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.
4.2 A brief history of the synthetic-analytic distinction
Hanna shifts back into his metaphilosophical, history of philosophy mode.
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Hume's fork
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Hanna seems to suggest implicitly that Quine's straw-man two-pronged version of the synthetic-analytic distinction (from now on A-S distinction) is actually Hume's and most certainly not Kant's three-pronged one. Hanna review briefly some well-known facts about the history of analytic philosophy (from Bolzano to Quine) together with the puzzling situation of Quine's version becoming sociologically dominant. He then mentions the very dubious claims of Kripke and Putnam about necessary a posteriori and contingent a priori statments. For instance 'Water is H2O'. In order for this sentence to be 'necessary' we will have assume that there is a meaning or reference for 'water' in different possible worlds. A scientist could conceive of different possible universes (perhaps different evolutionary courses since the Big Bang) but in all these different worlds he would use H2O precisely to fix the reference of the term 'water'. For instance he could say: water may not have come to be in the universe. Hence referring to 'Water is H2O' as necessary is either meaningless or not a posteriori. Indeed it is posteriori that the sound or linguistic expression 'water' happens to used by a certain community to denote water, but obviously not necessary. The Gold example is similar and so is, although this may not appear obvious, the Cicero is Tully example. Because 'water' is actually very much like a proper name in that it is subject-dependent and dynamically growing and revisable. The alleged contingent a priori are even more dubious and we will return to them later. The mention of Direct Reference Semantics does not go into any kind of detail and we have discussed the 'I am, I exist' in a previous post and argued that it is not contingent.
p.157 The second paragraph is very important for undertanding Hanna's views. If Hanna is a common sense realist he also strongly criticizes the pre-Kantian naivety of analytic metaphysics (Lewis, Chalmers, Williamson, etc.) ! But upon what grounds exactly ? Because of the acceptance of the noumenon, because of the avoidance of the problem of the A-S distinction. Hanna suggests that important work on the A-S distinction has for some reason been systematically ignored, for instance Gillian Russell's Truth in Virtue of Meaning (2008)
.4.3 Why the A-S distinction matters. Finally !
First. We do not agree. The concepts of a priori, a posteriori, necessary and contingent if difficult are patently clearer than analytic vs. synthetic. Recall that to us the analytic must be understood in terms of a certain invariant trinitarian mutually reflective core subset of logic, arithmetic and recursion theory.
In the Second to Sixth reason Hanna puts forward his thesis that the A-S distinction is the key to logic, semantics and theory of knowledge - in particular those core aspects which are presupposed by analytic philosophy itself if it wants to carry out 'conceptual analysis' at all....we await the proof further ahead.
We not not agree with the expression postmodernist anti-rational nihilist skepticism at least for the normal meaning of the word skepticism which presupposes rationality or at least willingness to engage in the rules and social framework of rationality. The skeptic may be personally anti-rational but he has to engage in rationality, act rationally and agree to 'play the game'. Also postmodernism is seeped in dogmatism and not skepticism because it does not produce much of what could even be termed an 'argument'. In the second paragraph of p.159 Hanna basically says as much. We would add than a human being can indeed be irrational and verbally promote irrationalism/nihilism/postmodernism but we have no reason to attach any value or significance to what such an irrational individual says or writes. If we you do not believe you it is possible to prove anything that you cannot claim to be proving something, etc.
On the rest of p.159 we are heralded with the thesis that they are two kinds of necessity, one of a 'logical' or 'conceptual-semantic-intensional' kind, another of a more ontological, metaphysical kind. A very interesting thesis.
4.4. Critique of Quine.
p.160 We are boggled by the first sentence which seems to jumble together all classical notions in the philosophy of language...but then it is rectified and we are introduced to Hanna's terminology: sentences are the formal-syntactic stuff, statements are object-stuff entities, propositions in the Bolzano-Fregean sense but not quite. Statements are propositions with potentially but not necessarily a truth-claim.
But were is the mind-stuff, the subjective psychological component (entangled with intentionality) here ?
p.161 Argument 1.1. This is a complete fallacy. There are meaningful statements in number theory which cannot be derived from the restricted logic which both Hanna and Quine would associate with being analytic (for instance Gödel's sentence in Peano arithmetic) and also which cannot be empirically verified (just as 'there is an infinite number of primes' cannot be verified). Hence the premise is false and the argument does not conclude. Likewise 1.2 fails because of the false premise. Mathematics is a priori knowledge which is not analytic (in the current sense) and yet does not presuppose transcendental idealism. This appears to be Hanna's answer (3) (see further ahead).
