Ethical Realism

August 13, 2012

Not All Good Arguments Are Logically Sound

Filed under: philosophy — JW Gray @ 11:53 pm
Tags: , , , , , , ,

More than one person has believed that all good arguments are logically sound, but this is a mistake. Not all good arguments are logically sound. Even so, understanding why not all good arguments are logically sound can help us better understand what good arguments are. I will discuss what good arguments are, I will explain what it means for an argument to be logically sound, explain the distinction between deductive and inductive arguments, and present an argument that proves that not all good arguments are logically sound.

What are good arguments?

For our purposes here a good argument is one that is rationally persuasive and does not make use of informal fallacies (informal errors in reasoning). Good arguments give us a sufficient reason to rationally agree with a conclusion. I will not discuss “informal fallacies” in detail here.

However, it is not entirely clear what a “good argument” is because it is not entirely clear when an argument is rationally persuasive. What exactly “rationality” consists of is a controversial topic that is studied by epistemologists (philosophers who study reasoning, justification, and knowledge).

Even so, there are uncontroversial examples of good arguments. A common example of a good argument is the following:

  1. All men are mortal.
  2. Socrates is a man.
  3. Therefore, Socrates is mortal.

(“Socrates” refers to a real historical figure discussed by Plato and other ancient philosophers and Socrates is said to have died by drinking hemlock.)

This argument gives us a sufficient reason to rationally agree with the conclusion that “Socrates is mortal” because the premises are highly justified, and anyone who believes the premises are true has no choice but to think that the conclusion is true. A person would not be irrational to believe the conclusion and it might even be rationally required for us to believe the conclusion—perhaps anyone who knows about this argument yet believes that Socrates is immortal (or is even undecided about it) is irrational considering how highly rationally persuasive this argument is.

What does it mean for an argument to be logically sound?

“Logical soundness” requires that an argument is both logically valid and that all the premises are true.

What’s a valid argument?

Logically valid arguments have a form that guarantees that the argument can’t have true premises and a false conclusion at the same time. For example, consider the following valid argument:

  1. If all dogs are mammals, then all dogs are animals.
  2. If all dogs are animals, then all dogs are flowers.
  3. Therefore, if all dogs are mammals, then all dogs are flowers.

This argument is logically valid because we can’t imagine that the premises are true and the conclusion is false at the same time. If we imagine that both the premises are true, then the conclusion must also be true.

To better understand why an argument is logically valid, it can be a good idea to consider the logical form. In this case the logical form is the following:

  1. If a, then b.
  2. If b, then c.
  3. Therefore, if a, the c.

All arguments with this logical form are logically valid. Each variable (a, b, and c) can stand for any proposition. Keep in mind that valid arguments can have false premises or conclusions. However, if an argument with this form has true premises, then it’s logically sound—and we are guaranteed that the conclusion is also true. Why? Because valid arguments can’t have true premises and a false conclusion at the same time.

It can also be a good idea to consider an invalid argument to see how it differs from a valid one. An example of an invalid argument is the following:

  1. If all dogs are mammals, then all dogs are animals.
  2. All dogs are animals.
  3. Therefore, all dogs are mammals.

In this case we can imagine that the premises are true but the conclusion is false insofar as both premises could be true even if not all dogs are mammals.

The logical form of this invalid argument is the following:

  1. If a, then b.
  2. b.
  3. Therefore, a.

Any argument with this form is invalid. We can replace the variables with new propositions to show that an argument with this form can have true premises and a false conclusion at the same time. Let’s replace a with “all cats are reptiles” and b with “all cats are animals.” In that case we get the following invalid argument:

  1. If all cats are reptiles, then all cats are animals.
  2. All cats are animals.
  3. Therefore, all cats are reptiles.

Now both premises are true, but the conclusion is false. The problem with invalid arguments of this kind is not that a premise or conclusion is false. The problem is that the premises do not give us a sufficiently good reason to think the conclusion is true—even if the premises are true, the conclusion can still be false.

What’s a sound argument?

