Valid Forms And Logical Fallacies

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6 mins read

Far too long ago, I did a quick intro to logic.
Let’s talk about valid forms. This is a longish read for our dopamine addicted society, but I have faith in you, reader, that you can handle this just fine.
With so many things, there are a lot of wrong ways of doing something. And I mean a lot. The more specific and precise you need to be, the more ways of going wrong there are.
When it comes to propositional logic, there are certain forms, or patterns, that are logically valid. (Side note: valid doesn’t mean sound. I’ll get to that in a bit.)
1. Modus Ponens (Latin for “mode that affirms”)
This is the easiest to start with.

If A, then B
A
Therefore B
If I was an American, then I would be awesome.
I am an American,
therefore I am awesome.
If you have a valid user name and password, then you can log into the website.
You have a valid user name and password,
therefore you can log into the website.
If I can think, I am.
I think,
therefore I am.

Toldja that was easy.
2. Modus Tollens (Latin for “mode that denies”)

If A, then B
Not B
Therefore not A.
If I was a Man of the West, then I wouldn’t be a whiny gamma.
I am a whiny gamma,
therefore I am not a Man of the West.
If the sky is blue, then Skynet hasn’t launched its war against humanity.
Skynet has launched its war against humanity,
therefore the sky is not blue.

That’s the first two basic valid forms.
And both of them are where many a logical fallacy happens.
Fallacies
A fallacy is, in short, an invalid form of an argument. The premises and conclusion might all be true, we just can’t tell logically if they are.
1a. Affirming the consequent
This is an invalid form.

If A, then B
B
Therefore A
If I suck at Dark Souls, then my controller is broken.
My controller is broken,
therefore I suck at Dark Souls.

There are other reasons why I suck besides a broken controller.

If Hillary was evil, then the Federal Reserve is evil.
The Federal Reserve is evil,
therefore Hillary is evil.

All of these are true, but the form is invalid so we can’t logically come to the conclusion. Hillary’s and the Fed’s evilness aren’t necessarily tied together.
2a. Denying the antecedent.
The invalid form is:

If A, then B
Not A
Therefore not B.
If it rains, then the streets will be wet.
It didn’t rain,
therefore the streets won’t be wet.

Well, no. The streets could be wet from road cleaners, or a burst pipe, or a flood upstream, you get the idea.
Here’s one I’ve seen far too often.

If God exists, then evolution is false.
God doesn’t exist,
therefore evolution is true.

Alright, we’ve covered two of the most commonly used forms and fallacies. There are more valid propositional forms which I’ll tackle in a future post.
Soundness
Logic, like math, has a unreasonable affinity with reality. But there’s a slight catch here, an argument might be valid in form but not sound. That is, not all the statements in the premises are true.
Took a look at this argument:

All moops are floops.
A doop is a moop,
therefore a doop is floop.

This is valid but it’s not clear if it’s sound, because no one knows what doops, moops, and floops are.
Let’s refine the error.

If birds fly, then they snorkel.
Birds fly,
therefore they snorkel.

Alright, I hope everyone can see the Modus Ponens form here. This argument is valid, but it’s not sound. We know that in this world birds can’t snorkel, no matter how many of them fly.
Here’s another one.

If all genders can have periods, then men can have periods.
All genders have periods,
therefore men can have periods.

Again, it’s a valid form, but it’s not sound. At all. It’s unsound in more ways than one, in fact.
Conclusion
To recap: a good argument has to be valid and sound. We’ve looked at two valid forms and their invalid counterparts, aka fallacies, and we’ve looked the difference between sound arguments and unsound ones.
Further reading here for the curious.
See: https://infogalactic.com/info/List_of_valid_argument_forms
I promise that someday before the Sun burns out, I’ll tackle more valid forms and fallacies.

5 Comments

  1. I dispute the way you’ve written this part:
    > If I suck at Dark Souls, then my controller is broken.
    > My controller is broken,
    > therefore I suck at Dark Souls.
    >
    > There are other reasons why I suck besides a broken controller.
    As written, it’s not a good example of affirming the consequent.
    This would be fine, as an example of the fallacy of affirming the consequent:
    > If I suck at Dark Souls, then my controller is broken.
    > My controller is broken.
    > Therefore I suck at Dark Souls.
    >
    > I could have a broken controller and yet still be good at Dark Souls.
    The fallacy that you’ve described is, from what I recollect, a different (informal) fallacy, namely that of the hidden premise.
    > (Hidden premise): I could only suck at Dark Souls if my controller were broken.
    > Exposed premise: I suck at Dark Souls.
    > Conclusion: Therefore, my controller must be broken.
    If the hidden premise were exposed, this would in fact be a valid argument. But not sound, as you go on to say.

    • I appreciate the feedback, but no.
      Affirming the consequent
      This is an invalid form.
      If A, then B
      B
      Therefore A
      I never used an iff. The argument might not gell with you, but it’s a, pardon the usage, sound invalid argument.
      I could suck, or I could be good at Dark Souls, but reaching the conclusion that I suck because my controller is broken, in the form I used, is affirming the consequent.

  2. On the other hand, this is an example of affirming the consequent:
    > If my controller is broken, I will suck at Dark Souls.
    > I suck at Dark Souls,
    > therefore my controller is broken.
    >
    > There may be other reasons why I suck besides a broken controller.
    The difference between, “If A, then B,” and, “If and only if A, then B,” is of course massive.
    Sadly, from what I’ve seen, most instances of “logical fallacies” one encounters in everyday life are actually rhetorical fallacies. That is, hearers are invited to reach the desired conclusion for reasons that have nothing at all to do with the premises and everything to do with emotional appeals.
    For example:
    * Most everyone believes X, therefore X must be true.
    * All the cool kids believe Y. You don’t want to be uncool, do you? (Substitute “popular”, “right-thinking”, etc. as required)
    * Adam doesn’t believe Z. Adam has a Ph.D. and is an expert (maybe in a field related to Z). Therefore, Z must be false.
    Sadly, people are not encouraged to think for themselves about much of anything these days.

    • ‘Sadly, from what I’ve seen, most instances of “logical fallacies” one encounters in everyday life are actually rhetorical fallacies.’
      Yeah, that’s a whole ‘nother post. Rhetoric doesn’t really have fallacies, since rhetoric doesn’t use formal forms, but rhetoric has to hew somewhat to the truth, otherwise it can lose its persuasiveness quickly and fail to move others into accepting your position.

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