Hanna's answer (1) is just the classical response that the verification principle is neither analytic nor empirically verifiable. (2) is interesting in itself. The common core of all forms of 'transcendental idealism' presuppose some kind of conformity or correspondence between the 'world' and something 'innate' or 'in us' - put this is very vague and ambiguous. The fact that we can write down a differential equation corresponding to a certain controlled physical experiment, go to the blackboard (or computer) and do some computations and then come back and check that the experiment has evolved to exactly the same result predicted by our a priori logical computations - surely this is a striking form of (Wignerian) conformity...
Hanna here explains his contrast between the 'strong' and 'weak' versions of transcendental idealism. Let us look at the definition of the 'strong' version. (i) does not seem to be a good description of Kant's critical philosophy; noumena cannot be said to 'cause' perceptions, for the category of causality only applies to (and is meaningful with regards to) concretely given empirical intuitions. (ii) is certainly a mouthful. But it appears to hinge crucially on Hanna's rather Heideggerian-sounding notion of 'manifestly real world' . The highest categories are: self-stuff, mind-stuff and object-stuff as well as their mutual relations. Maybe we are to understand (ii) as Berkeleyian idealism: object-stuff is nothing more than mind-stuff organized or elaborated by self-stuff ? But (ii) leaves open the possibility that there may be secondary empirical aspects of the object which cannot be found a priori. As for (iii), does this mean: without self-stuff there would be no mind-stuff and no object-stuff ? But what if we locate the most important object-stuff in self-stuff itself ? But if '5 is a prime number' is object-stuff, a Bolzano-Fregean proposition-in-itself and it can be known to us (some combination of self-stuff and mind-stuff...) then there must be some kind of conformity involved. Unless Hanna gives us a better definition of 'manifestly real world' then it is difficult not to consider iii) as mistaken if this 'manifestly real world' is not to be taken as a timeless mathematical object (à la Tegmark) - because any concept of 'now' or dynamism as well as qualia presuppose consciousness and a conscious reference point - we are in danger of this manifestly real world fading into a noumenon. A Parmenidean thought: can even existence or being be conceived apart from consciousness ?
Now for weak trascendental idealism. (i) methodological eliminativism or agnosticism regarding noumena. An a priori 'knowably unknowable' is certainly a bold claim which demands careful analysis - but it is also an interesting twist to Kant's theory. (ii) the conformity thesis: to understand this better we must explore what is meant by 'type-identical'.
(iii) appears circular. How could 'rational minded animal' be called rational if it did not cognize veridically ? And of course (iii) presupposes a theory of truth. (iv) is quite dubious as we saw above.
But the general point of argument (2) is valid: transcendental idealism is a tricky concept and we cannot rule out (at least without careful investigation lacking in Quine) different variants which do not fit the description of the 'strong' version. Conformity, correspondence, isomorphism between subject and object - remains indeed a key aspect of all these variants.
(3) This was the argument we put forward when discussing (1). However we do not know at present the precise bounds, the precise strength of the 'logic of the analytic'. So given a mathematical statement it is still not clear whether it is included in the logical validities of a strong analytic logic or else should be considered synthetic. For instance Fernando Ferreira (Zizgzag and Fregean arithmetic) uses a fragment of second-order logic and modified version of Frege's law V to obtain an adequate theory of finite sets.
The paragraph beginning 'Now, it is true...' contains a very interesting remark about Gödel's own interpretation of his famous result (and a reference to Tiezen, one of the rare philosophers who actually attempted to continue Gödel's philosophical program, as far as it could be reconstructed from the documents available at the time). Let us recall the first incompleteness theorem (for simplicity we do not go into the details about $\omega$-consistency). The standard account is as follows: we are given the recursive-axiomatic system $PA$ whose axioms are held to be self-evident, intuitively certain. Then it is shown that there is a sentence $G$ such that neither $G$ nor $\sim G$ are theorems of $PA$. And yet if we inspect the meaning of $G$ then $G$ is self-evidently true. $G$ is an internal reflection or representation in $PA$ of a meta-theoretic truth concerning $PA$ which $PA$ cannot proof-theoretically grasp or determine (to us this whole situation is an example of a more general, purely formal scheme which we will not go into here). All this seems indeed to be in the spirit of Hanna's previous transcendental argument for the a priori analytic from semantic content or intentionality. Yet Hanna put forward the case that the fluid boundaries of the analytic are expanded or contracted as convenient in order to swallow up candidates for the synthetic a priori.
