Dummett's Backward Road to Frege and to Intuitionism - Tripod

and are thus scientifically certain. Namely, they are stipulations! This is very different from
explications.
Frege’s view in Grundgesetze is that we cannot figure out subsentential references unless we
already grasp as primitive the apparatus of identity and quantification, much as in Quine, and also
negation, material implication, and some other functions. In particular, Frege’s stipulation of logical
determinacy for the identity relation in vol. 1, § 7 is not a definition, since Frege lists “ξ = ζ“ as a
primitive name in vol. 1, § 31, and argues elsewhere that identity is indefinable because every
definition is an identity (1970c: 80). Thus § 7 can only be a regimentation of identity merely to ensure
its logical determinacy. Frege says he has been talking about identity all along, i.e., prior to its
regimentation (Grundgesetze vol. 1, § 7; compare 1979f: 210).
Some terms need less regimentation than others, since some explications are more determinate
than others to begin with. It is a short jump from the ordinary sense of “gleich” to the regimented sense
of the formal identity sign. Similarly for negation. But notoriously, truth-functional “or” is a big
regimentation. And the horizontal stroke is a big regimentation that prevents any well-formed sentence
from lacking a truth-value for categorial reasons. E.g., “5 is pink” is arguably an indeterminate
statement, but prefixing the horizontal stroke imposes falsehood on it.
For Frege, explications (Erläuterungen) are not stipulative definitions, or even stipulated
regimentations. Explications are hints. Frege says right in Grundgesetze vol. 1, § 0 (last para.) that he
must indicate what he intends by his primitive names by “hints,” since not everything can be defined.
For Frege, communication always begins with hints, metaphors, or suggestions, and thus with an
element of uncertainty. 6 Thus explications logically can fail. This is essentially different from
regimentations and definitions. This is why Frege requires explications to occur in a propaedeutic,
while definitions, and perhaps also regimentations, occur within the scientific notation. Before we can
start a formal notation at all, “we must be able to count on a meeting of minds.”Thus explications are
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