Logical fallacies in arguments

[~Sophia~]

I have been asked to write a summary of logical fallacies (I have used multiple sites and sources - if you want to find more information type logical fallacies into your search engine).

What is an argument?

An argument is a connected series of statements to establish a definite proposition. A proposition is a statement which meaning is either true or false.

If we're interested in establishing A, and B is offered as evidence, the statement "A because B" is an argument. If we're trying to establish the truth of B, then "A because B" is not an argument, it's an explanation.

The most precise and the most persuasive are deductive arguments which provide conclusive proof of their conclusion. (they can be either valid or invalid). Deductive arguments have three stages: premises, inference, and conclusion.

Premises are the core assumptions on which the argument is built on (Since.... Because....). They are the reasons for accepting the argument. Premises are only premises in the context of a particular argument. One should always state the premises of the argument explicitly and it is a good idea to get your opponent to agree with the premises of your argument before proceeding any further.

Once the premises have been agreed, the argument proceeds via a step-by-step process called inference. In inference (.....therefore... or.....implies.....), you start with one or more propositions which have been accepted and then use those propositions to arrive at a new proposition. If the inference is valid, that proposition should also be accepted. You can use this new proposition for inference later on.

Hopefully you will arrive at a proposition which is the conclusion of the argument - the result you are trying to prove. The conclusion is the result of the final step of inference. It's only a conclusion in the context of a particular argument but it could be a premise or assumption in another argument.

Spotting an argument is harder than spotting premises or a conclusion. Lots of people shower their writing with assertions, without ever producing anything you might reasonably call an argument.

There are a number of common pitfalls to avoid when constructing a deductive argument; they're known as fallacies. A fallacy is a technical flaw which makes an argument unsound or invalid. (there are too many to list them all here - I will just pick few which I think are the most relevant here).

Argumentum ad hominem (argument directed at the man)

Abusive form:

example: You claim that atheists can be moral -- yet I happen to know that you abandoned your wife and children.

(This is a fallacy because the truth of an assertion doesn't depend on the virtues of the person asserting it.)

or

to reject a proposition based on the fact that it was also asserted by some other easily criticized person.

example: This sounds like something Hitler would say.

an attack on the bias of a person:

example: Sure you would say that tobacco companies have a right to exist - you are as smoker.

guilt by association:

example: You are pro-choice but lets not forget that communists are also pro-choice therefore you are a communist.

Argumentum ad ignorantiam (argument from ignorance - something is true because it has not been proven wrong)

example: Of course the Bible is true. Nobody can prove otherwise.

Argumentum ad numerum

example: All I'm saying is that thousands of people believe in pyramid power, so there must be something to it

Appeal to Authority

example: Newton was a genius and he believed in God.

Circulus in demonstrando

circular argument: the premise is the same as the conclusion

Begging the question

(the premises are at least as questionable as the conclusion reached - the premises of the argument implicitly assume the result which the argument purports to prove)

example: If such actions were not illegal, then they would not be prohibited by the law.

Red herring

introduction of irrelevant material to the issue being discussed, so that everyone's attention is diverted away from the points made, towards a different conclusion.

example: You may claim that the death penalty is an ineffective deterrent against crime -- but what about the victims of crime? How do you think surviving family members feel when they see the man who murdered their son kept in prison at their expense?

The slippery slope argument

example: If we legalize marijuana then more people would start to take crack and heroin, and we'd have to legalize those too. Before long we'd have a nation full of drug-addicts on welfare.

Straw man

The straw man fallacy is when you misrepresent someone else's position so that it can be attacked more easily, knock down that misrepresented position, then conclude that the original position has been demolished. It's a fallacy because it fails to deal with the actual arguments that have been made.

example: To be an atheist, you have to believe with absolute certainty that there is no God. In order to convince yourself with absolute certainty, you must examine all the Universe and all the places where God could possibly be. Since you obviously haven't, your position is indefensible.

Non sequitur

an argument where the conclusion is drawn from premises which aren't logically connected with it.

example: Since Egyptians did so much excavation to construct the pyramids, they were well versed in paleontology

Equivocation

when a key word is used with two or more different meanings in the same argument

example: What could be more affordable than free software? But to make sure that it remains free, that users can do what they like with it, we must place a license on it to make sure that will always be freely redistributable.