Before moving on the next argument of Quine let us mention a problem that can be raised concerning our discussion of analyticity above. How are we to understand the notion of the same objective structure (for instance set of propositions) being formalized or captured (to a certain extent) by diverse formal systems ? What are logical truths or arithmetic truths considered in themselves, just out there independently of our formal approach ? It seems arguable that there must be a formal structure which is the right one in some sense. That is for any set of formal systems T1,...,Tn (or infinite set) which represent the objective structure there must be some formal relationship between the Ti and certain formal system S. A universal object or classifying object in the mathematical sense. This recalls somewhat Hanna's conformity thesis.
p.164 The conventionalist theory of necessarily true by convention seem to us to be meaningless. For if we say 'sentence' then we have already fixed some language L of which the sentence is a sentence of. And given a language L and a sentence S we can always device a recursive axiomatic-deductive system in which S is theorem, for instance by making S an axiom. The 'come what may' part does not make much sense. It may be that there are some aspects of all possible words which are fixed and invariant and yet we ourselves (note the word 'assert'.. asserted by who ?) would not have the confidence to state the corresponding propositions 'come what may'.
The citation from p.104 of Quine's Truth by convention is just a weaker version of the argument we gave previously. The human mind must be Turing complete before-hand in order to deal in recursive-axiomatic deductive systems. Therefore it is absurd to postulate that logic is epistemically-cognitively derived from any particular recursive-axiomatic system. We postulate that analyticity is intimately bound up with this a priori computational competence and expressivity - but also with self-evident metatheoretic/semantic truths as well argued by Hanna.
However Quine's logocentric predicament is fallacious nonsense. It amounts to saying that nothing can be wet without water. Therefore the wetness of water is inexplicable. Logic cannot be justified or explained....but what do you mean by 'justified' or 'explained' ? Explanation involves inference and hence logic. But one particular system of logic may indeed interpret and show the soundness of another. Justification on the other hand can involve besides inference direct intuition and evidence and it is not clear from the start if many logical truths are not capable of such direct intuitive justification.
The conventionalist theory is plainly wrong and we do not consider Quine's arguments against it particularly illuminating. Nor do we see the point of Hanna introducing them in his discussion except to point out some glaring contradictions in Quine's views. It appears that what Hanna calls Quine's Universal Revisability Principle was itself revised ! But we would put things as follows: the statement that the Halting problem is unsolvable is not revisable (exercise: why not ?). But in order to state it we must assume a core axiomatic-deductive system which can be interpreted as encoding both some non-trivial fragment of a logic and a fragment of arithmetic. If these were revisable than the Halting problem would either be unstatable or revisable. Hence core logical, arithmetic and recursion-theoretic truths are unrevisable - all of which goes way beyond the principle of non-contradiction discussed by Hanna. p.166 We must wait for chapter 5 for a fuller discussion of the justification of logic.
3. Quine's circularity-of-synonymy argument. p.167 Let us consider Quine's conception of his two classes of analytic statements. Quine's description of the first class is interesting. We have in the past put forward the question: what is the most general concept of axiomatic-deductive system we can have ? We then proceeded to sketch an answer and to define the very concept of 'logical constant' (Quine: logical particle) in terms of a more general notion. But what is the context of Quine's definition (which seems inspired by the most basic semantics of classical propositional calculus) ? It seem that is must involve the syntax of some formal language in which the demarcation between logical and non-logical symbols has already been made. But what would be, for instance, the status of parentheses ? It is odd to consider them 'logical' and yet they cannot be reinterpreted. Class 2 suggests to us the problem: can we speak of definitions in a formal language without having introduced an axiomatic-deductive system ? Note how the standard semantics of classical propositional calculus only works directly with atomic statements. Defining interpretations/semantics for formal systems with new symbols introduces via definitions is not so simple. Indeed it would seem that some axiom or deductive rule involve substitution and logical-semantic equivalence is already called for. This is clearly part of Quine's synonymity circularity argument for class 2 which we will return to further ahead. p. 167-168 Hanna points out that the first class is indeed unchallenged and itself an intelligible distinction between analytical true statements and other truths. He then touches on the question of which logic is the correct logic for analytic truth and brings up the monadicity thesis which we have already discussed and which Hanna will return to in section 5.2. He points out that Quine's case-by-case argument involving synonymity has not been shown to be exhaustive. On pp.169-170 Hanna just points out that Quine accepts 'holistic' explanations that go beyond mere 'reductionist' ones so he must be willing to accept holistic explanations of analyticity or the A-S distinction. But nothing in Two Dogmas can be construed as an argument against the possibility of such holistic explanations.
4. Quine's argument from confirmation holism and universal revisability. Quine conflates the A-S distinction with verificationist reductionism - that truth are either 'analytic', unrevisable or reducible to logical operations on predicates related to 'observations'. But from the presuppositions of Quine's (i)confirmation holism, (ii) semantic holism and revisability principle (iii) we conclude that verificationist reductionism is false. Hence the A-S distinction is meaningless.
