On the connection between a proper view on compositionality and strict finitism: Weyl’s idea that universal formulae ranging over the natural numbers are not statements, but ‘Anweisungen auf Urteile’ (as cited in Marion, Wittgenstein, Finitism, and the Foundations of Mathematics, chapter 4) is congenial. The assumption that there exists an infinite number of sentences that satisfy a pattern in quite a similar manner can be seen as the result of mistaking rules with the set of all their instances. As actual sentences of a language these simply do not (yet) exist.
Martin Stokhof from: Interpretation date: fall 2001
If we look at the starting point of learning a first language as involving (lots of) triangulation situations which are special in the sense that in those situations there necessarily is an asymmetrical relation of authority between the parties involved, is that not, pace Davidson, a form/source of social externalism?
If this is right, then one could make the case that first-person authority exists only as the result of successful communication. And that would make throw a different light on the appeal that Davidson makes to first-person authority in his argumentation against social externalism à la Burge.
The reason that Davidson wants to keep social externalism at arm’s length is probably that he thinks it might interfere with his claim that language is not an epistemic intermediary. After all, if we accept social externalism and accept the possibility of variety in sources of such external elements, then some form of relativism seem to ensue.
Martin Stokhof from: Aantekeningen/Notes date: 20/10/2015
First person certainties illustrate the distinction between grammatical meaning and situational meaning in an interesting way. Cf., ‘My name is NN‘, as said by NN. This utterance has grammatical meaning, but whether it also has situational meaning depends on the perspective we view it from. For the hearer this utterance supplies contingent information (at least, possibly). But that does not hold for the speaker. So, there is indeed a use for this sentence, –after all, this is typically the way in which we tell someone what our name is. But it has situational meaning only for the hearer, not for the speaker. The speaker needs a hearer to be able to use the sentence in the first place. And that distinguishes this sentence for its second and third person variants: ‘His name is NN‘ always has situational meaning. One could say that in the first person case the speaker uses the grammatical meaning to generate situational meaning for the hearer.
Martin Stokhof from: Aantekeningen/Notes date: 17/07/1994
Concerning Dummett’s criticism of Davidson’s semantics (cf., ‘What is a theory of meaning? (II)’ ). First step: a semantic theory is (also) a theory of competence, i.e., of the ability to use the language with its semantics. That much is unproblematic from a Davidsonian perspective, it is what Davidson starts out with (cf., the opening paragraphs of ‘Truth and meaning, and ‘Radical interpretation’). Second step: adding the requirement that this ‘knowledge of language’ must be manifested (or, at least, manifestable). As such that does not seem to be objectionable from a Davidsonian perspective, the crux of the matter is what will count as manifestation of semantic knowledge.
Next, Dummett seems to make two moves. First he constructs semantic knowledge as the ability to observe that truth conditions obtain, and then, correctly of course, notes that taken in a more or less `literal’ way, this is problematic for sentences that have truth conditions that involve counterfactual or past situations or infinite domains. One reply to that could be that observation of truth conditions being fulfilled is not a very representative case anyway, and that it seems much more natural to construe manifestation of knowledge of truth conditions in terms of having knowledge of ways of ascertaining that truth conditions hold. (So, with regard to the past, a basic knowledge of historical methods; with regard to infinite domains, the concept of a proof by induction; etc.) This is not something Dummett spells out, but he seems to tie in with this, since the next move he makes is to suggest that verification actually is what we are after: the ability to manifest semantic knowledge is the ability to verify sentences (statements). That is a crucial move, since now the semantic and the epistemological are intimately tied: semantic competence, viz., the ability to use language correctly, has now been identified with what at first sight seems to be an epistemological `competence’, viz., the ability to verify a statement (always ‘in principle’, of course).
Here, I guess, Davidson would object. In ‘A coherence theory of truth and knowledge’ he makes an effort to carefully dissociate the semantic and the epistemological, and in a criticism of his ideas that effort cannot simply be neglected. It must be shown defective before this further step can be taken. For Davidson verification, as a particular form of justification, belongs to the coherence notion of truth, which is not to be mistaken for the `mild’ correspondence notion that plays a role in semantics and semantic competence.
