Soundness is neither a necessary nor a sufficient condition being a good argument

I had been meaning to write something about this, but I decided to bump it up my to-do list after seeing this comment from Ashtad:

If you aren’t denying its validity (and by your apparent admission in the comment I replied to above, you aren’t), then you’re admitting that it is, at least, “halfway good” (as is all Plantinga claims within that text) and you aren’t criticizing anything in the actual text of ‘The Ontological Argument’ at all.

This is going to be another exercise in explaining some slightly esoteric concepts which may end up in the new book, and I’m not sure if my explanation will end up being clear enough. So I’m hoping for lots of comments on this.

First, some definitions from Wikipedia:

A necessary condition of a statement must be satisfied for the statement to be true. In formal terms, a statement N is a necessary condition of a statement S if S implies N (S => N).

A sufficient condition is one that, if satisfied, assures the statement’s truth. In formal terms, a statement S is a sufficient condition of a statement N if S implies N (S => N).

In other words: if X is a necessary condition for Y, you can’t have Y without X. If X is a sufficient condition for Y, then if you have X, you have Y.

Now, validity and soundness. Here, I will be talking in these terms in the special sense used by philosophers, not their ordinary English meanings. Here are the definitions, again from Wikipedia:

“An argument is valid if and only if the truth of its premises entails the truth of its conclusion. It would be self-contradictory to affirm the premises and deny the conclusion.” Or, most importantly, if an argument is valid that means that if its premises–the assumptions the argument makes–are true, then the conclusion is true. And “An argument is sound if and only if (1) The argument is valid. (2) All of its premises are true.”

Philosophers define “valid” and “sound” this way because doing so is useful, but is also very confusing because it has no basis in how the words are ordinarily used. Because if this, if you are confused by these terms, I sympathize with you. When this happens, look back to the definitions of the “valid” and “sound” I’ve given. Don’t try to go on what they seem like they ought to mean.

What makes validity and soundness useful is just that if an argument is sound, then its conclusion must be true. Thus, if you can make a strong case that an argument is sound, you have made a strong case that the conclusion is true. However, it is important to emphasize that neither validity nor soundness, as defined by philosophers, mean an argument is a good argument. In fact, it is pretty uncontroversial soundness is not a sufficient condition for an argument’s being good. In other words, it takes more than being sound to make an argument good.

First, take a closer look at validity. Nothing in the definition of validity prevents the premises of an argument from being completely crazy. “All men are mortal, Socrates is a man, therefore Socrates is mortal” is a valid argument, but so is “All cups are green, Socrates is a cup, therefore Socrates is green.” If the premises of the second argument were true, the conclusion would have to be true, but in fact the premises are completely crazy. The argument is valid but not sound.

It may be tempting to think that if an argument is valid, this must at least count for something, that this must mean the argument is at least not terrible. But this is wrong. The argument that assumes Socrates is a cup is not even halfway good. Also, as one of my professors used to say, validity comes cheap. All it takes to turn an invalid argument into a valid one is to add a premises that says, “if all of the above premises are true…” followed by the argument’s intended conclusion. But obviously it takes more than that to make an argument even halfway good.

Though it is slightly less obvious, an argument can be sound and still not be any good. Imagine arguing with someone who believes that the Sun orbits the Earth rather than the other way around. Now imagine giving them the following argument: “Premise: the Earth orbits the Sun. Conclusion: the Earth orbits the Sun.” If the premise of this argument is true, the conclusion must be true, and the premise is true. Thus the argument is sound. Yet you couldn’t blame anyone for not being persuaded by that argument. The argument is circular, which is to say it assumes what it is trying to prove.

(Edit: so the moral of circularity is that an argument’s being sound is not enough if you, or the person that you’re trying to persuade with the argument, can’t see that the argument is sound.)

Thus, the reason it is useful to ask whether an argument whether an argument is sound is not because all sound arguments are good arguments. Rather, the reason is that if an argument can be shown to be sound, then you have shown the conclusion of the argument to be correct.

Everything I’ve said so far is, to the best of my knowledge, uncontroversial, rare as that is in philosophy. But now I’m am going to say something more controversial: soundness is not a necessary condition for being a good argument. That is to say, there are good arguments which are not sound in the special sense of “sound” that philosophers have defined.

Here’s why: Arguments that aim at being sound are known as deductive arguments. However, some arguments do not even try to be sound, for example, the argument, “The sun has risen every day for all of recorded history, therefore the sun will rise tomorrow.” This argument is invalid, because there’s no contradiction in imagining that the sun does not rise tomorrow, even though it has always risen in the past. Arguments like this argument about the sun are known as inductive arguments. (There is some disagreement about how broadly or narrowly to define “inductive argument,” though that won’t matter for my purposes.)

The argument about the sun seems to me to be a good argument, even though it is not valid. Some philosophers disagree. The usual way to frame the issue is in terms of “solving the problem of induction,” but this is a bad approach because it assumes from the start there is a problem with induction. This problem is helped only a little by clarifying what is meant by “the problem of induction.” For example, defining “the problem of induction” as the question of “can induction be justified?” encourages us to skip over questions like “does induction need justification?” and “does it even make sense to talk of justifying induction?”

The real question, in my view, is whether we have any reason to doubt that the argument about the sun, and arguments like it, are good arguments. And philosophers don’t often try to give such a reason. David Hume’s Enquiry Concerning Human Understanding–usually cited as the source for the problem of induction–does try to do something like that, though his actual conclusion is not about which arguments are good, but rather that, “All inferences from experience, therefore, are effects of custom, not of reasoning.”

