# Isn’t every inference a fallacy?

Unless the conclusion after a set of premises is necessary or from a deductively valid argument, isn’t every inference technically a fallacy?

And so if every inference is a fallacy, why the need for things like fallacies in the first place? There is no inference that logically follows.

For example, appealing to popular opinion to defend an argument is often considered a fallacy. But clearly, there are many things we believe in based on popular opinion and yet don’t doubt and don’t consider them to be fallacies.

Even observing that there is a rock in front of you doesn’t imply that there is a rock there. Of course, the alternatives seem wildly implausible, but the fact remains that the inference as a logical matter is invalid.

But if every inference (unless deductive, which is usually not an interesting inference) is invalid, why bother with the notion of fallacies? It is not as if certain non deductive arguments are better than others apriori. They all don’t follow.

• You are saying essentially that tautologies are fallacious. Contingent inferences --like tautologies-- are not fallacious. They are just not necessary. E.g. `RAIN -> WET. It is wet, which is true`. There you have a contingent inference and a tautology: no fallacies. Commented Sep 10, 2023 at 12:33
• You’re getting caught up in semantics and missing the point. Noone argues the equivalent of “Bob is Bob.” That’s redundant. It’s just a statement.
– user62907
Commented Sep 10, 2023 at 12:39
• Rain -> Wet is necessary in the sense that the definition of rain involves wetness
– user62907
Commented Sep 10, 2023 at 12:40
• @thinkingman "And so if every inference is a fallacy" Where is it that you have established that?! You move from Those A which are B are C to All A are C. This is: (A ∧ B) → C ⊢ A → C, and this is of course fallacious. Congratulation. Commented Sep 10, 2023 at 15:34
• @MauroALLEGRANZA you may want to revise your example? 1+2=3 is true. Commented Sep 11, 2023 at 7:48

I think you are confusing 'fallacious' with 'invalid'. They are not the same thing. An argument is fallacious if it is defective in some way that conforms to an identifiable pattern. The term is actually quite vague. Some fallacies are formal, many are informal, some are pragmatic in character, many are little more than rough rules of thumb. By contrast, the term 'valid' is a technical term in logic. An argument is valid, or if you wish to be more precise deductively valid, if the conclusion is the logical consequence of the premises, or the conclusion follows necessarily from the premises.

So an argument that is not deductive, e.g. one that is abductive or inductive or analogical, is not valid, but this does not imply that it is defective, so it is not automatically a fallacy. It may be a perfectly cogent abductive argument, but if it is possible for the premises to be true and the conclusion false, it does not qualify as valid.

On the other hand, a circular argument is always valid, but it is usually regarded as a fallacy. So not all invalid arguments are fallacies, and not all fallacies are invalid.

This piece of terminology is an issue that many newcomers to logic have trouble with. Like any technical discipline, logic comes with its own vocabulary. Terms like premise, argument, proposition, satisfaction, interpretation, model, entailment, etc., have a distinct technical meaning in logic. Most newcomers get used to these fairly quickly, but the problematic one is 'valid'. We are accustomed in ordinary usage to treating 'valid' as an evaluative word: it commonly indicates a good argument or a cogent argument. It takes some practice to get into the habit of using it in the technical way logicians do.

It remains the case that some non-deductive arguments are better than others, even though we don't assess them as valid or invalid.

• I am aware that not all non deductive arguments are fallacies. But the reasoning for these fallacies are that they ultimately don’t follow. But every non deductive argument doesn’t follow…by definition.
– user62907
Commented Sep 10, 2023 at 14:36
• Being a fallacy isn't really just a case of 'doesn't follow'. It matters why it doesn't follow. Many fallacies are epistemic in nature: the premises do not support the conclusion, or do not provide an adequate reason to accept it. Cogent arguments do support the conclusion, but not by necessity. Think of a closing speech by a lawyer. It might be well argued and draw on a great deal of evidence, but it is not deductively valid. This does not make it fallacious. Commented Sep 10, 2023 at 15:32
• Most of the reasoning behind fallacies is just that the argument doesn’t follow though. “Just because something is popular doesn’t mean it’s true.” “Just because I feel anxious doesn’t mean something bad is going to happen.” Etc etc
– user62907
Commented Sep 10, 2023 at 15:41

It's nice to get in touch with our skeptical side.
Agrippa's Trilemma goes ...

1. Infinite Regress
2. Circularity
3. Axioms

Allegedly, all of the three are dukkha (unsatisfactory). However, infinite regress is more of an impossibility (supertask) than a fallacy and axioms have been vindicated by mathematics and religion (1.2 billion Kristians) has embraced circularity (re: The Bible Fallacy).

This form of radical skepticism has its critics and one supposed flaw is Agrippa's Trilemma is a peritrope (self-refuting). Call this argument A.

However, for argument A to be sound, Agrippa's Trilemma has to be sound. If so argument A is no good (it's also a peritrope).

Il est facile de voir que ... we can't make a case against Agrippa's Trilemma without implicating ourselves. Agrippa, bless his soul, has to be right to be wrong. We could call this Agrippa's Paradox (as he is right he is wrong and and as he is wrong he is right).

