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I’ve read many times and places that an argument is sound iff

1.      The argument is valid.

2.      All the premises of the argument are true. [1]

Let’s call this the standard definition of a sound argument. Now consider this argument:

1.      If the Earth is a planet, then there is a satellite above Denmark this moment.

2.      The Earth is a planet.

3.      Thus, there is a satellite above Denmark this moment.

The argument is valid. (Form: Modus ponens.) Is this argument sound? The second premise is true. The first is true from time to time but I guess it is false most of the time. It follows then, given standard definition, that this argument is sound from time to time.

But still this argument should never convince anyone. Why not? It should not because the first premise is never justified for anyone. Even though the argument is sound from time to time given the standard definition, it should not be convincing for anyone at anytime. This flies in the face of the normal practice in discussions of trying to establish that one’s arguments are sound.

Consider this revised definition of a sound argument. An argument is sound iff

1.      The argument is valid.

2.      All the premises of the argument are justified.

This seems to solve the above problem but it’s still not good enough. Here is why. In the second condition, justified for whom? Oneself? If so, then soundness becomes subjective. I take this as a reductio. Soundless is an objective matter. Thus, the revised definition is false.

Perhaps a new definition of soundness is not what is needed but rather a distinction between the soundness and convincingness of arguments. There are at least two kinds of convincingness of arguments. One kind of convincingness is that the argument convinces someone to change their beliefs. The argument may be completely bogus (e.g. invalid) but the person does not realize that.

But philosophers are usually not interested in rhetoric. Philosophers usually, thus, talk about arguments being rationally convincing. This is the second kind of convincingness. I take it to mean that an argument ought to convince a rational person. Let’s work with this.

What are the criteria for an argument being rationally convincing? Soundness is neither a sufficient nor a necessary condition of rationally convincingness. I wonder what is. Maybe a subjective definition works here. Consider this definition of a rationally convincing argument. An argument is rationally convincing for person p iff

1.      The argument is valid.

2.      All the premises of the argument are justified for person p.

A person may not recognize when something is justified for him to believe, and so he can fail to be convinced (i.e. change beliefs) by an argument that is rationally convincing for him.

A person may know of an argument that is rationally convincing for him. Suppose that I don’t know that argument and it contains some proposition that I’ve never heard of. Then it follows that the argument is not rationally convincing for me. Further, suppose that I know the argument and one of the premises are not justified for me. Then, the argument is rationally convincing for him but not for me. I’m happy with the implications above. They seem to capture what is meant with rational convincingness.

So, next time when we are in a discussion, we are not really trying to prove that our arguments are sound. We are trying to prove that they are rationally convincing for the other person. The confusion might arise because the two, soundness and rationally convincingness, overlap much of the time.

The reason why I started thinking about this is a fine tuning argument. I don’t particularly recall the argument but let’s suppose that it has three premises. I think that two of them are true but the last one I don’t know about, and neither does the proponent or anyone else. The last premise is unjustified for everybody. The argument might be sound but no one knows. The interesting thing seems to be whether it is rationally convincing not whether it is sound.

Readers of this essay may want to read this essay as it is relevant.[2]

[2] http://deleet.dk/2009/02/23/jtb-and-the-first-person-perspective/