Hume’s argument for this conclusion, though, is unclear. One thing he says is that “all inferences from experience suppose, as their foundation, that the future will resemble the past,” and from there he argues that there is no way to prove this without circularity. But it’s not clear why he thinks that all inferences from experience suppose this. Maybe what he thinks is that reasoning, to be reasoning at all, must be deductive reasoning, so the only way an inductive argument can count as “reasoning” is if it has a hidden premise that turns it into a deductive argument.

But why think that? It seems to me that some inductive arguments are perfectly good as-is. Because of that, I think soundness is not necessary for being a good argument. That is to say, there are good arguments that are not sound in the special philosopher’s sense of “sound.”

And now I’m blanking on how to end this post, because I feel there must be something more to be said about induction, but I can’t think of what. I say this as someone who used to accept the common line on the “problem of induction,” but who upon re-reading the books I got this idea from, can’t see why I thought them so persuasive. But as I said at the beginning: does all of this make sense to people?

And incidentally, does anyone know of an example of a philosopher who thinks soundness is sufficient for being a good argument?

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  1. does anyone know of an example of a philosopher who thinks soundness is sufficient for being a good argument?

    I don’t. Since we’ve been talking about Plantinga, I reminded that he liked to say that his ontological argument is sound, but that this gives an atheist no reason to accept it.

    On the question of whether inductive arguments are invalid: Different philosophers (and different texts) present this in different ways.

    Some will agree with you that such arguments are invalid (and hence unsound, regardless of how compelling the argument is). However, some will say that valid and invalid (and sound and unsound) apply only to deductive arguments (or putatively deductive arguments).

    Inductive arguments are to be evaluated using different terms (more or less compelling, or something). So just like you can’t say that a car is invalid, you can’t say that an inductive argument is invalid either.

    If I recall, Salmon’s baby logic text follows this line (but it’s been a few years since I’ve taught it, so memory might fail).

  2. Oh, and your dismissal of the problem of deduction reminds me of Goodman’s “New Riddle of Induction,” in which he says that we now recognize that it’s foolish to try to deductively justify inductive inferences. Instead, we just need to sort out good inductive reasoning from bad. But, of course, that leads us into new problems.

  3. (make that “problem of induction

  4. i’m a little lost. this argument seems slightly chaotic. you seem to be loosely conflating validity and soundness (very different things, as you’re obviously aware); and even deduction/induction.

    validity: a well-formed deductive argument
    soundness: a well-formed deductive argument, fed by true premises, yielding a true conclusion

    i don’t see what your point is in your illustration (“All cups are green, Socrates is a cup, therefore Socrates is green.”). definitionally, a valid deductive argument w/ absurd premises can yield nonsense in its conclusion and still be valid. (it can even accidentally yield a true conclusion.) a valid and sound deductive argument is different; therein, the combination of valid deduction and true premises yield a necessarily true conclusion. I.e.,

    1. all x’s are y’s.
    2. z is an x.
    3. therefore z is a y.

    is valid and, if its premises are true, necessarily true.

    philosophers who believe a valid deductive argument with true premises is a good argument? yes. aristotle, russell, moore, ayer, quine, davidson, lewis, kripke, etc. one small example, the virtuoso performance required of g.e. moore to evicerate the counterintuitive ‘rampant essentialist’ argument of his idealist mentor, mctaggart; an argument which maintains with compelling surface plausibility that had any entity in the universe lacked *any* of the properties that it in fact possesses, the universe itself would not have existed. it took moore a densely-reasoned couple dozen pages to tease out the circularities buried inside modal ambiguities having to do with the scope of necessity in two of the argument’s premises. an important argument of its day refuted entirely via analysis, without even having to inspect the truth of the argument’s premises.

    That said, some of course argue that as deductions are tautologies, they’re trivial. More significantly, in my view, Quine has argued that, except in the most trivial cases, apriori analytic deductions, i.e., arguments reliant on synonymy, are synthetic aposteriori.

  5. Perhaps what I said about validity would have been clearer if I hadn’t said, “First, take a closer look at validity” and instead said something like, “But before I explain why that is [that it takes more than being sound to make an argument good], a bit more about validity…”

    I don’t understand the relevance of your discussion of Moore.

    If “aristotle, russell, moore, ayer, quine, davidson, lewis, kripke” all think that being sound is enough for an argument to be good, well, so much the worse for those poor fools. But sources?

  6. Another note: based on feedback received via Facebook, I’ve decided that when I write about this in the future, I’ll say deductively sound/valid for clarity. Thanks to Ashtad and Arthur Boyer.

    Also thanks to Arthur for pointing me towards a textbook which I shall surely comment on next week.

  7. At this point, I’m just writing notes to myself, but: inductive arguments are not the only kind of argument that can be good without being deductively sound.

    If you have a valid argument, and you’ve got every reason in the world to think its premises are true, I’d say that’s a good argument, even if you happen to be mistaken through no fault of your own.

  8. And deductive arguments can vary in strength, depending on how good your reasons are for thinking they’re sound.

  9. Is this a valid argument?

    1)God is a defined to be a necessary being and exists in all logically possible worlds.

    2)There is at least one logically possible world in which the evil in that world is incompatible with an omnibenevolent god. (That logically possible world may not be our world.)

    3) Therefore, there is no God.

    Which of the premises 1) and 2) would , say, Plantinga claim is false?

  10. i suspect i’m missing something crucial. but it seems if you’re in the business of making a deductive argument in support of a deductively supportable conclusion AND your argument is logically valid AND your premises are true; the argument is sound. so, in terms of the conclusion in question, i would think the argument should thereby be regarded as “good”, at least by any measure i can think of. what i’m not grasping (i think) is some distinction in deduction you’re drawing between soundness and goodness. i.e., there seems to be some quality beyond the standard valid argument + true premises that you’re suggesting “goodness” in a deductive argument requires.

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