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That is, are some fallacies considered worse than others, or does each fallacy have the same weight? For example, are formal fallacies considered "worse" than informal fallacies or vice versa? For another example, is it more damaging to an argument to commit an ad hominem fallacy than the probabilistic fallacy? Is there some accepted rubric by which one would measure how damaging a fallacy is to an argument based only on the type of fallacy committed, or does one need to consider what premises a fallacy applies to?

I ask because I am ultimately aiming at creating a bipartite, quantitative measure for the soundness of an argument, one component of which applies to the argument's validity. A colleague and I were discussing this and he suggested that, whatever the measurement model, it's likely that not all fallacies are equal in their influence upon the soundness of an argument.

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    Thanks so much, this looks great to me! Welcome to Philosophy, by the way :) – Joseph Weissman Aug 13 '13 at 1:34
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    Ultimately any fallacy is not inherently damaging to the point the argument is trying to make because it may or may not be true regardless of poor arguments made. Any fallacy invalidates an argument, and it is difficult to quantify the degree of damage--if you mean how far it forces the conclusions to deviate from the truth, then it can be anywhere from no damage to irrepairable damage (i.e. it is difficult to see how the conclusion can be made from the premises at all). But I don't see how that is relevant to the argument. A bad argument is a bad argument--it fails to prove the conclusion. – called2voyage Aug 13 '13 at 18:23
  • Thanks for your input @called2voyage. Why not stick it in an answer so I can compare its upvotes to any other answers that arise? – Brash Equilibrium Aug 13 '13 at 22:13
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Of course not all fallacies have the same weight of importance. A logical fallacy is an error of argument that renders the argument invalid (e.g. assuming the consequent) and depends only on the logical form of the argument, but a fallacy of relevance (argument by authority) depends on judgment of that authority.

Within logical fallacies, the severity of the error depends on its primacy in the argument, (how close to the root in the proof tree it is), or its fixability (it is sometimes easier to fix "A->B,B then A", than it is to fix something with an accidental negation dropped in).

And within fallacies of relevance, an argument by authority or numbers is less serious than an argument by force (ad baculum).

Are you trying to quantify relative strengths objectively, give numeric strengths to errors? That might be possible with logical fallacies, but fallacies of relevance really depend a lot on qualitative real world assessment, (one person's fallacy by authority is another's expert witness), so I expect that will be very difficult, like trying to quantify esthetic judgments. It can be attempted, but might be difficult as nailing down jello.

  • Thank you for your proposed answer. (1) How might one measure primacy/fixability? (2) Please define objectively relative strengths. (3) In my system, every accusation of a fallacy (which is itself an argument, either formal or informal) can be assessed for its truth and validity by multiple raters, and we aggregate ratings and incorporate uncertainty and prior beliefs, which is more like putting the jello into a mold than trying to nail it down. – Brash Equilibrium Aug 15 '13 at 16:12
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    Sorry, those were vague usages. By primacy I meant for a logical proof, how close to the root of the tree the error occurs: if far away from the proof, the error might only affect a small part of the tree; nearer the root, the error definitely affects more of the tree. By fixability, I mean that some logical errors are easier to fix than others: assuming the consequent is just an error of direction of modus ponens (since so many implications turn out to be reversible (and why affirming the consequent is so often accidentally made), the other direction of implication might be easy to prove)... – Mitch Aug 16 '13 at 0:16
  • I'd love to talk more about representing an argument as a tree with a root. I think you've got something there. – Brash Equilibrium Aug 16 '13 at 5:07
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    Natural deduction and analytic tableau are tree methods for logical proofs. – Mitch Aug 16 '13 at 12:32
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I'm not aware of anything that's accepted that is exactly what you want, but I will note that Bayesian reasoning is a framework that is great at modeling exactly what you want.

See the Wikipedia entry, for example.

In particular, you can include your inference steps as part of the model. So a valid proof of A assuming B would have p(A|B) = 1; if you have any invalid step you can swap in the probability of the actual step taken (or an estimate thereof).

