Chapter 4: Truth in Virtue of Intentionality, Or, The Return of the Analytic-Synthetic Distinction
The classical Kantian distinction between analytic and synthetic judgments is clearly very important in Hanna's broadly Kantian philosophy and so-called weak transcendental idealism. Our aim here is to examine in great detail Hanna's arguments upholding the above distinction against its foes and to determine i) whether the arguments could still remain valid from the perspective of philosophical suppositions distinct from Hanna's and ii) whether additional arguments can be adduced in favor of the analytic-synthetic distinction.
First of all does the analytic-synthetic distinction make any sense to us ? And why should it matter ? Understanding Kant's precise notion of this distinction in the CPR is no easy matter. While the distinction between a priori and a posteriori knowledge is both classical and more-or-less clear, the analytic-synthetic distinction is difficult...it seems to hinge upon the question of what constitutes purely logical knowledge, purely logical propositions...which in the light of the diversity of modern systems of formal logic would appear to be no easy question. And yet this very diversity hides behind a single underlying question: what is recursivity and how does it relate to logic and to the mind ? In order for any human mind to be able to understand a recursive axiomatic-deductive system it must possess a logic $L$ of sufficient strength so as to contain a fragment $L'$ capable of representing and expressing recursion theory - furthermore for any other human mind with logic $G$ and corresponding fragment $G'$ it must be that $L'$ and $G'$ are fundamentally equivalent. The equivalence class of these fragments is what constitutes the core analytic logic which guarantees that the human mind can understand and carry out rules in a self-reflecting way (and this is an important characteristic). This has a close connection to Church's thesis. Put in another way: core analytic logic cannot have been learnt through rules and procedures because rule and procedure cognition and competence presupposes precisely such a logic. Core analytic logic - a kind of Rosetta stone - can be expressed (but not identified uniquely with) in turn in a minimal formal system, for instance monadic second order logic (and in which the first-order aspect is also monadic except for some basic binary relations). Monadic logic (and Hanna seems to want to identify its first-order variant with analytic logic) is certainly close to some of Kant's definitions of analyticity in terms of 'containment' though of course it will be very important to elucidate if such containment is intensional or extensional (or both). A passing note: this recall's Husserl's definition in the Logical Investigations.
p.147 'Kinds of truth'. Does this make sense ? How is 'truth' being used here. Sometimes 'truth' is used in the sense of a true proposition as in the beginning of Jane Austen's Pride and Prejudice: It is a truth universally acknowledged that ... So either Hanna means that there are different kinds of true propositions or different ways for a proposition to be true, that 'being true' is equivocal. This seems countersensical. Hanna then introduces 'true-in-virtue-of' (with the subsequent baffling clarification further head). So presumably true propositions are being classified by the type of inference which is used to derive them. But many problems arise. Are we talking about different deductive systems ? And yet the same body of propositions can be organized deductively in different ways, how do we know which inferential system is the 'right' one ? For instance we could divide a certain class of sentences in set-theory into those that can be proven without the axiom of choice and those that can. Or those that can be proved constructively and those that cannot. But then we see that this is not what Hanna means at all. 'Necessary truth in virtue of conceptual content'. What is 'necessary truth' ? Propositions are necessary or can even involve necessity but a necessary truth can only be about circumstances and conditions of truth not truth itself. 'Conceptual content'...so semantics enters the stage. It is no longer about inference. Tarski's definition of 'truth' has nothing to do with truth or meaning but is merely a formal translation of one formal system into another formal meta-system (some variety of set theory) wherein is set up the definition of the binary relation $\Vdash$. We take the language of set theory and add a predicate $\Vdash$ together with representations of the symbols of a given system L. Then we give a formal recursive definition of $ M \vdash [\phi]$.
In this paragraph it appears that we have 'conceptual content' and 'manifestly real world content'. These we can only take to be mind-stuff content and object-stuff content though doubtlessly for Hanna the latter is comprised chiefly of so-called natural world objects. So a proposition involves necessarily both mind-stuff and object-stuff. Analytic propositions are true in virtue of their mind-stuff component (alone) while synthetic propositions are true in virtue of their object-stuff component. Apparently such object-stuff is also in turn always found in conjunction with mind-stuff (here Kant montre ses oreilles).
Notice the circularity: to define what it means for a proposition to be 'true in virtue of' something one just introduces the condition of another proposition being true. What then is it true in virtue of the proposition that a given proposition is true in virtue of its concept content ?
Normally a recursive axiomatic deductive system $D$ allows one to define an entailment relation $ \Delta \vdash \phi$. Sentences $\phi$ such that $\vdash \phi$ (i.e. they can be entailed without antecedents) are called $D$-validities. Our first proposal would be that a $D$-validity $\phi$ is analytic in $D$ if $\phi$ can be derived using a subset of axioms and rules $D'$ of $D$ which are equivalent to a system of logic capable of expressing all recursive structures. But Hanna's notion is not this one, but is semantic - or even epistemic ! Let the natural world object-stuff be represented by a model $M$. Then given that we know that $M\Vdash \phi$ then either we know this necessarily because of inspection of $M$ or it is possible to know this by inspecting $\phi$ alone. But of course 'logical' truths can also be semantically verified in particular cases...