An example of a sound argument is plausibly the following:

  1. If all dogs are mammals, then all dogs are animals.
  2. If all dogs are animals, then all dogs have DNA.
  3. Therefore, if all dogs are mammals, then all dogs have DNA.

One problem with just about any example of a “sound argument” is that there’s some uncertainty involved. Our best science tells us that the premises are true, but there’s a chance that the science is wrong. We can say that this argument is “probably sound” but we can’t say we know it is sound for absolute certain. It is possible that one of the premises are false and that the conclusion is false as a result.

If it were true that all good arguments are logically sound, that would imply that we almost never know for sure if an argument is good. The best we could do is say that it’s probably a good argument.

What’s the difference between inductive and deductive arguments?

Inductive arguments are meant to give us a conclusion that’s probably true based on limited data, but deductive arguments are meant to guarantee that the conclusion is true. Deductive arguments are meant to be valid, but inductive arguments are not meant to be valid. The above arguments were all deductive, but not all good arguments are deductive. For example, consider the following good inductive argument:

  1. The laws of nature existed throughout human history.
  2. Therefore, the laws of nature will probably exist tomorrow.

This argument could be considered to be logically invalid, but it’s not meant to be logically valid. It’s only meant to tell us what is probably true based on limited information. This is how scientific arguments for theories work. Science makes predictions based on limited data. The predictions could always have a chance of being false. For example, it is possible that the laws of nature will not exist tomorrow. We predict they will, but we can’t prove they will for absolute certain.

The fact that we can have good inductive arguments is potential proof that not all good arguments are logically sound. If all good arguments are logically sound, then the above argument about the laws of nature would fail to be a good argument—and all scientific arguments for theories would be also fail to be good arguments. And yet many of the most persuasive rational forms of reasoning to believe anything is based on science (and inductive arguments).

Proof that not all arguments are logically sound

An argument against the belief that all good arguments are logically sound is the following:

  1. At least some good scientific theories were proven to be false.
  2. If at least some good scientific theories were proven to be false, then not all good arguments are logically sound.
  3. Therefore, not all good argument are logically sound.

Premise 1 – Is it true that “at least some good scientific theories were proven to be false?” Yes. For example, I think Newton’s theory of physics is a good example. It was believed that Newton’s theory of physics was complete and could predict any physical motion, but it failed to predict the motion of Mercury. However, Einstein’s theory of physics was able to predict the motion of Mercury and is now considered to be a better (and more complete) theory of physics.

Premise 2 – Is it true that “if at least some good scientific theories were proven to be false, then not all good arguments are logically sound?” Yes. Scientists give good arguments in favor of good scientific theories. If all good scientific theories are proven to be true by sound arguments, then they can’t be proven to be false. Sound arguments would guarantee the theories are true because the premises would be true and the arguments for the theories would be valid—valid arguments can’t have true premises and false conclusions at the same time.

Given that we should accept these justified premises, the conclusion should also be accepted. We seem to know the premises to be true, so we have no choice but to think we can know the conclusion is also true. Why? Because this argument uses a valid logical form. The logical form is “a. If a, then b. Therefore, b.” This valid logical form is well-known to be valid and is called “modus ponens.”

Conclusion

I am all for good arguments, and I think people should know more about what good arguments are. I want them to know more about what it means to give people a sufficient reason to rationally agree with a conclusion. Saying that not all good arguments are logically sound doesn’t mean we shouldn’t try to present sound arguments now and then. However, it does mean that we can’t condemn all arguments that fail to be sound.

(Updated 11/21/13 to add clarification.)

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17 Comments »

  1. i like to say in my own way that logic is only correct within the scope of its rules (the premise), and there will not be logic if there is no rules. And that is why sometimes I muse that logic is not truth, and get dissapointed when learning mathematics or computer science.