The difference between Dummett’s and Davidson’s position is a substantial one. By separating semantics and epistemology Davidson makes room for the possibility that we might be able to understand statements that are epistemologically unassailable, whereas in Dummett’s approach this becomes impossible. Mathematics provides an example: Dummett’s view on meaning forces him to adopt a constructivistic approach to mathematics, whereas for Davidson such an approach would need additional arguments that do not hinge on the semantics of mathematical statements.
What is the right approach is not obvious in any way, the point here is simply that the transition from the requirement that one be able to manifest one’s semantic knowledge to the requirement that one have a method of verification is one that stands in need of argumentation and that part of that argumentation is essentially non-semantic.
Martin Stokhof from: Interpretation date: fall 2001
Hand or hammer. An ideal language is an artificial, constructed language. (Historically this is not quite correct. Cf., ideas about Hebrew being the language spoken in Paradise. Cf., also, Heidegger on philosophical languages.) An artificial language is an instrument like a hammer. Constructed by us, and used by us by means of our natural ‘instruments’. And an artificial language can be used only by means of a natural language (this includes its construction), the same way a hammer can only be used by someone who has hands. This holds also for artificial languages that in some sense (precision, clarity, scope) surpass the natural languages by means of which they are constructed. (Cf., Frege on the telescope and the eye.) In some settings this dependence may not be so obvious: mathematics, programming languages, machine code. But think about what we mean when we say that a machine calculates, thinks, … In the end it comes down to interpretation, or translation, into our vernacular. That seems implausible only as long as we forget that our experience (action) is much broader than that which is covered by means of our natural language. (Cf., note dd. 14/07/98: “The role of experience. Experience is not what is expressed in language, at least not solely, but what makes language possible in the first place. It is therefore both transcendent and transcendental. This holds not just for empirical statements and empirical concepts, but across the board. Cf., Wittgenstein on the relation between mathematics and experience. “)
Hence, it seems plausible to consider a natural language to be like a hand, and not like a hammer. However, although we call a natural language ‘natural’ it is not something we were born with: it has to be acquired. This leads straightforward to the assumption of a language of thought. It is the LoT that is the true natural language. (Cf., the biological metaphors in Chomsky’s work, for example: ‘language organ’.)
But then the problem arises as to how this LoT has meaning (and hence conveys meaning to the acquired language. Question: on such a picture would an artificial language need the mediation of a natural language? Or could it be considered to be tied directly to the LoT, in the same way as a natural language?), i.e., how the LoT relates to the world. Explaining that in terms of a natural language (and its relation to the world) obviously leads us straight into a vicious circle. To sharpen the issue, consider theories of direct (rigid) designation. Given some assumptions about the inherent (i.e., non-reducible) indexicality of natural languages, such theories seem at least partly right. From thereon we can turn straight to the steamship metaphor of Putnam: neither natural languages nor a LoT is a natural instrument in the sense of a hand.
Interesting question: could we discover an ideal language? I.e., could we come up against some code that turns out to be (more) ideal? Not clear what that means. Notice that we would need to be able to interpret such a code in our own language, in order for it to be recognisable as a language in the first place.
Martin Stokhof from: Aantekeningen/Notes date: 22/07/1998
One issue that seems relevant to the question what the status of formal semantics actually is, concerns the ontological commitments of the formal theories employed. Does the “metaphysics vs. natural language metaphysics” distinction answer this question in a satisfactory manner? Only, it seems, if we are willing to shield the speakers of the language in question from its very metaphysical assumptions: the semantics of their language has certain metaphysical implications that they, as speakers of that language, need not share (or even be aware of). But this does create a tremendous distance between speakers and their language, and as such it seems to point toward a much more instrumental interpretation of the various theoretical (logical, metaphysical) concepts which are involved in the description of the language.
Martin Stokhof 
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