Crítica, Revista Hispanoamericana de Filosofía, Volume 21, number 62, agosto 1989
Certeza, duda escéptica y saber
Samuel M. Cabanchick
Universidad de Buenos Aires

Abstract: Traditionally, the skeptic has been considered as a threat to our claims to true and justified knowledge. Also, certainty appears to be as the highest possible degree of knowledge. Knowledge and certainty are thus opposed to skepticism.
This paper wants to show that 'certainty' and knowledge are, probably, incompatible notions, and that the possibility of a doubt about the assumed certainty is a necessary condition to distinguish between belief and knowledge, and to construe any kind of knowledge.
Its starting point is Moore's notion of cerfainty, Moore demands that the expression of certainty (and, consequently, its formalization) should assume certain basic intuitions. One of them is the non-transmissibility of certainty; another intuition, fundamental to its Proof of the Existence of the World, is that certainty should be implied by knowledge.
The claim of certainty:

(1) "1 know with absolute certainty that p"

can be considered as a 'residusl meaning' ofthe followingformal expression in the epistemic logic of Hintikka:

(2) "SySyp",

where 'S' is the epistemic operator which stands for knowledge, 'y' is the personal pronoun 'I', and 'p' refers to the proposition claimed to be known. In other words, we would claim to know that we know a given proposition.
This proposal has some disadvantages: in Hintikka's view, it is virtually equivalent to 'Syp', that is, to 'I know that p', and, even if Hintikka went astray, because knowledge is transmissible, certainty would be transmissible too, and this contradicts Moore's intuition concerning the nontransmissibility of certainty.
Another interpretation of (1) is

(3) "N Sy p" ("I necessarily know that p")

where 'N' is the necessity operator. But this interpretation fails because it also contradicts the non-transmissibility, and intuitively it is very hard to believe that "Sy p → N Sy p", that is to say, it is very hard to believe that it matches the intuition that knowledge implies certainty. An alternative would consist on relating certainty and belief. If 'C' is the belief operator in epistemic Iogic, the following theorem by Galván comes close to Moore's demands:

(4) "Cy(Cyp - p)",

that is, "I believe that I believe only truths", It can also be put as:

(5) "Cyp - CSyp" ("If I believe that p, therefore I believe that I know that p").

Unfortunately, neither (4)1nor (s) are warrants of truth, but warrants of the imposeibility of doubt. This is opposed to Moore's claim that we know that the premises of the Proof of the Extemal World are undebatably true.
Luis Villoro has pointed out the necessity of taking into consideration the epistemic communities when we speak of knowledge. This requirement is stated thus:

(6) (Syp) → Cy(∃x)(P(-SxP. -Sx - p) . (x ≠ Y))),

which can be read as: "If I know that p, therefore I believe that there is an x such that it is possible for him not to know that p and not to know that no-p, and x is not identical with me". This can be generalized thus:

(7) (z)((Sxp) → Cx(∃x)(P(-SxP. -Sx - p) . (x ≠ z)))

Moreover,from this formalization it followsthat a subject should be able to doubt about the truth ofhis belief: he must admit the possibility of error, and this conflicts with certainty.
In order to be able to get knowledge I must abandon a strictly subjective warranty of truth, such as certainty, and this is possible when I accept the existence of a point of view which differs from mine, a point of view which lets undecided the truth or falsity of a proposition. In this way it is p088ible to distinguish between believing and knowing, because knowledge still demanda the possibility of error.
So, there is a certain interpretation of skepticism that can see it not as a threat to the claims to justified knowledge, but as the position that truly offers the poesibility of knowledge, because it fights the solipsistic assurance of the subject of certainty.

[Francisco Hernández]

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