Quantification concerns itself with existence and the properties of existents. For example, take the minimal claim ‘Socrates exists’. This can be quantified thus:
$x(x = Socrates)
To translate: there is at least one thing, x, such as that thing must be identical or equal to the object we call ‘Socrates’.
In other words, ‘Socrates exists.’ Or, alternatively, Socratic-hood is instantiated or there is something, and this something Socrat-izes (as Quine’s Pegasus ‘Pegas-isers’).
In terms of existence, identity and the use of name-symbols, Frege wrote that
if we are to use the symbol a to signify an object, we must have a criterion for deciding in all cases whether b is the same as a, even if it is not always in our power to apply the “criterion”’ (From his Foundations of Arithmetic).
This means that because we often have two or more different names for the same individual or object, this dissimilarity must be matched by the referent’s identity in terms of both names. And in order to do this, the object must have a ‘criterion of identity’, to use Quine’s phrase; or a ‘criterion for deciding’, to use Frege’s. Only then will we know that a and b refer to one and the same object despite, perhaps, their different Fregean ‘senses’. However, Frege hints at the Kripkean or Russellian theory that when it comes down to naming or reference, we may not be able to describe it. That is, our relation to the named object may be ‘direct’, as in ‘direct reference’, and therefore non-conceptual or non-descriptive. In addition, Frege’s words also antedate Russell’s theory in that all we need when naming an object is an act of ‘direct acquaintance’ with the named object. Indeed, this acquaintance, or even the object itself, provides the ‘meaning’ of the name. Frege puts it another way and in terms of a criterion of identity for an object. He writes that it may ‘not always [be] in our power to apply the criterion’. Does this mean that if the object has a name, or is named, then that name cannot have a Fregean sense? Or does it simply mean that the object without an applied criterion of identity attached to it, as it were, itself does not have a sense (if that makes sense)?
This Fregean position on object-naming, or the ‘initial baptism’ in Kripke, amounts to two points:
i)‘No object without identity’.
ii)‘No naming of an object without a criterion of identity.’
The latter implies that we cannot name an object without a Fregean ‘mode of presentation’ and/or a Fregean sense. After all, Frege said that ‘sense determines reference’. In that case, a name’s sense may supply us with a criterion of identity for the object we are in the process of naming. In addition, these Fregean positions back up Quine’s problem with meanings, propositions and other abstract objects in that he argues that such things have no criteria of identity, and, perhaps, they disobey the strict rules laid down by his nominalism.
So we need to know whether or not a criterion of identity can be supplied by a Fregean sense or a Fregean mode of presentation. In turn, we also need to know whether these terms are more or less synonymous. If they are not, then how do they differ?
