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Abbreviate Argumentum ad Hominem to AAH. For consistency, I use 'credibility' to mean both believability and credibility. Source: p 133, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley

Here is an example of an argument that discredits a witness:

[1.] Mickey has testified that he saw Freddy set fire to the building. But Mickey was recently convicted on ten counts of perjury, and he hates Freddy with a passion and would love to see him sent to jail. Therefore, you should not believe Mickey’s testimony.

  [2.] This argument commits no fallacy. The conclusion is not that you should reject Mickey’s argument but rather that you should reject his testimony. Testimony is not argument, and the fact that the witness is a known liar and has a motive to lie now is relevant to whether we should believe him. Furthermore, note that the conclusion is not that Mickey’s statement is literally false but rather that we should not believe the statement. It is quite possible that Mickey really did see Freddy set fire to the building and that Mickey’s statement to that effect is true. But if our only reason for believing this statement is the mere fact that Mickey has made it, then given the circumstances, we are not justified in that belief. [3.] Personal factors are never relevant to truth and falsity as such, but they are relevant to believability.
  [4.] Yet there is often a close connection between truth and believability, and this provides one of the reasons why ad hominem arguments are often effective. In evaluating any argument there are always two issues to be considered: the quality of the reasoning and the truth of the premises. As noted, both are irrelevant to the personal characteristics of the arguer.

[5.] But whether we accept the premises as true may depend on the credibility of the arguer. Knowing that the arguer is biased or has a motive to lie may provide good grounds for distrusting the premises. [...]

I summarise [1]-[4] as 6, and [5] as 7 and 8::   

  1. Truth and falsity must be distinguished from credibility, as AAH does not affects the former but affects the latter.

  2. AAH affects credibility.

  3. Credibility may affect our evaluation of the premises.

To me, 4 appears to mean:   9. But our evaluation of the premises affects our evaluation of the quality of reasoning and the Validity and Soundness of an argument.

So Modus Ponens applied to 7-9 and Hypothetical Syllogism produce:
10. AAH affects our evaluation of the quality of reasoning, Validity and Soundness.

Is 10 correct? To me, 5 contradicts everything above it.

  • Did you go through the answers to your previous question? Arguments stand or fall on their own, without considering who is arguing. – gnasher729 Jan 13 '16 at 19:14
  • @gnasher729 Yes, I have been reading the answers albeit slowly. – Greek - Area 51 Proposal Jan 14 '16 at 19:41
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Usually, validity is not affected by the credibility of the arguer, as any competent logician is capable of distinguishing a valid vs. invalid argument. Exceptions may include where the logician is incompetent, or where the argument is so complicated that some measure of trust is accorded that the presenter of the argument has already checked validity. However, as credibility is going to play into whether or not we trust the claims of an individual, it seems to me that this will usually affect our trust in the premises of an argument and not its validity (or cogency).

That said, here is the answer to your question. Technically speaking, your inference [7,8,9]->[10] is invalid without some kind of rule of inference regarding transitivity of affectation. But that is not a controversial rule, I shouldn't think, so I suppose [10] follows from [7,8,9] together with such a rule. None of this contradictory, that I can see.

  • Thanks. In your last paragraph, you appear to agree that [10] is a true conclusion. If so, then how are 1-4 still true? To me, 1-4 oppose 10. – Greek - Area 51 Proposal Jan 20 '16 at 17:05
  • Would you please respond in your answer, which is easier to read than comments? – Greek - Area 51 Proposal Jan 20 '16 at 17:06
  • I can't really respond until I understand why you think 1-4 oppose 10. – Ben W Jan 20 '16 at 17:38
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The idea of any fallacy is that an argument is (formally) valid or invalid, (informally) strong or weak as a matter of pure structure. So strength or validity of argument must be judged as its own thing, independent of any "accidents" such as who framed or conveyed the argument. Every fallacy is an attempt to discredit the structure of an argument with a non-structural claim.

Credibility affects the surety of the premises. An argument is formally sound (valid and possessing true premises) or unsound, informally cogent (strong, and possessing likely premises) or non-cogent as a matter of correspondence with the truth.

Your [9] is part right and part wrong. The evaluation of the premises does NOT affect the strength/validity of the argument, but only the cogency/soundness of it and its conclusion. The argument can still be strong (structurally) even if the premises are false, it's just a non-cogent, irrelevant, strong argument.

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So I previously answered this;

The fallacy arises because ad hominem has no unbiased axiomatic value to the original argument. While arguing a topic and attacking(not refuting) the arguments of your opponent and not addressing the argument you commit a fallacy; a failure in reasoning that renders an argument invalid. Why? Because you do not address the original argument, that is the failure in reasoning, ad hominem argues toward a topic NOT being debated. ---Void Serpent

Note: You can debate someone's credibility within another venue/forum and as long as it is separate from the original debate, what WAS ad hominem is now valid argument.

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