The first question is of course whether all of (i),(ii) and (iii) are essential to Quine's argument. Is it sufficient to show that one of these presuppositions fails ? The revisability principle (iii) appears to be the weakest link in the chain. Hanna points out, as it obvious that (iii) is self-defeating, as is the verification principle. We can also point out that revisability itself presupposes core conceptual apparatus pertaining to recursivity (i.e. the ability to manipulate recursive axiomatic-deductive systems) which mirrors a corresponding core unrevisable portion of arithmetic and logic. We can question what it means for 'there are infinitely many prime numbers' to be revisable - without the concept of 'number' changing being replaced a concept which has nothing to do with our current concept of number. But this is not 'revision' in any cogent sense. Also (iii) contradicts Quine's own Sheer Logic principle. Another obvious point is, as we have seen before, the verification principle cannot be identified with the A-S distinction as attested by multiple different theories of the latter which deny the verification principle, for example Hanna's own theory that will be expounded later or the sketch of our own proposal of the 'core analytic' computational a priori supported by meaningful mathematical statements (such as the continuum hypothesis) which cannot be considered analytic and also which are not capable of reduction to any empirical observation. In (3) Hanna states that a fusion of C.I: Lewis' and Dewey's pragmatism (LD) would entail (i) and (iii). We do not see the point of this remark as it makes Hanna's argument more convoluted and less clear. Let us try to clarify it a little. Hanna's argument seems to be the following:
LD + (i) => (iii) Hanna does not really explain why we should accept this premise
(iii) + (i) => Revisability of the law of non-contradiction. Supposedly this means that even if we take (i) in a sense which preserves the sheer logic principle the violation of this principle will be forced by (iii) according to the citation of Quine on pp.171-172.
Revisability of the law of non-contradiction + sheer logic principle => Quine's predicament. Hence we have grounds to reject not only (i) and (iii) but the apparently stronger LD as well. Against Hanna does not explain at this point why LD is introduced.
The concept of 'reevaluation' is interesting and it should be clarified and rendered more precise by formalization. It is not clear whether 'reevaluation' in the case of mathematics works in the same way as in the case of natural science. In mathematics we fail to see the 'holism' that Quine rather vaguely describes. The most obvious example of this process in when given a system of axioms $T$ we find that: (i) the system is inconsistent or (ii) it is incomplete, in particular some important sentence for the theory cannot be derived. What then is revised or extended is $T$. However in a paper on the ancient theory of definition we haved explore an interpretation of holism in mathematics.
5. The flight from the circle of intensionality/intentionality. p.172 we should note that for Aristotle meaning was not conflated with 'essence' and also that the intension /extension distinction was clearly present. For instance for Aristotle 'having the ability to laugh' had a meaning, was coextensional with 'man' but did not express the 'essence' of the term 'man'. So Quine's historical remark is not only argumentatively redundant but not even accurate. We refer the reader to the books of Claire Ortiz Hill for a masterful and detailed refutation of Quine's eliminationist approach to intentionality and intensionality (as stated in the citation from Word and Object in p. 173). Indeed this citation is important because there Quine unambiguously states his faith in physicalist, reductionist and behaviorist dogma.
p.173 Hanna notes that Quine's definition of logical truth in Truth by Convention (discussed above) is itself intensional. Logical constants have an 'essential occurrence' in true statements.... Quine held that Aristotelian essences and metaphysical necessity were unintelligbile and indefensible. p.174. the discussion here seems rather pointless and misguided. We fail to see the historical importance of Kripke or Fine in terms of defending Aristotelian essences, metaphysical necessity or intentions per se (except for sociologically in the history of analytic philosophy). Since Hanna does not offer any further elucidations we shall skip this and pass on to Hanna's point (3). It is observed that Quine's argument depends on physicalist dogma and furthermore that the rejection of intensions does not even follow necessarily from such a dogma: a fallacious inference from a pragmatic ought to a factual is. Our position (which we have argued for elsewhere) is that the whole concept of 'natural' in Quine's notion of natural science is vague and ill-defined and as such physicalism as a position is meaningless, incoherent - if not plainly question-begging (i.e, by assuming from the start that intensions are beyond the scope of science). In (4) Hanna claims that eliminativism regarding semantic content entails the elimination of reason itself and uses the expression already criticized and discussed above: 'postmodernist anti-rational nihilist skepticism'. We would say rather that the concept of eliminativism itself presupposes a host of logical, semantic, epistemic and metaphysical notions. In other words it is saying both: (i) rainbows do not exist and (ii) rainbows can be explained by metereological processes.