    Comment by ck — August 14, 2012 @ 5:55 am | Reply

  2. “However, it does mean that we can’t condemn all arguments that fail to be sound.”
    true, for example, if i made a logical error in my proof of a math theorem, that doesn’t make the theorem invalid.
    but people who are eloquent like to exploit this illusion when they are quarrelling with others, sometimes it is fun if I am the one exploiting it =)

    Comment by ck — August 14, 2012 @ 6:01 am | Reply

  3. “Socrates” refers to a real historical figure discussed by Plato and other ancient philosophers who died by drinking hemlock.

    How many people read this to mean that there was a group of philosophers who died by drinking hemlock that discussed Socrates?

    Comment by Guy — August 15, 2012 @ 1:30 pm | Reply

  4. [...] James Gray on whether all good arguments are logically sound. Understanding why helps us appreciate good arguments. Proof that not all arguments are logically sound An argument against the belief that all good [...]

    Pingback by Not All Arguments Are Logically Sound — August 16, 2012 @ 12:21 pm | Reply

  5. [...] argue for their vision of Europe’s political future.A post at Ethical Realism makes the somewhat surprising claim that good arguments need not be logically sound.Quentin Meillassoux unpacks Mallarmé in a video at [...]

    Pingback by The Stone Philosophy Links - NYTimes.com — August 22, 2012 @ 5:40 pm | Reply

    • I had a book on logic by a man named Cope (I believe). He said that there is ‘L’ true and there is ‘R’ true. Some things are both and some just one. Also, as an example, a good argument can be based on the consequences of a series of acts. In this case the argument is based on what happens when a particular act happens. This is not logical but is experiencal, is cause and effect. Logic is a wonderful tool and can us help sort and learn; It is not the end all.

      Comment by Alan Shapiro — August 23, 2012 @ 3:08 am | Reply

      • I’m not sure what your post means. What does L true or R true mean? You might want to elaborate a bit more.

        Comment by JW Gray — August 23, 2012 @ 5:18 am

      • Logic true and ‘real’ true.

        Comment by Alan Shapiro — August 23, 2012 @ 2:19 pm

  6. A suggestion for a clearer example of invalid argumentation:
    If all professors wear eye glasses then all professors are human.
    All professors are human.
    Therefor all professors wear eye glasses.

    Or in a valid form:
    All who wear eyeglasses are human.
    All professors wear eyeglasses.
    Therefor all professors are human.

    This conclusion is valid based on the premises, and is likely to remain true regardless of whether, on closer investigation of such matters, those premises fail some time in the future. Is it a “good” argument? There aren’t any fallacies involved, and inductive research would indicate that both of the premises hold true in the vast majority of cases at least, so many would be convinced on this basis. (The exceptions of people putting eyeglasses on their dogs for gag photos and professors removing their reading glasses for photos on the dust jackets of their books wouldn’t necessarily invalidate the premises entirely.) Yet future research might more thoroughly prove both premises to be weaker than Newtonian physics.

    I suppose the “goodness” of this argument depends on how many students are seriously in doubt of the humanity of their professors, and how thoroughly this argument lays their fears to rest.If it works in that respect we don’t necessarily need to fix it. In any case, it is a far better argument than most you will hear on the campaign trails this year. ;-)

    Comment by dhuisjen2 — August 23, 2012 @ 8:09 am | Reply

  7. I find the proof that not all arguments are logically sound difficult to follow. I think you’ve buried a crucial premise, namely, that good scientific theories are supported with good arguments, in the middle of your discussion. Here’s a version that might be more perspicuous:

    1. Some good scientific theories were proven false.
    2. All good scientific theories were supported with good arguments.
    3. If some good scientific theories were proven false and all good scientific theories were supported with good arguments, then not all good arguments are sound.
    4. Hence, not all good arguments are sound.

    Comment by Dan Hicks — August 24, 2012 @ 11:49 am | Reply

    • Yes, and there are other assumptions. You could continue this process of breaking the argument down. I did mention why I think premise 2 is true in consideration of what you are saying.

      What I stated was not technically missing a premise from the logical standpoint, but there are assumptions to every argument that can be spelled out in greater detail.

