I want to try to give a couple of textual references over a few posts here to elaborate points from Dummett I was trying to make during the discussion. For instance, one of the pieces we picked on Frege about was his designation of "the True" and "the False" as objects in his ontology, which was done to make sense of the idea that concepts are functions: e.g. "is green" is a function that maps green objects to "the true." Here are some bits from pages 183-185:
It is generally agreed that, if Frege had to ascribe reference to sentences at all, then truth-values were by far the best thing he could have selected as their referents: at least, he did not go down the dreary path which leads to presenting facts, propositions, states of affairs or similar entities as the referents of sentences...
...It is assumed that, once Frege took the step of holding sentences to have a reference, he was doomed to conclude that truth-values are objects, and that a sentence is just a kind of complicated name for such an object... But there is absolutely no necessity about it at all: on the contrary, it would have been in line with everything that Frege had said to date if he had held that sentences were of a different logical type from names, and that therefore truth-values were no more objects than concepts are.
The identification of truth-values as the referents of sentences, taken
together with the thesis that truth-values are objects, led to a great simplification in Frege's ontology, at the price of a highly implausible analysis of language. Sentences being only a special case of complex proper names, and truth-values only a special case of objects, it follows that predicates and relational expressions are only a special case of functional expressions... and concepts and relations only a special case of functions... The doctrine that every function must be defined for every object (to avoid the occurrence of proper names without a reference) now yields the result that, not only must a sense always be provided for inserting any name wherever some name
may meaningfully go, but for inserting a sentence in any such place as well.
It now becomes a requirement upon a properly constructed language, not merely that if, for example, it contains both numerals and the predicate '5 is green', a sense must be provided for '5 is green', but also that a sense must be provided for '(5=2+4) is green' as well. It is tragic that a thinker who achieved the first really penetrating analysis of the structure of our language should have found himself driven into such absurdities...
...Frege's earlier departures from the forms of natural language... were founded upon deep insights into the workings of language; whereas this ludicrous deviation is prompted by no necessity, but is a gratuitous blunder...
The new development had one thing to recommend it: namely, if the notion of incompleteness seems more intuitively comprehensible, when applied to functions, than it does when applied to concepts and relations, then a doctrine that enabled one to view a concept or a relation as a special kind of function at least made the notion of incompleteness, as applied to them, more comprehensible. Under the new doctrine, what it means to say that an object falls under a concept (that an object has a certain property) is just that that concept maps the object on to the value true rather than the value
[However], in the case of functions, the metaphor could be pressed, to give a sense for the 'completion' of a function by an argument to yield a value of that function, in the case of concepts and relations there seems no place for thus extending the metaphor, no meaning to the idea of 'completing' a concept or relation. But, even here, there was no necessity to insist that truth-values actually were objects, concepts actually were functions. All that was necessary was to admit the existence of an analogy: if a need was felt for a notion of 'completing' a concept, then the upshot would be a truth-value, as, by completing a function, we obtain an object. Too great a price can be paid for making a metaphor palatable.
Another ontological point made in passing in his second paragraph above: "...truth-values were no more objects than concepts are." This I think was hard to grasp in our discussion: concepts (predicates) are not objects, and so aren't in the ontology, which is just a list of what exists according to the philosophy (as opposed to what can be in some sense analyzed away into components that are part of the ontology, or what is just fictitious).
I'm interested to hear if our listeners had any take on our various ontological complaints in the discussion. Can a philosopher of language get away with ignoring ontology in the way Frege (and other folks we referred to) seems to?