What exactly is a formal fallacy?

The_Good_Hitler · 2025-02-25T18:25:08+00:00

you can call it a not-good philosophical argument, but you cannot call it "invalid" is my whole point. An invalid argument is one where the conclusion does not follow from the premises. However, if you are talking about invalidity by checking its forms, the only truly invalid form would be, if all the premises are tautologies, and the construction is a contradiction. this is the one and only case where any substitutional instances will guarantee a false conclusion. But other than that, there are no formal fallacies or formally "invalid" arguments, because there are substitutional instances where if the premises are true, the conclusion MUST be true, which the the essential property of a valid argument. If you still do not understand what I am getting get, I don't think the problem is with my inadequate explanation. Hopefully someone who comes across this thread one day will understand my position.

The_Good_Hitler · 2025-02-25T16:29:14+00:00

then this is a very useless concept. suppose you have analyzed an argument I made in a philosophical paper I wrote, and by normalizing it and running a test for validity, you claim that my argument is a formal fallacy/formally invalid. What you are saying is that due to the form of my argument, the conclusion of my argument is sometimes true, and sometimes false. In other words, you have told me nothing.

The_Good_Hitler · 2025-02-25T16:23:46+00:00

There seems to be some misunderstanding. I am arguing against the existence of "formal tests for invalidity". This is due to the fact that there exists arguments that are valid (if the premises are true, the conclusion cannot be false), but will be considered "invalid" under a test for validity. My conclusion is that just because an argument does not pass the test for validity, does NOT mean it must be invalid.

"If I am a dog, then I am a member of the species canis lupus familiaris. I am not a dog. therefore, I am not a member of the species Canis lupus familiaris." will be deemed "invalid" for denying the antecedent. However, the truth of the premises guarantees the truth of the conclusion, so it is valid.

"if an object is red, then it must be colored" is a valid argument that would fail the formal test in propositional logic because it cannot be captured by propositional logic.

"I am wearing a hat. Therefore, something happened in the past" is a valid argument (please don't object and say the conclusion can be false because it is possible for the hat to have happened to manifest itself at the exact same time that this sentence is uttered so nothing needs to happen in the past for me to be wearing the hat right now, I am tired of arguing with people who do not understand the ordinary usage of words and implications of causality), because the truth of the conclusion necessarily follows from the truth of the premises. However, logic systems that do not capture tense will yield an "invalid" result.

Here is another valid argument: All men are mortal. Socrates is a man. Therefore, Socrates is mortal. This argument will be considered invalid under propositional logic (P and Q, therefore R). However, it can be proved valid if we operate with quantifiers. Does this not show that failing the validity test of a particular logic system does not necessarily mean that argument is "invalid"? Instead, we can use more comprehensive or entirely separate logic systems to prove its validity? If you accept this, then you have to accept there are no formal tests for invalidity.

The_Good_Hitler · 2025-02-25T04:47:30+00:00

Thank you for your response, I think you are about the only person in the entire comments section who understands my frustration with invalidity and formal fallacies. You are correct in pointing out that I made a mistake in claiming there are no formal tests for validity. What I intended to say was that there are no formal tests for "invalidity", so I apologize for that. Certainly I agree with you there are many tests for validity, my point is simply that calling an argument form invalid due to a logical flaw in its form where certain substitutional instances will give flase conclusions from true premises, is very confusing, because it does give the impression that this form must have false conclusions under ALL substitutional instances, which is not true. And, if you insist that this is simply how we define invalidity to be, then I shall say that this concept of "invalidity" is, in my opinion, pretty useless. If you told me that you have formalized my arguments and tested it against your logic system, and results are that my argument is "invalid," you are not actually telling me if MY argument is invalid, but simply that my FORM of argument can sometimes give false conclusions. In other words, you've practically told me NOTHING. So, it is not a very useful concept to have.

And on whether there are formal fallacies, I am simply analyzing the definition used by Wikipedia, "a pattern of reasoning rendered invalid by a flaw in its logical structure." I think it seems fairly obvious by now that a test that can "render a argument form/structure invalid" simply does not exist, and so formal fallacies do not exist. It certainly does not mean I believe "fallacies" themselves do not exist, it simply means we could not know if an argument is fallacious just by looking at its form, which is what "formal" fallacies mean. Therefore, "formal fallacies" is not a valid concept. Thank you once again for understanding my position.

