Is it possible for an argument that contains a fallacy to be valid? I have been told that fallacious arguments by definition are invalid. Is this true? Thanks!

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    Well, fallacious proof can be "valid" if you assume wrong premises, but then the premises themselves are invalid, therefore it all boils down to what you mean by validity. – rus9384 May 19 '18 at 14:00
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    @rus9384 - you are mixing valid with TRUE. – Mauro ALLEGRANZA May 19 '18 at 15:07
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    @MauroALLEGRANZA, I am not, take, e.g. an argument where premise itself is a predicate and is invalid. – rus9384 May 19 '18 at 15:11
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    A predicate is not true or false. A statement is TRUE or FALSE. A premise of an argument is a statement; thus it is TRUE or FALSE and not valid. An argument is a set of statement: one conclusion and one or more premises. – Mauro ALLEGRANZA May 19 '18 at 15:17
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    See the related post : logically-valid-but-fallacious. – Mauro ALLEGRANZA May 19 '18 at 16:34

Bradley Dowden writes in his article "Fallacies" (Internet Encyclopedia of Philosophy):

Researchers disagree about how to define the very term "fallacy." Focusing just on fallacies in sense (a) above, namely fallacies of argumentation, some researchers define a fallacy as an argument that is deductively invalid or that has very little inductive strength. Because examples of false dilemma, inconsistent premises, and begging the question are valid arguments in this sense, this definition misses some standard fallacies.

By this view some fallacies may be valid arguments.

Wikipedia distinguishes formal from informal fallacies. A formal fallacy is described as:

A formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a flaw in the structure of a deductive argument which renders the argument invalid.

An informal fallacy is described as:

In contrast to a formal fallacy, an informal fallacy originates in a reasoning error other than a flaw in the logical form of the argument. A deductive argument containing an informal fallacy may be formally valid, but still remain rationally unpersuasive.

By this view a formal fallacy implies that the argument is invalid, but an informal fallacy does not require that the argument also be invalid.

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  • +1 for the ref to the distinction formal/informal. – Mauro ALLEGRANZA May 19 '18 at 15:21
  • So then an informal fallacy can be valid but still fallacious? – Curious May 19 '18 at 20:12
  • @Curious Yes informal fallacies may be valid, but formal fallacies would be invalid, that is, the form is what is invalid about the argument. At least that is how Wikipedia sees it. – Frank Hubeny May 19 '18 at 22:55

I very much like Frank Hubeny's answer, and starting with the distinction between formal and informal fallacies.

I thought it might be helpful to look at some examples of valid constructions that contain, or at least look like they contain, fallacies. I'm going to give examples that are quite informal but I think are illustrative and could be tied up properly with sufficient pedantry.

The simplest example is that a construction that contains redundancy may remain valid. For example, consider this which includes a fallacy of affirming the consequent: "If it is raining the ground will be wet. The ground is wet. Oh, also there is water falling from the clouds. Therefore it is raining." While the wet ground doesn't prove that it's raining, it doesn't have to because the falling water does. This might be seen as contrived because it is good practice, not to mention good manners, to strip invalid redundancy from your argument. However it's important to keep in mind when assessing an argument, to avoid committing the fallacy fallacy.

Other than redundancy, it does depend very much on the sort of fallacy we're talking about.

Fallacies such as begging the question, listed in Frank's quote of Dowden, are valid by definition. These are the fallacies that smuggle in the dodgy bits into the premises. They're just a bit useless, because they don't prove anything new.

A second group of fallacies come from using approaches that we are used to allowing in one system of reasoning, but aren't allowed in this one. For example, when talking about validity "probably" isn't good enough. That is actually where a lot of informal fallacies come from: they are heuristics that often but not always give us good results because the expert or the consensus or the small but suggestive data set are often but not always right. Now, a valid construction may be formed by including as premises the axioms from the other logical system. For example something like
"Warren Buffet is buying ACME shares, therefore ACME shares are going to go up"
is not valid (and in particular is an appeal to authority). Conversely
"A good investment is one that will on average make money. On average people investing the same as Warren Buffet make money, and Warren Buffet is buying ACME shares, therefore ACME shares are a good investment." is valid because it is explicitly restricting the claim scope to probabilistic risk calculations.

The group of fallacies including things like "moving the goalposts" and "red herring" are harder to place. They exists too deeply in the ettiquete surrounding the back and forth of debate rather than actual arguments. Simply put, whether an argument that includes "moving the goalposts" can be valid depends on where they are moved to.
A "Global warming isn't happening."
B "It is. Can you even find one year in the last fifty which was cooler than the 1800s average"
A {finds one}
B "OK, but global warming is still happening. After all 49 of the last 50 years have been hotter."
A "That's not fair. I met your challenge and you're just moving the goal posts."
B "Yes, you did. My challenge was to do something that doesn't actually prove your side, and I'm sorry. But global warming is still happening."

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Invalidity as a sufficient condition of fallaciousness ?

