as a presmise
"We must believe the there is a God because it is so taught in the Holy Scriptures, and we must believe in the veracity of the Holy Scriptures because they are the word of God"
Some people like to note that circular arguments are trivially valid. They are right: - circular arguments are valid. But the validity of a circular argument should not impress us seeing as the 'validity' stems from the fact that we are merely holding that a thing is identical to itself!
Deductive arguments work just like mathematical equations: a set of equivalences - we can even reformulate such arguments as tautologies. Therefore, the point of such arguments is to demonstrate some equivalence (or lack thereof) between two categories. So, yes, plugging the same statement into both a premise and the conclusion gives us an equality, but the fact that that the same exact statement gives us an equivalency is not exactly noteworthy! This is why we call this an informal fallacy - nothing is being proven here, we aren't demonstrating an equivalancy, the equivalency is already a given prior to the argument!
A specific form of circular logic, a complex question is a question that assumes its own conclusion so that any attempt to answer the question necessarily leads to accepting the conclusion. The most famous example of the complex question fallacy:
"Do you still beat your wife?"
If this question is answered, it becomes an argument with the conclusion that you have in fact beaten your wife at some point in time. The problem is that a complex question is really two questions that demand one answer. This can be committed out of ignorance, but it can also be a purposeful deception.
Another form of this fallacy is to ask for an explanation of something which is untrue or not yet established.
Questions with statements that commit the existential error - i.e., items that do not exist. The ultimate example: What happens when an irresistible force meets and immovable object? The proper response to this question is to point out that if there were a irresistible force, ipso facto there could not be an immovable object (and/or vice versa.) Most meaningless questions are equally incoherent, because they are basically built upon contradictions, or make reference to non existent entities.
Also known as the fallacy of the excluded middle, the fallacy is committed when an argument presents a supposedly valid disjunctive premise, (an "Either... Or" argument) wherein the items presented either are not jointly exhaustive (a third choice exists) or are not mutually exclusive.
Example: You're either with us or against us.
This fallacy takes advantage of a truth: that the real world is a continuum. However, it takes from this truth an exaggeration: that a lack of clear demarcations precludes us from categorizing.
Example: Communists and Fascists achieve the same ends, so there's no real difference between them.
Appeal to Nature
"Is implies Ought". The Appeal to Nature is a common fallacy in political arguments. One version consists of drawing an analogy between a particular conclusion, and some aspect of the natural world -- and then stating that the conclusion is inevitable, because the natural world is similar:
"The natural world is characterized by competition; animals struggle against each other for ownership of limited natural resources. Capitalism, the competitive struggle for ownership of capital, is simply an inevitable part of human nature. It's how the natural world works."
Another form of appeal to nature is to argue that because human beings are products of the natural world, we must mimic behavior seen in the natural world, and that to do otherwise is 'unnatural':
"Of course homosexuality is unnatural. When is the last time you saw two animals of the same sex mating?"
Of course, such arguers often also deny any connection to nature when it does not suit them, such as on evolution. (See inconsistency) Also, animals DO have homosexual encounters, so this entire argument is bullshit.
Finally, this fallacy occurs any time something is identified as being good or desirable because it appears to be a natural characteristic
Everyone is basically self-interested, therefore pursuing one's self-interest is a virtue.
Everyone wants to be wealthy so systems should be designed based on economic incentives.
The "Fallacy" Fallacy
Argumentum ad logicam. This is the "fallacy fallacy" of arguing that a conclusion is false because it has been presented as the conclusion of a fallacious argument. Remember always that fallacious arguments can arrive at true conclusions.
"Take the fraction 16/64. Now, canceling a six on top and a six on the bottom, we get that 16/64 = 1/4."
"Wait a second! That answer must be wrong. You can't just cancel the six!"