There is problem: what do we mean when we say that a sentence is analytic ? Are we referring to the syntactic sense-perceptible representation or representation-type or are we referring to the mind-stuff-meaning or some associated object-stuff 'proposition' ? The property of being analytic must be language-invariant. Thus we can paraphrase: the proposition which is expressed in English by sentence X is analytic. So is the 'proposition' in question mind-stuff, object-stuff or a combination of both ? When we enunciate logical truths in a semi-formal way - do we suppose a given language and interpreting community ? Are we not saying: look ! there is this system of rules and this expression can be obtained from the rules.
Notice how logical validities cannot really be expressed in the full and natural generality in first-order logic - only in particular instances (this is also the reason for axiom-schemes). For that we need second-order logic. For instance $\forall P \forall x(Px \rightarrow \exists yPy)$. A particular instance may in principle be deduced due to a property of the special $P$ at hand, rather than from 'pure logic'.
We have transcendental knowledge that a given formal system can represent the logical apparatus necessary for our computational cognition and competence and cognition in general.
But notice how Church's thesis is not clearly defined or else is circular. What is going on for instance when we prove that any partial recursive function can be represented by a TM or vice-versa ? What are we really saying ? This has to be said within the context of a formal system (presumably set theory) in which both recursive functions and TMs are formalized. Church's thesis can only be stated in set theory or a similar system...
We admit it is not easy to understand our computational a priorism. Think of the mind a proof assistant and proof checker in a Turing complete language that can also recognize other proof assistants...but this program also has a analogical, learning, exploring function...
There are no untranslatable languages (à la Davidson). For a 'language' that consists in finite expressions with a recursively checkable syntax/grammar. Because if this language cannot represent recursive functions it cannot understand its own structure and it does not deserve to be called a language and will have little interest. If it can then at least some part of it will be translatable (in principle).
We should study the relationship between recursion and arithmetic. Indeed this is an argument for logicism according to our computational a priorism. If a certain fragment of arithmetic is inextricably bound up with recursion theory and transcendental logic must express computational competence and representational capacity then it follows that a fragment of arithmetic must be part of transcendental logic itself and hence be 'analytic' . The 'analytic' appears thus to be a trinity comprising a certain minimal logic, a fragment of arithmetic and the theory of recursive functions.
While the distinction between a priori /innate knowledge and a posteriori /empirical knowledge is both clear and important and impossible to ignore - the considerations above and many many more lead to the conclusion that it is still not clear what exactly the analytic /synthetic distinction means or why it is important. 'True in virtue of meaning alone'...could this description apply to Gödel's sentence ?
After the first dense and enigmatic paragraph on p.147 Hanna shifts gear and launches into metaphilosophy and the history of philosophy. He waxes eloquent on how important and glorious the analytic-synthetic distinction is and how analytic philosophy ignored it or continues to ignore it at its own peril. Hanna says: no notion of semantic content (and hence rationality itself) without the the analytic-synthetic distinction ! Quine's Two Dogmas is quoted where Quine describes the synthetic as 'grounded in fact'. Now what about the continuum hypothesis ? This is indeed, according to Gödel, a plausible candidate for a synthetic proposition...and yet it is difficult to conceive how it could be 'grounded in fact'. Then it is recalled that in Word and Object Quine expressed exactly what we wrote in a previous post:
However there remains the problem of infinite regress: no matter how we effect an analysis in the web of ontology, epistemology and semantics this will always involve elements into which the analysis is carried out. These elements in turn fall again directly into the scope of the original ontological, epistemology and semantic problems.
Here it is a pity that Hanna does to refer to Claire Ortiz Hill's books which provide many illuminating discussions and cogent refutations of Quine's anti-intentionalist stance.
The second paragraph on p.148 is not clear at all. Granted that the analytic-synthetic distinction can be defined or explained in terms of intentionality - or more generically semantics and rationality - we do not see how this per se furnishes an argument against Quine's anti-intentionalist stance.
But the third paragraph is much clearer. Hanna says that the analytic-synthetic division mirrors an essential division in the structure of intentional acts...and it appears that for Hanna intentional acts must be comprised both of mind-stuff (the 'conceptual') and (natural) object-stuff...for otherwise how can we understand 'autonomous essentially non-conceptual content' ?
A pertinent question regarding the end of this section: why exactly is the question of there being contingent analytic or necessary a posteriori statements important ? The examples adduced of a priori knowable and yet contingent propositions (such as 'I exist') appear to be only very dubiously thus and to furthermore spring from a faulty grasp of the category of self-stuff.