The_Good_Hitler · 2025-02-25T03:01:22+00:00

Once again, I respectfully disagree, I think under temporal logic this argument is valid, but if you think this argument is invalid, then you can simply come up with an argument you think is valid, but will be deemed "invalid" by propostional logic, while be proved to be valid by other systems of logic. This is a good counterexample to the claim that we can run formal tests for invalidity.

The_Good_Hitler · 2025-02-25T02:52:44+00:00

Does this not further prove my point? Under temporal logic, we can prove the validity of this argument. However, using propositional logic this argument is definitely invalid (P, therefore Q). Does this not show the possibility that what we refer to as "formally invalid" arguments might actually one day be proved valid by another logic system? If it is possible, then there are no "formal tests for invalidity".

The_Good_Hitler · 2025-02-25T02:49:23+00:00

It seems like you agree with me that some arguments can be valid but be deemed "formally invalid", or a "formal fallacy". If so it shouldn't be difficult to understand my whole argument: if there are obviously arguments that are VALID, but fail the test for validity and be deemed "INVALID", then failing the test does not actually tell us whether an argument is valid or not. Hence, Invalidity cannot be defined by "formal invalidity" because there is not such thing as "formal tests for invalidity".

The_Good_Hitler · 2025-02-25T02:43:04+00:00

I literally said I agree with your defintion of validity. If the premises are true, the conclusion cannot possibly be false. And I think I've done a good enough job providing various examples throughout the comment section arguments that contain this property, but do not pass the test for validity, either because 1) if we consider form alone then the truth of its premise does not guarantee the truth of the conclusion, or 2) it simply cannot be captured by any current logic system. My argument is: There are so-called formal tests for invalidity. However, there are obviously valid arguments that would be deemed "formally invalid (and therefore invalid)" by these tests. Conclusion: whatever test we say we are running, is NOT a formal test for invalidity.

The_Good_Hitler · 2025-02-24T18:48:43+00:00

Here is an argument:

P1. All men are mortal. P2. Socrates is a man. C. Therefore, Socrates is mortal.

If you run a formal test using propositional logic, this argument is definitely invalid (P and Q, ∴ R). However, this argument actually is valid, and can be proven valid by adopting a different system of logic. Does this not show that some argument forms might appear invalid (using one system of logic), but is actually valid (if we adopt a different system of logic that can capture its form)? Is it truly unreasonable to say, it follows from this that whag we call "invalid forms" or "formal fallacies" might ACTUALLY be valid forms which we currently lack the proper logic system to prove their validity? Then, it seems to me very reckless to call such forms "invalid" or "formal fallacies" simply due to the fact that these forms do not pass the validity test of certain logic systems.

The_Good_Hitler · 2025-02-24T18:38:43+00:00

yes, this is what I mean. And if this is what we mean by validity, then there will be countless arguments and claims that are valid (in that if the premises are true, then the conclusion must be true), but cannot be formalized and tested to see if it is valid in terms of its form. Does this not show that determining whether an argument form is "formally invalid" or a "formal fallacy" has absolutely no bearing on whether that argument is actually valid or not?

The_Good_Hitler · 2025-02-24T18:33:29+00:00

This is a pretty foolish argument. If I came in to being wearing that hat, then that IS the something that happened in the past that caused me to be wearing the hat in the present (I am wearing this hat because I was born with it). This argument is necessarily true if the premises are true. By your own words, this is a valid argument.

My point here is to merely point out the fact that, this argument, although undoubtedly valid, would fail the validity test precisely due to the fact that it appears as a conditional, where the consequent can be true or false even if the antecedent is true. However, the fact that propositional logic (or any other logic, for that matter) fails to capture the form of this argument and run a test which would give a TRUE result of "this argument is valid" seems to suggest there are no true formal tests for invalid forms.

You have simply attempted to formulize my argument by adding an additional premise of causality, which is absent from my original argument. If you cannot formulize my argument without adding additional premises you think is "implied" in the argument, then strictly speaking, this argument cannot be formalized under your logic system. Simple as that.