Sweeping generalization

a general rule is applied to a particular situation, but the features of that particular situation mean the rule is inapplicable.

example: Most women like flowers. You are a woman, so you must like flowers.

Edited May 26, 2007 by ~Sophia~

[ian]

Maybe you could also mention the distinction between premises and axioms, a premise being something true for a particular argument but an axiom being something that is always true for any argument.

Also Ayn Rand identified some fallacies...

"Stolen Concept"

"Context-dropping"

"Reification of the Zero"

"Stepping into Limbo"

"Non-differentiation between Existence and Consciousness"

[Old Toad]

In addition to Sophia’s listing of the most common fallacies, consider the organizational structure for fallacies by Dr. Bruce Thompson, a philosophy and logic instructor and reference librarian at Cuyamaca College in California:

Introduction:

http://www.cuyamaca.edu/bruce.thompson/Fal...o_fallacies.asp

“Classification of fallacies should be based on where the fallacy occurs”

http://www.cuyamaca.edu/bruce.thompson/Fal...explanation.asp

(I question whether his classification “retroduction” is a valid logical form of reasoning, however.)

“Table of Fallacies”

http://www.cuyamaca.edu/bruce.thompson/Fal...lacies_grid.asp

“Index of Fallacies – In Alphabetical Order”

http://www.cuyamaca.edu/bruce.thompson/Fallacies/index.asp

I would be curious what others think of his organizational structure. Dr. Thompson does not appear to be aware of the fallacies Ayn Rand discovered (as listed above in Ian's post). I would be interested in trying to integrate those into Dr. Thompson’s table, and perhaps I will call them to his attention.

Edited May 26, 2007 by Old Toad

[Robert J. Kolker]

I would be curious what others think of his organizational structure. Dr. Thompson does not appear to be aware of the fallacies Ayn Rand discovered (as listed above in Ian's post). I would be interested in trying to integrate those into Dr. Thompson’s table, and perhaps I will call them to his attention.

The fallacies in the Rand list were epistemological fallacies, not logical fallacies.

Ignoring or violating context is a type of epistemological equivocation.

Here is a typical logical fallacy (affirming the consequent) A implies B, B therefore A. The nature of this fallacy is obvious by writing up a truth table for -implies-. A implies B if and only if it is not the case that A is true and B is false.

A logical fallacy can always be detected and corrected using truth tables.

Bob Kolker

[LaszloWalrus]

Isn't there a difference also between logical fallacies and argumentative fallacies?

Affirming the consequent and denying the antecedent are logical fallacies, whereas ad hominem and poisoning the well are argumentative fallacies.

[Robert J. Kolker]

Isn't there a difference also between logical fallacies and argumentative fallacies?

Affirming the consequent and denying the antecedent are logical fallacies, whereas ad hominem and poisoning the well are argumentative fallacies.

Ad homs are special cases of a class of fallacies called ignoratio elenchi. Such fallacies are arguments supporting a proposition other than the one presumably under discussion.

See http://en.wikipedia.org/wiki/Ignoratio_elenchi

Bob Kolker

[Spano]

The fallacies in the Rand list were epistemological fallacies, not logical fallacies.

This is a false alternative. Objectivism holds that logic (non-contradictory identification) is the method of reason, i.e the method of a proper epistemology. It makes no sense then to distinguish between epistemological and logical fallacies. One important contribution Ayn Rand made to philosophy was to add to the understanding of logic. The fallacies she identified are logical fallacies because the logic that flows from Objectivism is much richer than traditional academic formal logic. Specifically, she placed much greater importance on induction as opposed to deduction, because objectivity involves a constant process of looking out at reality and making sure one's consciousness conforms to it. That is why formal logic is antithetical to the Objectivist epistemology -- it dismisses the importance or even the need for induction and treats logic as a game played with arbitrary premises. I made the mistake when I first started learning Objectivism to think that it was a system deduced from the axioms, is if Ayn Rand sat down with existence, consciousness, identity, and wrote a few thousand pages of syllogisms. To the contrary, her method was thoroughly inductive, meaning that she was constantly identifying and integrating different facts of reality.

So while an understanding of the traditional logical fallacies is useful, it doesn't give the whole story.