      Comment by JW Gray — August 24, 2012 @ 6:57 pm | Reply

  8. I agree with Dan Hicks’ remarks. But if anyone doubts JW Gray’s original thesis, or Hicks’ abbreviated argument, perhaps their doubts will be undermined by puzzlers like the following:

    1. A syllogism may be a sillygism.
    2. Some good jokes are sillygisms.
    3. Therefore, a bad syllogism may be no joke.

    1. Socrates was a Greek.
    2. Greeks make great pizza.
    3. Therefore, Socrates ate pizza!

    Comment by Fred Bird — August 24, 2012 @ 8:39 pm | Reply

  9. Near the end of this essay claiming that not all good arguments are logically sound, you imply that you were instead “[s]aying that not all good arguments _aren’t_ logically sound.” [emphasis is mine) Please explain why you claimed the direct opposite of your original position.

    Comment by Kate Gladstone (@KateGladstone) — August 31, 2012 @ 1:17 pm | Reply

    • I said the following: “Saying that not all good arguments aren’t logically sound doesn’t mean we shouldn’t try to present sound arguments now and then.”

      It was not phrased properly. I will correct it.

      Comment by JW Gray — August 31, 2012 @ 8:15 pm | Reply

  10. Either your “proof that not all good arguments are logically sound” is logically sound, or it is logically unsound.
    If your “proof” is logically unsound, then you are begging readers to accept a logically unsound proof before you’ve finished proving to them that they may do so.
    If, however, your “proof” is logically sound, you will then have to tackle the task of deciding— and justifying — whether there remains any difference at all between “soundness” and “unsoundness” In proofs: given that you recommend accepting both sorts as good argument.

    Comment by Kate Gladstone (@KateGladstone) — August 31, 2012 @ 1:24 pm | Reply

    • Either your “proof that not all good arguments are logically sound” is logically sound, or it is logically unsound.
      If your “proof” is logically unsound, then you are begging readers to accept a logically unsound proof before you’ve finished proving to them that they may do so.

      It looks like you are arguing the following:

      1. We shouldn’t use sound arguments unless we prove sound arguments could be good arguments.
      2. I did not prove sound arguments could be good arguments.
      3. Therefore, I shouldn’t use sound arguments.

      I disagree with the first premise.

      First, let’s say we don’t know for certain if my argument is sound or not. What difference does it make? The argument could be a good argument either way. If we should accept the premises, then we should accept the conclusion; and I think we should accept the premises.

      I did argue that we need not know for certain if our arguments are sound for certain. That implies that I need not prove that sound arguments can be good arguments. Why? Because it doesn’t matter either way. (See where I said, “One problem with just about any example of a “sound argument” is that there’s some uncertainty involved. Our best science tells us that the premises are true, but there’s a chance that the science is wrong. We can say that this argument is “probably sound” but we can’t say we know it is sound for absolute certain. It is possible that one of the premises are false and that the conclusion is false as a result.”)

      Second, people rightly use sound and cogent arguments without proving sound or cogent arguments can be good arguments beforehand. Being sound or cogent is a property of an argument. We don’t have to prove that every property is compatible with being a good argument. Another property of an argument is referring to dogs. That doesn’t mean that I can’t use a good argument that refers to dogs without first proving that good arguments can refer to dogs.

      Even so, I have written about the possibility of having good “sound” arguments (and bad sound arguments). I talk more about good arguments here: https://ethicalrealism.wordpress.com/2012/08/28/what-are-good-arguments/

      If, however, your “proof” is logically sound, you will then have to tackle the task of deciding— and justifying — whether there remains any difference at all between “soundness” and “unsoundness” In proofs: given that you recommend accepting both sorts as good argument.

      I did explain if there is a difference. There is a difference. Do you mean you want to know if sound arguments are better than unsound ones? If we know a deductive argument is unsound, then we know it’s not a good argument. However, the premises of an unsound argument can be highly justified. When the premises are highly justified, then we will think it’s probably sound.

      Comment by JW Gray — August 31, 2012 @ 8:42 pm | Reply


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