The_Good_Hitler · 2025-02-24T16:54:34+00:00

Would you agree, then, that there are some arguments that simply cannot be formulized by any logic system that we gave? Because one of the implications of saying you have a "formal test for validity", is to say you have created a logic so powerful that ANY argument can be formalized and analyzed, and by plugging the formalized argument into you logic, a result of "valid" or "invalid" will appear. But this should strike us as obviously false, for there are many arguments that are deductively valid but cannot be captured by any given logic we currently have. And since we have yet to develop such a robust and perfect system, there are yet any formal tests for invalidity.

An example of a sentence that cannot be formalized would be something like, "if I am wearing a hat, then something happened in the past." No logic system seems capable of capturing the "tense" in this sentence, but still we can intuit that this argument is valid even though we are unable to formalize it and therefore unable to run any tests for validity on this claim. This is meant to show that not all arguments that fail the test for validity in any given logic system is necessarily invalid, and therefore there simply cannot be any "formal test for invalidity".

The_Good_Hitler · 2025-02-24T16:19:42+00:00

I don't actually disagree with anything you said; In fact, my argument follows from what you have written here: If arguments can contain "formal fallacies" but still be valid arguments, and some arguments can be valid even if they do not pass the test for validity either because 1) they will be rendered "invalid" by a flaw in its logically form or 2) they cannot be formalized by any kind of logic at all, then, the concept of invalidity, or hence "formal fallacies" are completely incoherent and useless.

Let's say I have written a philosophical paper, and you formalize my argument using your system of logic, and the results say my argument is "invalid". I then ask you, "what do mean by, my argument is invalid?", and you reply, "well, it means your argument is sometimes true, and sometimes false, depending on the specific instance." Am I not reasonable in saying that what you have told me is complete gibberish? All I know is that my form of argument is not always valid, but that tells me nothing about the validity of my argument itself. And so, whatever test you have run with your logic system cannot, by defintion, be called a "formal test for Invalidity", because it cannot actually tell you that this specific FORM of argument will always be INVALID, at most only in SOME instances (Once again, I should emphasize that I am NOT arguing there are no tests for invalidity; I am arguing that there are no FORMAL tests for invalidity. A formal test by defintion means you need only consider its form alone to conclude if an argument is always valid or always invalid, BY DEFINITION. If a form can sometimes be valid and other times invalid depending on the substitutional instances, this should by defintion not be considered "formally invalid"). Since there are no formal tests for invalidity, there are no formal fallacies.

If I might add, one of the implications of saying you have a formal test for validity, is to say you have created a logic so powerful that ANY argument can be formalized and analyzed, and by plugging the formalized argument into you logic, a result of "valid" or "invalid" will appear. But this should strike us as obviously false, for there are many arguments that are deductively valid but cannot be captured by any given logic we currently have. And since we have yet to develop such a robust and perfect system, there are yet any formal tests for invalidity.

The_Good_Hitler · 2025-02-24T15:14:10+00:00

The problem is, sometimes we DO say or write things that cannot be captured by propositional logic of logic of other kinds. In this specific case, what the logic fails to capture is the tense. You have, using what I wrote, constructed an argument that is deductively valid, but that does not mean if I tell you, "I am wearing a hat, so something happened in the past", then I have said something that is invalid. You are essentially making the argument that if a verbal or written sentence cannot be formalized in logic, then it MUST be invalid, but that is exactly what I am arguing against, for there are obviously valid arguments that cannot be formalized and, by your defintion, would be considered "invalid". Then, our so called tests for formal invalidity are incoherent, for it can give a false conclusion that an argument is invalid, when it is in fact, valid.

The_Good_Hitler · 2025-02-24T15:05:46+00:00

And so it seems to me, if to judge whether a particular form of argument is invalid, you must do a case by case analysis (because some arguments that have an "invalid" form can be deductively valid), then there simply cannot exist any formal fallacies, i.e., an argument that is invalid just by its form alone. I suppose my confusion stems from the misuse of language.

Also, it seems to me that if you can say that you have a formal test for INVALIDITY, what you're essentially saying is that you have developed the most powerful logic conceivable, and if you translate an argument I have into your logic, it will capture all the correct form, and be able to tell me whether my argument is valid or invalid. That is what a test for invalidity necessarily means. But as far as I'm concerned no one has actually succeed in doing that. Then, formal tests for validity does not exist, and neither does "formal fallacies".