Edited May 27, 2007 by Spano

[Robert J. Kolker]

This is a false alternative. Objectivism holds that logic (non-contradictory identification) is the method of reason, i.e the method of a proper epistemology. It makes no sense then to distinguish between epistemological and logical fallacies. One important contribution Ayn Rand made to philosophy was to add to the understanding of logic. The fallacies she identified are logical fallacies because the logic that flows from Objectivism is much richer than traditional academic formal logic. Specifically, she placed much greater importance on induction as opposed to deduction, because objectivity involves a constant process of looking out at reality and making sure one's consciousness conforms to it. That is why formal logic is antithetical to the Objectivist epistemology -- it dismisses the importance or even the need for induction and treats logic as a game played with arbitrary premises. I made the mistake when I first started learning Objectivism to think that it was a system deduced from the axioms, is if Ayn Rand sat down with existence, consciousness, identity, and wrote a few thousand pages of syllogisms. To the contrary, her method was thoroughly inductive, meaning that she was constantly identifying and integrating different facts of reality.

So while an understanding of the traditional logical fallacies is useful, it doesn't give the whole story.

Formal logic is NOT antithetical to induction. It is simply something else.

Physics progresses using both formal(i.e. mathematical) modes of inference and inductive modes of hypothesis formulation. This is no contradiction between the two. If is like saying football is antithetical to golf. Not so. They are just two different activities.

Bob Kolker

[Old Toad]

Some of the comments above may come from our not having considered a definition of “fallacy.”

Regarding the definition of fallacies, Dr. Bruce Thompson:

A fallacious argument contains an error of some kind. We can classify fallacies based on where this error occurs. Fallacies are traditionally divided into two groups, formal fallacies and informal fallacies. Formal fallacies are fallacious because there is an error in their form; informal fallacies are fallacious because they have a false premiss.

http://www.cuyamaca.edu/bruce.thompson/Fal...explanation.asp

More particularly, regarding the questions regarding “logical fallacies” and “argumentative fallacies,” the following by Dr. Bruce Thompson may be helpful to consider:

I don't recognize the "formal fallacies" as fallacies because (in my view) failing to be deductively valid is not sufficient to make an argument a fallacy. Inductive arguments are (presumably) not deductively valid, and neither are Retroductive arguments. If failing to be deductively valid were, by itself, grounds for calling an argument fallacious, then Inductive and Retroductive arguments would all be fallacious simply by virtue of being Inductive or Retroductive rather than Deductive. Hence, if we are going to recognize forms of reasoning other than Deduction, we must not dismiss arguments as fallacious merely on the grounds that they fail to be deductively valid.

For Dr. Thompson’s complete discussion of formal fallacies: http://www.cuyamaca.edu/bruce.thompson/Fal...alfallacies.asp

Is this helpful?

Edited May 27, 2007 by Old Toad

[Spano]

Formal logic is NOT antithetical to induction. It is simply something else.

Physics progresses using both formal(i.e. mathematical) modes of inference and inductive modes of hypothesis formulation. This is no contradiction between the two. If is like saying football is antithetical to golf. Not so. They are just two different activities.

Bob Kolker

To clarify, I meant that the way usual formal logic is approached in the academic setting is antithetical to Objectivism because it treats logic as a contextless game played with arbitrary premises. In fact, there is no distinction to be made between logic and epistemology, except that the former is the method of the latter. To say that there are both logical and epistemological fallacies implies, at least to me, that there is some seperation between the two. Is this what you're suggesting?

[Chops]

There's also "Argument from Intimidation" (last chapter of VOS): stating that a particular position is self-evidently condemning.

Example: Only someone completely out of touch could believe that modern art is uninspired and not the product of a genius.

[DavidOdden]

Formal logic is NOT antithetical to induction. It is simply something else.

In fact, induction is not antithetical to formal logic or "something else", and you very well know (because we have had these conversations before) that induction is formalizable.

[Cogito]

In fact, induction is not antithetical to formal logic or "something else", and you very well know (because we have had these conversations before) that induction is formalizable.

Really? Could you give an example or a link?

[Robert J. Kolker]

In fact, induction is not antithetical to formal logic or "something else", and you very well know (because we have had these conversations before) that induction is formalizable.

I don't recall. Do you have a reference in the vetted mathematical literature for the formalization of induction. If so, would you share it. Thank you.

Do you mean arithmetic induction or empirical (enumerative) induction? They are not the same. Arithmetic induction is one of Peano's Axioms for arithmetic. Empirical induction is the derivation of a universally quantified assertion from a partial or complete sample of a domain of individuals. Having seen a million black crows, one assumes all crows are black. (It isn't true, by the way. There are albino crows). As a -general rule- of inference enumerative (empirical) induction is not a valid mode of inference. If a predicate P applies to a proper subset of some domain D, it does not follow that it applies to the entire domain.