6. Argument from the indeterminacy of translation. On p.176-177 Hanna observes that Quine held that the alleged indeterminacy of meaning does not apply to logical constants and hence to the truths of classical sentential logic. But this entails that there is a meaningful concept of analytic (type (i) discussed above) and hence a distinction between analytic of the first type and other sentences. Hanna gives on p.175 a long citation from Word and Object intended as a reply to Carnap's behaviorist account of synonymity. Then he gives a rational reconstruction of the argument (for the indeterminacy of translation and hence indeterminacy of meaning) on p.176 which appears to us to be lacking in clarity and to be couched in the most naive and crude empiricist and behaviorist terms (and why do why are we assuming that intensions and the same as meanings: 1 + 1 = 2 means something but who would speak of the intension 1 +1 = 2 ?). This argument seems to be a muddled exposition of the general philosophical problem of translation. Is translation of an unknown language possible and if so how ? In particular how can we translate a language of a people by merely observing them from without ? But this brings in another question: semantic completeness. A natural language L or a fragment thereof is semantically complete if any meaning M expressed in another natural language L' can be expressed in terms of L or that fragment. A semantic universal is a meaning which is expressed precisely in any natural language. Now the argument mentions linguistic anthropologists and their talk of stimuli and rabbit parts...very 'scientific' and 'empirical'. And yet if we wish to go that way Anna Wierzbicka's Semantic Primes and Universals building on the work of other anthropologists and linguists presents us with abundant highly convincing empirical and scientific evidence for the existence of semantic universals which furthermore determine a semantically complete subset of all known natural languages. So to assess the meaning of 'gavagai' we should avoid crude reductionist behaviorism in terms of stimuli but rather let the natives tell us their story of 'gavagai' couched in terms of semantic primes...and recall Wierzbicka's important distinction between folk concepts and scientific concepts.
p.177 Now we come to the question of the relation between the three 'categories' analyticity, apriority and necessity (which are respectively logical-semantic, epistemic and metaphysical). For our conception of analyticity it is clear that is must be contained in apriority. Analytic statements correspond to logical truths in a logic strong enough to express any recursive predicate. In other words, core analyticity corresponds to the logic required for the human mind to be Turing complete. Thus core analyticity truths cannot be derived from experience and from application of rules because some equivalent logic is presupposed in the ability to learn from experience and apply rules. But far be from us to suggest that analyticity 'exhausts' the apriority. But Quine's third category of 'firm truths', necessity, is another matter. Necessity seems to us to be the least clear of the triad. Indeed does it even make sense to pose the question if a analytic or a priori known statement is necessary or not ? Should not necessary statements be about the world ? Anyhow the objective of section 4.5 is clear: tackling the famous arguments of Kripke, Putnam and Kaplan for the detachment of analyticity, apriority and necessity. This would entail the rejection of the A-S distinction. After making an important historical observation that Kripke himself did not consider his arguments as undermining the A-S distinction and that Putnam held the existence of at least one a priori necessary truth, Hanna states that he will deal with the popular conception that such authors as well as Donellan really did undermine the A-S distinction. So Hanna is going to deal with arguments for:
i) the necessary a priori
ii) the contingent a priori
iii) the analytic contingent
p.178 But first Hanna gives a rather brief overview of the latest views upholding the A-S distinction which detach the three categories (i.e. they need not even be strictly contained in each other), for instance Katz and Gillian Russell. Hanna then puts forward conditions which he holds that the classical concept of analyticity must embody. To us at least the idea of an analytic truth not being a priori is sheer nonsense (as discussed above). So we are in full agreement with Hanna with regards to condition ii).
Boghossian's theory of the A-S distinction rejects the listed conditions but from a framework that rejects a semantic conception (i.e. truth in virtue of meaning) and takes instead a Quinean epistemic-pragmatic view of analyticity. p.179 But this has already been discussed above and Hanna's arguments, the thought screen helmet and the revisability of 7 + 5 = 12 though sound are far from exhausting the failures, defects and absurdities of the Quinean account. For instance the statement 'there are infinitely many prime numbers' cannot be confirmed or denied by 'experiment' (in the crude sense) - is not synthetic a posteriori - and yet is not an 'armchair belief' but requires inquiry and mathematical experience. Hence Quine's fork is untenable.
p.180 The meaning of the first paragraph is not clear at all. Does Hanna consider that his arguments on p.179 apply to Boghossian's position or not ? Hanna qualifies this position as 'deft' and 'subtly detailed' and yet does not really answer this question. What precisely does he mean by internal vs. external objections ? To us an internal objection would be one which accepts some or all of the premises of the argument. Could there be 'deft' and 'subtly' detailed arguments for the existence of the Easter Bunny ?