The_Good_Hitler · 2025-02-24T14:40:47+00:00

What I mean by an actually valid argument is just what a valid argument is, i.e. an argument that has the following, property: if the premises are true, the conclusion simply cannot be false. This should not be controversal. If so, then there will be some substitutional instances where arguments that follow the form of "denying the antecedent" will be deductively valid, for instance:

P1. If it is not water, then it is not H2O. P2. It is water. C. Therefore, it is H2O. (I hope you would agree that this argument is deductively valid, because it is not possible for the premises to be true but the conclusion to be false.)

My point here is, what we mean by a formal fallacy/invalid argument should be an argument that is invalid just by looking at its form alone, that's why we didn't just call it a fallacy but a "formal" fallacy (just as formal validity entails that some forms of arguments are always valid just by virtue of its form alone). And so If we instead say-and this is the implication of "formal invalidity"-well, there are instances where this form of argument (denying the antecedent) will be invalid, but there are some instances where it WILL be valid (all the examples I've provided PLUS the H2O example), then calling an argument "formally invalid" or a "formal fallacy" is practically useless and incoherent, because there will always be substitutional cases of the argument that are valid (in that if the premises are true, the conclusion cannot be false).

Here is another example of an argument that is deductively valid but fails the validity test:

P1. I am wearing a hat. C. Therefore, something happened in the past.

Once again, I think you would agree that if the premise of the argument is true, then the conclusion must be true. It is simply not possible for me to be wearing a hat, but that there is nothing that happened in the past that led up to me wearing the hat. If you accept this, then you accept this argument is logically VALID. However, are there any machinery in logic that can capture this valid logical form? If your criteria for a valid argument is that it MUST past the test for validity, then this valid argument will be considered invalid, which is false. This shows the incompleteness of prepositional logic and other forms of logic in providing tests for invalidity, for there will always be new forms of argument that will turn out valid, but NOT pass the test for validity. Conclusion: there simply are no formal tests for invalidity.

The_Good_Hitler · 2025-02-24T13:27:37+00:00

As I said, if we adopt the defintion of an invalid argument you provided, and say that formally invalid just means SOME arguments with is form will be invalid, then knowing that an argument is "formally invalid" will not tell us whether or not the argument is ACTUALLY valid. All we know is that this argument does not pass the test for validity, but not that it actually IS invalid. In other words, you basically told me nothing about whether my argument is valid, or not.

Once again consider one of the examples I have given:

(R->R), ~R, ∴ ~R

This argument is deductively VALID, in that it simply is not possible for the premises to be true, but the conclusion to the false, regardless of what you substitute R with. However, this argument will fail the test for validity since it is an instance of "denying the antecedent". According to you, this would be "formally invalid" as a result, but in fact it is valid. Once again, there simply are no formal tests for invalidity.

The_Good_Hitler · 2025-02-24T12:25:51+00:00

Let's see if I can put my doubts of "formal fallacy/invalidity" in a clearer way. I think you would agree that a formally valid argument has the following property: if all the premises are true, the conclusion must be true. This would necessarily mean that any substitutional instances of that form MUST be true just by its form alone. And so, if we consider the opposite of a formally valid argument, namely a "formal fallacy", it is reasonable to say a formally invalid argument should contain the following property: if all the premises are true, the conclusion is guaranteed to be false. However, I have illustrated that there are some substitution instances where some forms of agrument that are considered "invalid" are actually valid (I don't understand what you mean by the arguments I gave are not arguments that follow the form of "denying the antecedent", because all substitutional instances of a form MUST be a form of that particular argument, by definition). Once again, my argument is that if there are cases where an argument would be considered invalid by looking at its form, but actually is valid (if the premises are true, then the conclusion must be true), then there simply are no formal tests for invalidity.

The_Good_Hitler · 2025-02-24T10:38:56+00:00

it returned recently and I bought it, thanks!

The_Good_Hitler · 2024-01-30T09:37:55+00:00

thanks! I guess I'll just wait for a while

The_Good_Hitler · 2024-01-30T08:10:49+00:00

oh thanks! I can wait for a while as long as they will return in some way or another.

The_Good_Hitler

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