Let's suggest two alternate hypotheses, A1 and A2 that cover all cases, and we'll let B be our evidence (either a logical proof or the presence of an argument from authority or whatever). Then, according to Bayes' theorem

p(A1|B) = 1/(1 + (p(B|A2)p(A2))/(p(B|A1)p(A1)))

or equivalently, where ! means "not",

p(A|B) = 1/(1 + (p(B|!A)(1-p(A)))/(p(B|A)p(A)))

Let's try an example to see what these things mean. Let's let A be our thesis, and B is "an expert says A is true". p(A|B) is our estimate of how likely our thesis is presuming that an expert says it's true.

Let's evaluate each of the terms on the right.

p(A)

This is how likely we think the thesis is in the absence of expert opinion. Let's suppose that we really doubt this claim, and are relying heavily on our experts, so p(A) = 0.001.

p(B|A)

This is how likely it is that an expert will say a thesis is true if it is in fact true. Assuming we limit ourselves to considering experts who have an opinion on a thesis, this could be pretty high--let's say it's 99%.

p(B|!A)

This is how likely it is that an expert will say a thesis is wrong even though it's true (and again we'll restrict ourselves to experts who ought to know). Let's say they're pretty accurate, but someone will slip up sooner or later, so we'll say it's 5%.

Now, our radically unlikely hypothesis looks like so:

p(A|B) = 1/(1 + 0.05*0.999/(0.99*0.001)) = 1/(1+50.45) = 1.9%

Well. That's better,but it's hardly a proof.

If it had been a proof, we would have had p(A|B) = 100%.

And the difference in these percentages gives us a quantitative measure of just how bad it was to use argument from authority instead of a proper proof.

  • If possible, please expound on what role Bayesian reasoning would play in constructing a quantitative measure of an argument's adherence to logic from the number and type of fallacies committed. I will use Bayesian INFERENCE to account for uncertainty in the measurements arising from several factors, but I think you mean something different. Do you? – Brash Equilibrium Aug 15 '13 at 17:27
  • @BrashEquilibrium - Just make everything an inference. A proper proof is a very robust inference. An argument from authority is less robust. I've calculated out an example above. – Rex Kerr Aug 15 '13 at 21:29
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Ultimately any fallacy is not inherently damaging to the point the argument is trying to make because it may or may not be true regardless of poor arguments made.

Any fallacy invalidates an argument, but it is difficult to quantify the degree of damage. If you mean how far it forces the conclusions to deviate from the truth, then it can be anywhere from no damage to irreparable damage (i.e. it is difficult to see how the conclusion can be made from the premises at all).

But I don't see how that is relevant to the argument. A bad argument is a bad argument. It fails to prove the conclusion.

Sources:

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Beside the answers already given regarding comparitive logical weights in the abstract, it might be of interest to weigh the real world consequences of a given instance of a fallacy against some arbitrary scale comprising classic errors -- i.e. measured against a rogues gallery of the most destructive historically verifiable instances of a given fallacy as used to promote the acceptance of errors.

Such a gallery might be divided into categories by intention and knowledge:

  1. Ruthless for when the author knew the error was an error and used a fallacy as a tool to mislead the common understanding.

  2. Kindly for when the author did not see the fallacy as fallacious or the error as erroneous.

  3. Patronizing for when the author deliberately used a fallacy to promote an error they believed to be true.

  4. Careless for when the author unknowingly used used a fallacy to promote something knew to be wrong.

So far as I know, no author has yet attempted such a thing. Fallacy book examples tend to be:

  1. Ad hoc made up. (For some reason, perhaps not to offend or divide students, the made-up examples tend towards the trivial.)
  2. Historical folklore passed down from author to author, i.e. the ad hominem about Thomas Massey-Massey and Christide.
  3. Cribbed from current newspapers, advertisements, and political dialogue.

One benefit of such a rogue's gallery might be discovering whether or not the most logically weighty fallacies are also the most historically destructive. Perhaps the more lightweight fallacies do more psychological and cultural harm. Similarly, there's the question of whether ruthless or kindly usages do more harm.

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