There are cases where invalidity is a sufficient condition of fallaciousness. Consider the following :

  1. If p then q

  2. q

  3. Therefore p

This is plainly invalid : if it is raining then the pavements are wet; the pavements are wet; therefore it is raining. But p does not imply q. If it is raining then the pavements are wet but because the pavemements are wet it does not follow that it is raining. They may be wet because of a broken water main or the activity of the fire brigade. Here invalidity is sufficient for fallaciousness; and the fallacy has a name, that of 'affirming the consequent'.

Invalidity as a necessary condition of fallaciousness ?

Here matters are less straightforward:

Is invalidity a necessary condition for fallaciousness? There seem to be several good arguments for rejecting this implication. For instance, any argument form having a necessarily true conclusion, or alternatively, a necessarily false premise, is valid; yet some substitution instances of these argument forms are fallacious. The following argument:

(1) Mathematics is a study of odd entities.

(2) Mathematics investigates the number seven.


(3) Seven is an odd number.

is, on one reading at any rate, an instance of equivocation, although the argument is perfectly valid on that reading since (3) - its conclusion - is necessarily true. Similarly, the argument below:

(4) Some bachelors are married.


(5) Some bachelors have served as President of the United States since 1940. is valid since its sole premise - (4) - is necessarily false; nevertheless, the argument is an instance of ignoratio elenchi [ignoring the question].

[A self-contradictory statement, e.g. 'Some bachelors are married', implies any other statement whatever, here 'Some bachelors have served as President of the United States since 1940'.]

In this and the previous (mathematical) case, a logically valid argument is fallacious. So invalidity is not a necesssary condition for fallaciousness. In other words, not all fallacious arguments are invalid.

In a previous issue of this journal, John Woods and Douglas Walton have reviewed some additional considerations which suggest that invalidity is not a necessary condition for fallaciousness:

(i) Many instances of the traditional ad verecundiam [appeal to authority] turn out to be quite legitimate appeals to genuine authority or expertise; (ii) Some instances of composition may be inductively valid yet fallacious if considered as deductive arguments; (iii) Some deductively valid argument forms, such as 'p, therefore p' have substitution instances that commit the fallacy of petitio principii [begging the question].


Charles J. Abaté, 'Fallaciousness and Invalidity', Philosophy & Rhetoric, Vol. 12, No. 4 (Fall, 1979), pp. 262-266: 262.

John Woods and Douglas Walton, "Fallaciousness Without Invalidity?", Philosophy and Rhetoric, 9 (1976).

John Woods and Douglas Walton, 'More on Fallaciousness and Invalidity', Philosophy & Rhetoric Vol. 14, No. 3 (Summer, 1981), pp. 168-172

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Absolutely they are invalid. The reason the argument is invalid is that the truth of the conclusion would be less than 100%.

That is if I reason in this horrible way I can get a corresponding true conclusion for right now. Using the same horrible form of argument with different subjects & predicates in the premises I will get a false corresponding conclusion.

This expresses that the method of reasoning is unreliable & cannot be trusted. Sometimes you can be correct but you must know the material of the argument well to pull this type of argument off. How would people outside of the premise content know the argument is corresponding to reality or Not? If they can't decern the argument they can be deceived. This kind if argument is also called a CON. This is common to get someone to fall for scheme to get money.

It is important to notice that valid has several contexts --- not only one. We all heard of valid arguments. One can have valid inferences such as obversion of a proposition which is not an argument. One can have a valid method of reasoning which may include non-deductive reasoning.

In the question you seem to indicate some reasoning is non-deductive and that the reasoning is informal. Well all arguments are formal in a way. The form is how we recognize the argument. If we can classify the argument, then it has a formal pattern. If there is a known fallacy, then we recognize some kind of pattern. By formal you may have meant in a classical syllogistic way or a mathematical logic way.

An informal argument in that context can be a rhetorical argument. These you will likely find in political candidates. As they don't speak as mathematical logic people do & they don't speak in classical syllogisms either.

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  • You might be confusing the validity of an argument with the soundness of an argument which assumes validity but also the truth of the premises. iep.utm.edu/val-snd – Frank Hubeny May 20 '18 at 15:59
  • I am not xonfusing the two things. Validity can mean other things than in math. I list the other contexts in which the term VALID can be used – Logikal May 20 '18 at 16:02
  • @Logikal Are you saying that all fallacies are invalid arguments? What about the fact that the source given says that arguments can be valid yet fallacious? – Curious May 21 '18 at 18:16
  • @curious, in the context of a reasoning method all fallacious arguments are invalid. That is the merhod has a flaw that will not always yield correct conclusions. Sometimes it will while other times it wont. A formal argument in mathematics often has blatantly unsound arguments but are formally valid. I was not taught to hone on validity as mathematical logic does but focus on soundness of arguments because all sound arguments must have validity. – Logikal May 21 '18 at 18:23
  • @Logikal Are you saying that in terms of mathematical logic, an argument could still be valid even though it's fallacious? – Curious May 21 '18 at 20:11

Premises are TRUE or FALSE.

Conclusions are VALID or INVALID.

Arguments (Premises+Conclusion) are SOUND or FALLACIOUS (UNSOUND).

-Formal Fallacies are Deductively Unsound.

-Informal Fallacies are Inductively Unsound.

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