4.1. Quine's strawmaning in Two Dogmas
It is very hard to grasp Kant's original meaning with regard to the analytic /synthetic division. Indeed this is born out by the meticulous analysis of the Kant's notion of analyticity in Hanna's earlier book on Kant and the origins of analytic philosophy. For Kant not all analytic propositions fit the semantic containment metaphor: some logical principles don't. In this difficult situation it is difficult to see how Quine could have 'refuted' something that cannot even be defined properly. So on p.149 we inevitably read that Quine's argument 'badly mischaracterizes Kant's theory'. Be this at it may Hanna still aims to show the unsoundness of Quine's arguments. The Forth concerns the nature of Quine's chimeric version of the the analytic-synthetic distinction. Kant's distinction was cognitive-semantic...ok. But Quine takes it to be 'epistemic-pragmatic'. We do not see the difference between 'epistemic' and 'cognitive'. And by 'pragmatic' we assume that this is related to 'use' in a Wittgensteinian sense. The way we use language in social contexts has nothing to do with Kant's original notion, that much is clear. Hanna goes on to spell out Quine's substitute distinction in detail. The question is: what is the purpose and significance of Quine's definition/distinction. Besides the analytic-synthetic distinction which Hanna is concerned with, we should ask does Quine's distinction even makes sense ? Is it exhaustive ? It is a valid characterization of the innate a priori vs. empirical a posteriori ? Consider Quine's vocabulary used in his version of 'a priori / analytic': 'experience', 'experiential evidence and inquiry' . Lets take the words according to the ordinary English usage. For us an analytic proposition (which is also a priori) pertains to a core fragment of formal logic, arithmetic and recursion theory. But epistemically, in order for us to arrive at knowledge of many important truths in this domain, we must resort to inquiry, to experimentation with various formal systems, to trial and error, to correction, verification, exploration... there is nothing 'triffling' (Locke) or armchairish about any of this. Mathematical knowledge, the finding of mathematical proof is all about experimentation - and there is a notion of mathematical experience. Also finding a proof becomes evidence for a proposition. And logical truths still demand - epistemically, and Quine is big on this - proof (see Gödel's Is mathematics the syntax of language ?). Basically in his definition i) Quine is giving a faulty characterization of logic and mathematics just as in ii) he gives a faulty Popperian or neopositivist characterization of natural science. Scientific beliefs or propositions are 'revisable' but not in the simplistic way described in ii). Also there are beliefs which are not recalcitrant to experience which yet cannot count as a priori - Popper's non-falsifiable theories, pseudoscience, etc. We will return to this when Hanna does.
p.150 states that the Quinean version of the analytic-synthetic distinction is the standard one in analytic philosophy. Furthermore Hanna informs us that most contemporary analytic philosophers do not think that the analytic-synthetic distinction is that important and also mentions a 'disconnect' from the a priori /a posteriori distinction. In the Fifth point Hanna turns to the metaphilosophy of analytic philosophy and makes a strong and valid point about the logical-epistemic-semantic presuppositions of analytic philosophy itself (which it cannot reject without being self-defeating). We have made a very similar point in our previous posts. Indeed analytic philosophy offers arguments hence it must assume a recursive axiomatic-deductive system (maybe not the same one for each argument or theory). And in each such system we must have axioms and or presuppositions and - if we are not in the presence of purely non-philosophical game - these must given some kind of epistemic justification and some kind of meaning.
p.151 it is stated again that the analytic-synthetic distinction is in reality tremendously important and cannot be discarded without the very notions of cognition, semantics, intentionality, etc, going down as well. We are told to await a transcendental argument for this distinction based on the idea of semantic content. We fail to see the point of Hanna's more formal definition of transcendental argument. Indeed we offered a transcendental argument for the a priority of a computationally competent and expressive logic - but this does not assume any version of transcendental idealism.
p.152 Now the transcendental argument from semantic content:
(1) & (2) We agree that the notion of truth cannot be eliminated and is semantic (otherwise we end up like in Lewis Carroll's paradox). Also with Claire Ortiz Hill that intensionality cannot be eliminated and that it implies meaning and reference. And of course logical consequence cannot be eliminated but why it is semantic should have been explained...we should should show this for our theory of the analytic. Thus semantic content cannot be eliminated. It is interesting to read A. Wierzbicka's Semantic Primes and Universals (1996) where the author argues against those linguists who would study language while discarding the very concept of meaning !
(3) Very interesting but too laconic. Also very Husserlian. For us this is the intimate relation between mind-stuff and object-stuff (and the self-stuff is also involved but we cannot go into this). Actual or possible extension: this is nice and recalls our deployment of sheaf semantics for dealing with modal logic or our treatment of Aristotle's modal syllogism published in the HPL.
(4) This is the heart of the argument. Our rationality, like a powerful formal system, can self-reflect and represent within itself the metatheory and semantics of itself or other systems. Most importantly there are metapropositions involving semantic and logical notions which unlike other non-logical propositions must hold necessarily.
(5) But these can only be analytic a priori proposition whose truth is evident upon inspection of the concepts involved. For instance in Peano arithmetic if we have truth predicate than it must hold that if $\vdash \phi$ then $\vdash T([\phi])$ or if we have a provability predicate than if $\vdash prov([\phi])$ then $\vdash \phi$.
This argument is quite interesting and suggests that we should expand our computational notion of analyticity to include self-evident metatheoretic truths.
No comments:
Post a Comment