The argument that I will be presenting and critiquing resides in Chapter 2 of Williamson’s “The Philosophy of Philosophy”. Three-value and fuzzy logicians offer the following argument in response to the proposition ‘Mars was always either dry or not dry’. Here, they offer support for their claim in saying that it is more of an indefinite answer as opposed to a borderline case of answering definitively with a ‘yes’ or ‘no’.
1. If it was once indefinite whether Mars was dry then it is indefinite whether Mars was always either dry or not dry
2. It was once indefinite whether Mars was dry
3. It is indefinite whether Mars was always either dry or not dry
This argument uses the basic rule of modus ponens ‘If P then Q. P, therefore Q’. The first premise is valid; that is, if something was indefinitely some thing at one point in time then it could not have been always been that thing. The second premise merely states that the first component of the first premise exists, and thus naturally its second component must also exist. Using the same structure from the first argument, let us consider what would happen if we substituted ‘Mars’ with ‘2+2=4’ and ‘dry’ with ‘true’.
1. If it was once indefinite whether ‘2+2=4’ was ‘true’ then it is indefinite whether ‘2+2=4’ was always either ‘true’ or not ‘true’
2. It was once indefinite whether ‘2+2=4’ was ‘true’
3. It is indefinite whether ‘2+2=4’ was always either ‘true’ or not ‘true’
The first premise uses the same logic again and therefore must maintain its validity. Since the proposition ‘2+2=4’ is a necessary truth, we can also substitute ‘2+2=4’ with ‘necessary truth’. While the second premise may have difficulty in obtaining support, it is easy to provide a time in history where indeed it might have once been indefinite whether the addition of two and two could have equalled four or that any other necessary truth is true for that matter. With that, we are left with the concluding premise that is false. We do know that ‘2+2=4’ or that any necessary truths were never indefinitely true, but always true, regardless of our beliefs in them. While both arguments may be valid in their structure, the second is obviously not sound, which casts doubt unto the soundness of the first.
Here is a reconstruction of a sound and valid argument one could use in favour of the original proposition:
1. At any given time, If Mars can never be both dry and not dry, then it may only be either dry or not dry.
2. At any given time, Mars can never be both dry and not dry
3. Therefore, at any given time, Mars must either be dry or not dry
Since this argument structure emulates that of a logical truth, it necessarily follows that either Mars is either dry or not dry at any given point of time. The ‘at any given point of time’ component was added to satisfy the temporal condition of ‘was’. It could also be used to satisfy an ‘is’ component if the example were taking specifically about a present example, as opposed to one being used from the past.