Bob Kolker

[Cogito]

As a -general rule- of inference enumerative (empirical) induction is not a valid mode of inference. If a predicate P applies to a proper subset of some domain D, it does not follow that it applies to the entire domain.

(Bold mine)

How did you arrive at this general rule?

[DavidOdden]

Really? Could you give an example or a link?

What I can do is say that I've gone over this nonsense about formalism vs. deduction with Bob, also Gordon Sollars and a number of others over on HPO between 2003 and 2004 when I left the pigpen. Bob has a blinders problem when it comes to logic, in that he is apparently only aware of garden variety monotonic FOP logic, and seems to think that that is what "formal" logic refers to. There is a large world of formal logic that relates to -- drum roll -- reasoning. The black crow "induction" is a classical Kolker-Sollars canard (or, corbeaux).

Formally speaking, the essence of induction is universal generalization. Logics can be contextual or reality-detached -- the latter being Bob's favorite kind. If a logic has rules of inference requiring quantification over the set of true propositions, it is contextual, otherwise it is detached (the former corresponds to a Peikovian "all evidence indicates... no shred of evidence points to an opposing conclusion" condition on logic; the latter refers to common "any arbitrary statement can be stipulated" kinds of logic). Universal generalization requires quantification over propositions, so that if the knowledge contexts includes P( a ), P( b ) and ^P( c ), you cannot induce Ax(P(x)), but if it includes just P( a ), P( b ) and P( c ) with no contradictor, then Ax(P(x)) must be inferred. The basic idea is that you have a proposition P asserted of all true propositions, based on the univocal evidence of individuals (P( a ), P( b ), P( c )....). So "if, for all x, 'P(x)' is true; then P is true".

One point that Mr. Kolker has never understood is that all inferences which arbitrarily assert "p->q; p" and then derive "q" from that have the flaw that the antecedents may be false.

[Robert J. Kolker]

One point that Mr. Kolker has never understood is that all inferences which arbitrarily assert "p->q; p" and then derive "q" from that have the flaw that the antecedents may be false.

Not a problem. Modus ponens states from p and p->q infer q. If p is false then the inference cannot happen. Two things must be true. p, the premise and p->q, the entailment. Then one can detach q and be assured of its truth.

Are we clear on that now? False premises do not permit detaching the conclusion from the entailment.

Bob Kolker

Edited May 28, 2007 by Robert J. Kolker

[DavidOdden]

False premises do not permit detaching the conclusion from the entailment.

It's odd that you can't apply that to induction.

[Jeff Younger]

I'm unsure of the issue at dispute here. Can someone state it affirmatively?

[DavidOdden]

I'm unsure of the issue at dispute here. Can someone state it affirmatively?

The specific question is whether induction can be a part of formal logic (it can be). The broader issue is what the nature (and purpose) of logic is.

[Jeff Younger]

The specific question is whether induction can be a part of formal logic (it can be). The broader issue is what the nature (and purpose) of logic is.

I see. It should be crystal clear that formal logic allows for mathematical induction. The definitions in every formal system I've seen are specifically crafted to allow for the construction of inductive sets of well-formed formulas.

It is just as clear that scientific induction is not mathematical induction.

Is that stipulated or is that a point of contention?

[DavidOdden]

It is just as clear that scientific induction is not mathematical induction.

I think what confuses Bob is that he does not understand that mathematical induction is not relevant to the discussion, and that we are talking about scientific induction; and that scientific induction is formalizable (though not in garden variety monotonic FOP logic).

[Cogito]

if it includes just P( a ), P( b ) and P( c ) with no contradictor, then Ax(P(x)) must be inferred.

What if it included just P( a ), and you had no b or c that applied to P in your knowledge context? If I see one Goldfish cracker (sorry, I'm eating) that's orange, can I say all crackers are orange if I've never seen another cracker?

[Robert J. Kolker]

The specific question is whether induction can be a part of formal logic (it can be). The broader issue is what the nature (and purpose) of logic is.

Could you provide a reference in the refereed literature for logic (applied or formal)?

Bob Kolker

[DavidOdden]

Could you provide a reference in the refereed literature for logic (applied or formal)?

Why?