• It is not even that I’m a skeptic, or atleast I might be from the sense of not being able to justify arguments through reason but still be able to do so on intuition or “faith”. It is moreso that the definition of every fallacy you find, such as on the SEP, amounts to “it doesn’t follow”. But every inference unless deductive doesn’t follow. So what’s the point of fallacies?
– user62907
Commented Sep 10, 2023 at 12:50
• I believe you're missing something important. Commented Sep 10, 2023 at 17:49

Unless the conclusion after a set of premises is necessary or from a deductively >valid argument, isn’t every inference technically a fallacy? And so if every >inference is a fallacy, why the need for things like fallacies in the first place? >There is no inference that logically follows.

I'm going to take this as an argument against there being a real distinction between valid and invalid arguments. I'll put aside certain worries about whether this argument is self-defeating, but suppose an argument is valid only if the following condition is met: if the premises are true then the conclusion is true.

You can thus have a "vacuous" argument with false premises and true conclusion, as will be any argument for a tautology. The interesting thing about valid arguments is that certain inferences are treated as being truth-preserving, rather than truth-generating.

For example, appealing to popular opinion to defend an argument is often considered a fallacy. But clearly, there are many things we believe in based on popular opinion and yet don’t doubt and don’t consider them to be fallacies.

Even observing that there is a rock in front of you doesn’t imply that there is a rock there. Of course, the alternatives seem wildly implausible, but the fact remains that the inference as a logical matter is invalid. But if every inference (unless deductive, which is usually not an interesting inference) is invalid, why bother with the notion of fallacies? It is not as if certain non deductive arguments are better than others apriori. They all don’t follow.

So far I've only talked about deduction, but here you start to consider induction. Deduction involves the aforementioned sort of truth-preserving inferences present in valid arguments. Induction involves inferences from the particular to the general, an argument for which will turn out to be invalid. But that's okay, there's a real distinction between invalid and valid arguments, and a real distinction between deductive and inductive reasoning, but these distinctions don't line up perfectly (deductive and possibly valid vs inductive and necessarily invalid.)

And it seems that arguments that involve deductive reasoning will be persuasive for different reasons to arguments that involve inductive reasoning. The arguments that fail in terms of deduction are declared instances of formal fallacies, and the ones that fail in terms of induction are declared (among other things) informal fallacies.

In the end, my takeaway from your thoughts is:

1. we need to consider inferences in the context of explicit arguments, and
2. we to consider why not all good arguments seem to judged as good in virtue of the same things.

Unless the conclusion after a set of premises is necessary or from a deductively valid argument, isn’t every inference technically a fallacy?

Yes.

... and? You make that sound as if that is novel or surprising, it isn't. Of course pretty much all inferences in real life are fallacious. What do you expect. We work with incomplete data, with assumptions, with data that is only measurable to a certain accuracy and you expect all of that to yield "the complete, eternal, unchanging truth"?

And so if every inference is a fallacy, why the need for things like fallacies in the first place? There is no inference that logically follows.

Now it's important to realize what that means and what it does not mean.

As implied in the previous paragraph it means that what you infer is not "the truth". Any story that is incomplete can not be the truth and should not be treated as certainty. So if you do treat it as certainty you are committing a fallacy. And or must be aware of the fact that you're making an assumption (setting an axiom rather dealing with something that has been proven to be true).

Now the other important thing to realize is that, just because it is a fallacy does not mean that it is necessarily "certainly wrong" or that it is useless.

Like suppose you have a rigged coin that lands heads more often than tails, you watch a few rounds and it's something like 80:20. Suppose you infer from that, that it is better to bet on heads than on tails, then you're likely correct more often than not. But if you were to infer from that that it is certainly better to go for heads rather than tails you'd commit a fallacy. You could make idk 5 games and happen to be so unlucky to get a 5-tails streak. It's rare but possible. Making the inference is useful and it is reasonable given the circumstances, but it is not TRUE.

For example, appealing to popular opinion to defend an argument is often considered a fallacy. But clearly, there are many things we believe in based on popular opinion and yet don’t doubt and don’t consider them to be fallacies.

As said there is a difference between a heuristic and a truth, a truth has a definitive truth value so you can make deductive arguments with it, a heuristic just works most of the time and so you can make arguments that are likely to be true, but not always. Which is better than making arguments that are false all or most of the time.

Also there are different reason to appeal to popular opinion and not all of them are fallacious. Like if you ask what you should eat for dinner and pick the one that most people liked and that no one is allergic to, that would be a good appeal to popular opinion. While if you asked 100 people if they agree with you whether 1+1 is 3, that would be a fallacy. In the first case the opinion of the people was relevant to the question in the second it wasn't.

But if every inference (unless deductive, which is usually not an interesting inference) is invalid, why bother with the notion of fallacies? It is not as if certain non deductive arguments are better than others apriori. They all don’t follow.

No, just because all inferences in the real world are wrong does NOT mean they are equally wrong or that there is equality in their wrongness.

Also as others have already remarked you can still use deductive reasoning and make interesting inferences by making axiomatic assumptions, "what if X were true?" Like it's a practice that is quite successfully used in math which has contributed massively to the development of our sciences so to cast that off as uninteresting is quite wrong. Now does saying that something is true, make it true in the real world? No. But it's a method to check the self-consistency of a statement, so if it fails in that regard it's already worse than one that doesn't.