Hanna then says that Williamson's view that the A-S distinction is uninteresting can be indeed derived from the acceptance of the Frege-Carnap conception of analyticity and the detachment arguments of Kripke, Putnam, etc mentioned above. Hanna intends to refute both the Frege-Carnap concept and these detachment arguments (as indicated previously). But then he suddenly jumps to the Harman-Juhl-Loomis conception of analyticity based on stipulation. Hanna calls his arguments 'worries'. As for 'individually or intersubjectively agreed-upon rule for the use of terms X' this presupposes the core analytic computationally adequate logic discussed above. For otherwise how can one understand and follow a rule in general, i.e. how can the subject be Turing complete ? In particular it presupposes that we a concept and criteria for the truth of statements of the form: result or process X follows from the application of set of rules Y. Thus truth cannot itself be defined in terms of following rules for the follow a rule we need the concept of truth, for instance in order for the following or not following of the rule to be intelligible. p.180 we agree that Hanna that a following the rule definition of truth will involve a truth about us (i.e. did individual X follow rule Y correctly with regards to Z) and will not be an adequate conception of truth for inference or states of affairs of the world. As Hanna rightly observes, nonsense can be stipulated and socially accepted. Socially accepted nonsense can have and follow elaborate rules. What is missing here is for Hanna to introduce the definition of 'stipulation' at hand, the usual English definition is:a rule that must be followed or something that must be done. Now this is irreducibly intentional as Hanna observes in his Second 'worry' in the second paragraph. Since the third 'worry' does not introduce anything new let us skip to the last paragraph in which Hanna comes against the classical Socratic dilemma (lucidly recognized by Kant): we can know something and yet not be able to define it. Hence there is always the danger that our proposed definitions are not really defining what they claim to define. Such is the case of analyticity: one may be defining an entirely different notion, 'schmanalyticity'. Hanna defends that any legitimate account of analyticity must satisfy his condition (i) to (v). They basically say that analyticity must be a priori, necessary, logical, conceptual/semantic, be presupposed by rational activity and give an account of logical truth itself. This is another reason to reject both Boghossian's and Juhl-Loomis' accounts. Hanna's key point is that the classical notion of analyticity is a condition for the very notion of semantic content and hence for human rationality in general. On p.183 Hanna finally gets down to business and tackles the existence of the necessary a posteriori, the Kripke-Putnam argument 7. This argument has in its essence already been criticized above in its form of the example 'water is H2O' where we argued that this sentence is either trivially true or meaningless - certainly not necessary a posteriori. To speak of 'water' across possible worlds we are implicitly fixing its definition as H2O, while any meaningful interpretation of the statement must shift to sociologically contingent facts. The argument based on standard modal logic given in the citation of Kripke's Naming and Necessity is obviously wrong because the substitutivity of identity cannot function based on referential identity but only on intensional identity (the old puzzles of Frege and Russell). But proper names or mass nouns are inherently intensional, besides being dynamic, revisable and subject-dependent. Now for Hanna's reply. His argumentation against 7 occupies pages 184 - 191.
p. 184 Kant's statement: Although all our cognition commences with experience, yet it does not on that account all arise from experience. (CPR B1)
The following paragraph is very hard to follow. We do not see how 'inner or outer sensory experiences' can be called empirical facts. In fact, we are not even sure what an empirical fact is (guess: a state-of-affairs known through sense-perception). Again Hanna's speaking of sense perception being 'causally triggered' does not seem to be very Kantian, as causality is a pure concept of the understanding that our cognitive apparatus imposes on experience - yet this is not an objection in itself to Hanna's avowedly merely 'broadly' Kantian position, a position espousing a kind of common sense realism. Supposedly by 'inner sensory experience' Hanna means for instance memory or imagination. The second sentence ends with: (...) non-inferential sense perception of empirical. There is clearly a typo here or a missing noun. And yet Kant's statement seems to simply convey that: cognition always has two components, one being experiential and one being non-experiential. Thus experience alone is not enough to determine a cognition and hence not enough to determine the truth, semantic content and justifiability of a cognition. Hanna expresses this by saying: cognition is not strongly supervenient on empirical facts. We confess we cannot make heads or tails out of the next paragraph until the sentence beginning: 'Otherwise put'. We find Hanna use of the term 'empirical fact' confusing and can only wonder at this stage why Kant much more appropriate term 'intuition' has been eschewed. It would have been better to put this as follows. According to Kant all cognition has both an intuitive and a non-intuitive component. And the intuitive component can either be pure or empirical. We now consider the three fallacies. Here the big traditional problems come in, namely, Kant's (dynamic) intuititionism or constructivism. We fail to see how the statement 'there are infinitely many primes' has any essential relation to 'intuition' in the Kantian (and Hannanian) sense: spatio-temporal imagination or Hanna's 'empirical facts'. In fact it seems patent to us the whole discussion ahead would gain in precision and clarity from a perusal of Husserl's Logical Investigations. p.185 Hanna introduces categorematic terms, by definition those that have both 'intension or meaning' and 'extension or reference'. We fail to see how 'If Kant is a bachelor, then Kant is unmarried' and 'Seven beer bottles plus five beer bottles equals twelve beer bottles' need to be confirmed by sense experience of empirical facts. We grant that the terms 'Kant', 'bachelor', 'unmmaried' and 'beer bottle' bear an essential direct or indirect semantic/conceptual relation to intuition /sense experience, but we fail to see how the sentences considered by Hanna must be confirmed in any empirical way, although of course they may be confirmed. Does he mean that they have to be empirically confirmed or that it is possible to empirically confirm them ? But what about: 'seven parallel universes plus five parallel universes equals twelve parallel universes' ? Supposing that the laws of physics absolutely ruled out any observation of parallel universes, I think most people would still hold that this sentence is both meaningful and true, albeit impossible to confirm empirically.
