I made heavy mention on the Frege episode of this book by Michael Dummett.
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
false...[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?
-Mark Linsenmayer
I would argue that in many (if not most) cases the true is the normative, or what Hegel means by the spirit in human affairs.
Robert Brandom is a contemporary American analytic philosopher who synthesizes Frege with Kant and Hegel by recognizing the true in talk about human affairs, such as justice and right, as a function of the normative in our language and practices.
Brandom also has an awesome ZZ Top-like beard:
http://en.academic.ru/pictures/enwiki/82/Robert_Brandom.jpg
Here is a clip from an interview where he discusses Frege’s influence on his own “inferentialist” project:
Q: Would you call yourself a neo-Fregean? How do you see the importance of Frege in your work and what do you think it is the main difference between your philosophy and the original Fregean project?
Brandom:
The closest affinities between the view of [my book] Making It Explicit and Frege’s original project (in his Begriffsschrift, of 1879) concerns the role of logic in semantics.
Frege there defines the “conceptual content” of an expression as its role in inference.
His “concept-script” is meant to express such inferential roles, to make explicit what follows from applying a concept, what would be evidence for it, and what is incompatible with it.
He understands logical vocabulary, paradigmatically the conditional and negation, as having the function of making explicit the inferential connections in virtue of which even nonlogical expressions mean what they do.
Thus “if…then…” lets us say (put into the assertible content of a claim) what follows from a claim and what is evidence for it, and “not” lets us say what is incompatible with it.
The mathematical development of the logic Frege invented has obscured for us this original expressive function he envisaged for logic, and so, I think, much of its philosophical importance. I aim to recover this aspect of his original vision.
Frege followed Kant in emphasizing that logic (and semantics) is a normative discipline: talk about concepts is talk about how we should talk and think, not just about how we actually do.
This insight is also very important for me. But Frege seems to have had a platonistic, ontological construal of these conceptual norms, whereas I follow a pragmatist line and see them as implicit in our practice. This is probably the greatest difference between the two approaches.
Here’s a link to the full interview:
http://www.dif.unige.it/epi/hp/penco/pub/brandom_inter.pdf
Cheers,
Tom
Mark,
I would argue that the whole analytic/phenomenological divide, and scientism/humanism divide generally, hangs on this problem. Analytic philosophers still tend to be Platonists about truth-values to the degree that they have not made the Kantian and Hegelian “Copernican turn” towards understanding the self-development of reason as the normativity in our practices. That is, understanding what really gives ‘ethical substance’ to the logic of our language. This is why Brandom’s work is so interesting. He and others like John McDowell might portend a long-awaited ‘waking from dogmatic slumber’ of analytic philosophy on this problem.
Best,
Tom
Yes, I definitely share your concerns with giving ontological status to “the true”. To construe truth as an entity is a classic example of reification, no?
William James repeatedly asked his rationalist opponents a rhetorical question; what metaphysical region does your truth inhabit? He was trying to get them to see that truths are conceptual instruments and that they can only used more or less successfully for specific purposes within actual and concrete experience. Despite all the profound differences between Frege and James’s Idealist opponents, they made the same mistake, namely mistaking an abstract concept for an actual thing.
As I was listening to the show it occurred to me that Frege’s Platonism, foundationalism and scientism is exactly the sort of thing Rorty spent so much time rejecting. Some Rorty fans I know talked about the dangers of Platonism and foundationalism but I always found such a view so ridiculously over the top and absurd that I assumed they were always presenting a silly straw man in a very hyperbolic fashion. No serious person could ever believe such a thing, I thought. But now it seems that Frege is exactly that; a serious person who believes an unbelievable thing. It still seems incredible no matter how many times I hear it. One of the reasons I became interested in philosophy in the first place is that I thought it would be a place to find refuge from the kind of religious fanatics who think they know something about eternal truths and divine purposes. It’s like finding out that Newton was secretly an alchemist and thought of the laws of physics as divine and eternal. It just kills me.
I’m sure that there are many facets of this that I simply do not understand, but in my opinion Frege was a logician/mathematician first and foremost because, even though his logicist ends were in a sense philosophical (he wanted to know the nature of mathematical knowledge), his methods bear the stamp of a mathematician. I believe that he sought an analysis of language that would be conducive to his logicist program. I have always taken Frege as having an assumed ontology of natural kinds, in a way, like Aristotle’s.
Take the question: how many objects are there in the world? I believe that Frege would point out that if one wants an answer to the question in the form of a mere number (say 359,521,852), then the answer is meaningless, because there is no way of saying what the number means. But, I believe if he were asked: how many (types of objects) are there in the world, he and Aristotle would (implicitly) agree that there can be a meaningful answer. But, I disagree with that as well.
This interpretation is mainly drawn from Frege’s analysis of sense and reference. In reality, I might be being too charitable. Frege might have to answer that there is a finite number of things in the world (i.e. the first sense of the question is meaningful). He might be committed to a sort of Leibnizian metaphysic, which wouldn’t be surprising at all, considering the similarities. Granted, the whole project of “philosophy as a theory of meaning” is pushed forward only later, by the logical positivists.
Hey Mark,
Just a point of clarification. You say at the end “concepts (predicates) are not objects, and so aren’t in the ontology,” but this is not exactly correct. Frege distinguished concept and objects. Objects are regular things obviously but also abstract things like sets. Concepts (or really functions) for Frege are “unsaturated” which means that they are incomplete without an object given as argument. It’s sort of like how the phrase “is blue” is incomplete without a subject.
Now, here it starts to get a little tricky. Frege also uses the term “concept” to pick out the characteristic function of some concept. A characteristic function of some function maps objects (all the objects in the world) to TRUE or FALSE (or 1 or 0 if you like thinking about functions in binary). The characteristic function of the concept that we mean to invoke when we use a phrase like “is blue” is the function that tells you for every object in the world whether it is in the set of blue things or not in that set. Frege also used a notion called a “course of values” for a concept which is the set of ordered pairs that (if we take our example of the concept of blue) map each object in the world to True or False. This set of ordered pairs is an object and is often called the “characteristic function” of the concept blue. But we must be careful here because for Frege the “characteristic function” set or “course of values” is always distinct from the concept or function itself. (If you are interested in this, I suggest looking up “the concept of a horse is not a concept” problem for Frege’s view.)
Now that I have (probably) sufficiently confused you I can get to my point. For Frege both concepts and objects are in his ontology. Concepts don’t fall out of the ontology just because they are not objects. He does countenance them as things that exist in some sense. He thinks that they can be quantified over. We can say “there are concepts,” which is pretty much all Frege means by “exists.” The above point made by Dummett is to say that Frege might have actually denied that The True and The False have to be taken as objects. They could instead have been taken to be some other sui generis kind of thing in Frege’s ontology right along side the objects and concepts.
Hope this helps clear that up.
Kyle
Thanks!