This Morning's Musings

An hour's worth of sketchy ideas for a possible paper on the Problem of Lost Facts...

Charles Sanders Peirce was the founder of ‘pragmatism’ - a view about the appropriate method for settling intellectual and metaphysical disputes. Peirce aspired to use this method to elucidate the ‘pragmatic meaning’ of important concepts such as truth. Specifically, the purpose of the method is to describe the role those concepts (in this case truth) play in our practices (in this case inquiry). Many Peirceans consider a claim such as the following to be part of a pragmatist conception of truth (n.b. the nested nature of the beast is marked by parentheses)

(T) If a hypothesis H is true, then (if inquiry into H were pursued long enough and well enough, then H would be believed).

(T) faces a standard objection, which is often called the ‘problem of lost facts’. (There are other objections of course, about triviality in particular, but I'm not tackling them here). I propose to defend (T) against this counter-argument, which begins with the putative lost fact that “Churchill sneezed 59 times in 1945” - a hypothesis we’ll call H1:

1. If a hypothesis H is true, then (if inquiry into H were pursued long enough and well enough, then H would be believed). (i.e. we assume (T) for reductio)
   
2. H1 is true. (Supported by the broadly realist intuition that there is some definite number of times Churchill sneezed in 1945. Prima facie it does not matter that we are unable to determine the correct number.)
   
3. If H1 is true, then (if inquiry concerning H1 were pursued long enough and well enough then H1 would be believed).
   
4. It is not the case that (if inquiry concerning H1 were pursued long enough and well enough then H1 would be believed). (i.e. the relevant fact is ‘lost’)
   
5. So H1 is not true.
   
6. H1 is true and H1 is not true. (i.e assuming T generates a contradiction.)
   
7. So it is not the case that if a hypothesis H is true, then (if inquiry into H were pursued long enough and well enough, then H would be believed). (i.e. by RAA the Peircean conception of truth is false.)
   

My attempts to render this formally suggest it is valid...

1. ∀x (Fx ⊃ (Gx ⊃ Hx)) Premise
   
2. ∃x (Fx) Premise
   
3. ∃x (Fx ⊃ (Gx ⊃ Hx)) From 1 & 2
   
4. ∃x ¬ (Gx ⊃ Hx) Premise
   
5. ¬ (∃x (Fx)) From 1-4
   
6. ∃x (Fx) ∧ ¬ (∃x (Fx)) From 1-5
   
7. ¬ ∀x (Fx ⊃ (Gx ⊃ Hx)) From 1-6
   

...since it relies on fairly safe logical moves such as the universal-particular syllogism, modus tollens and RAA. My current suspicion is that the fault with this argument lies in premise 4. Specifically, I’m not sure the opponent of pragmatism can get away with straight up asserting that H1 is lost. Isn’t the most they can assert that it is possible or perhaps likely that H1 is lost - that no amount of inquiry will lead us to the relevant sort of belief? If so, does this substantially weaken the argument (or am I being overly optimistic?)

Premise 2 is also a bit fishy though. Perhaps its prima facie harmlessness is only prima facie.