We will not go into the complex problems - already discussed - concerning the statements 'water is H2O' and 'gold is the element with atomic number 79'. These have the template, in Wierzbicka terminology: 'folk concept = scientific concept'. These sentences are probably very polysemic and dependent on context for their precise meaning. One way to understand 'water' in some of these contexts is to hold it to mean a set of macroscopic phenomenological properties of matter (but which will require specification of conditions in a way which must, perhaps, lapse from the folk conception to the scientific conception...). Also the very term 'H2O' presupposes we a certain context of a relevant scientific framework of interlocked observations and concepts. With a sufficiently advanced scientific theory and computational instruments it is not all inconceivable what all the homely macroscopic phenomenological properties of 'water' could not be mathematically, a priori, deduced from the fact that the substance in question has chemical formula 'H2O'. However the above sort of definition of 'water' is dubious in that it abstracts from the mental qualia and folk-connotation involved in the folk-concept of water.
p.186 Let's look at Hanna's three step verification for the a priori. (1) is not clear: 'retain' when or where ? - does Hanna mean across possible worlds ? 'Necessary-or-constitutive-determination-based of content...'. Now that is a mouthful. Does Hanna mean the intension/Fregean Sinn of the categorematic terms in question ? Or some other kind of extrinsic definition and identity condition for referents ? This all greatly lacks clarity. But looking at (2) and (3) it is patent that Hanna is considering possible worlds in which the intension of the terms remains the same but the referent may change drastically. The a priority condition could be read: a sentence A is a priori if it remains true across all possible worlds in virtue of the intension/meanings of the terms alone.
Our position (which is related to our radical non-physicalism/naturalism) is that when considering collections of 'possible worlds' we must have some kind of topological notion of deformation or some kind of metric which measures how far one world differs from another, or at least a distinction between essential and non-essential modification of the actual world. Without going into the problems of the meaning and reference of proper names - many of which we hold can be easily solved by ditching extensionalism, something long overdue - we concede that it makes sense to speak of Kant in neighbouring possible worlds to our actual world, non-essential modifications of our actual world (only in this neighbourhood is 'Kant' a rigid designator in some suitable sense). But it is difficult (as we have already discussed above for 'water') how we could connect this to a possible universe (assume that such is possible) in which mankind was not present. We will not go into this now. Folk concepts and possible words don't mix well !
It seems much more care is needed in the whole affair of 'possible worlds'. These need to be organized in categories based on continuous deformations. 'Kant' and 'beer' remain meaningful terms in their own category of possible worlds. Thus we could re-frame Hanna's a priori condition: a sentence A is a priori if it remains true across all possible worlds varying in the respective categories of the categorematic terms of A in virtue of the intension/meanings of the terms alone.
Definitions/conditions of truth of the form 'sentence A is true if condition C holds' are really just saying that 'A is true if B is true' . They are circular. The same goes for definitions/conditions of truth relativized to individuals and groups considered in the third paragraph about the voluntaristic a priori. 'sentence A is true for group G if condition C holds'. Even the concept of 'stipulation' presupposes the concept of truth. If this is a correct description of the doctrine of the logical empiricists, C.I. Lewis and Quine then indeed there is no difference from post-modernism and the whole analytic/continental divide myth is a hoax.
p.187 We have very serious problems with Hanna's treatment of the sentences 'Kant is a philosopher' (KP) and 'All philosophers are mortal' (PM). Hanna goes quite beyond deformations of the current world (in the sense above of neighbouring possible worlds) in which 'Kant', 'philosopher' or 'mortal' have their context and make sense. Worlds in which Kant was not born or did not become a philosopher: these are at least plausible. Worlds in which philosophers live for ever ? Definitely not ! This would be a contradiction in terms, it would not be a world; there is no such world in which the terms 'philosopher' and 'live' could possible make sense as it would not be a human world or a deformation of it at all. The terms in question would be category mistakes like 'green prime number'. The concept of 'mortal' is contained in the concept of 'man' which is contained in the concept of 'philosopher'. But besides this the idea that you can define an individual like Kant is far from clear (for the radical non-physicalist at least). It could even be argued more strongly that the any concept of 'Kant' which does not include 'philosopher' cannot have any relationship with our current concept of Kant. Again the revisability and dynamic relative nature of proper names.
But things get worse in the last paragraph. The term 'water' changing its empiric specific character in a possible world ? This is either trivial (in we mean the underlying graphical or phonetic stuff) or absurd. The whole concept of rigid designator beyond the neighbouring possible worlds is patently absurd. So too is the idea of a world in which H2O felt like sand. Sure, we could imagine universes (viewed strictly from the point of view physics) with different physical constants or different fundamental laws and different cosmological processes - but they would all be varying within a definite category. We would have to fix before-hand what we would consider to be Hydrogen and Oxygen across all these alternative universes.
So 'water is H2O' is either (i) trivial (because we need H2O to fix the meaning of 'water' across possible worlds) (ii) possibly a priori in some scientific theory and in any cases possibly necessary (iii) a category mistake mixing a folk-concept with a scientific concept (this might be rectified by adding 'the chemical composition of ...').
The error behind all these surrealistic possible worlds theories seems to be the notion from the Tractatus that reality can be totally described by a set of mutually independent contingent propositions and that any combination of their truth-values can be considered a possible world or state-of-affairs.
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Gulliver's travels to possible worlds
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However the concept of 'necessity' remains extremely obscure. So too the nature of scientific propositions. It would seem that 'necessarily true' only means something in the context of a collection of states-of-affairs (or experimental situations) $C$ (as is standard in the semantics of modal logic). Thus we should speak of 'necessary in $C$'. The problem is given such a collection $C$ we may conceive that $C$ is embedded in a larger collection $\mathcal{C}$ consisting of $C,C_1,C_2,...,C_n,...$. And thus what is necessary in $C$ may be only contingent or possible in $\mathcal{C}$. This process may be repeated. When we speak of something being necessary in science it is generally assumed that this is relative to the actual universe, that it is merely describing a law (universal) which applies to this universe. But we can conceive of other possible universes in which the laws of physics are different (supposing that this could be mathematically established). What does it means to speak of the laws of physics as being necessary without further specification ? We note that of course this kind of modal thought has been and continues to be important in theoretical physics.
Also, note the difficulty in understanding the meaning and reference of the term 'water'. Even if this is a mass noun it shares many difficulties with proper names. These difficulties are enhanced when we look at things from the scientific point of view. There seems to be no way to unequivocally define any specific spatio-temporal region or individual. Whatever is contained in the concept we have of a person, we do not see how this content could be (or ever be) sufficient to determine its reference once we take a large enough context. For instance, how would we describe the location of our solar system to aliens millions of light-years away ? It would seem that reference depends not only on meaning/intension but on a reference point (which itself must remain indefinable).
For a certain - plausible - interpretation of 'water is H2O' it may be that the sentence is a priori or it may be that it is not, depending on the thoroughness of underlying formal-mathematical theory needed to give 'H2O' meaning and context. That is, from the chemical composition H2O and the associated physical theory (let us say, quantum chemistry) it may be possible to formally, logically, mathematically deduce the macroscopic, phenomenological properties which we take to be (part of) the definition of 'water'. However we think that the fundamental biological role of water cannot be left out. If you cannot drink it, it is not water, no matter the other macroscopic phenomenological properties.
p.188 offers an argument that empirical facts can only provide the knowledge of 'water is H2O' but never the knowledge that this sentence is a necessary truth. For Hanna it is both analytic (Kripke is said to have pointed out that it at least required a priori knowledge) and while having an essential empirical content. We cannot accept footnote 94 because it assumes without any justification that 'gold' could maintain its meaning across possible worlds and yet in some world have a different atomic number (being 'schmold'). This is nonsense in we wish to preserve any trace of logic, mathematical truth and template of physical law across possible worlds (and we must always restrict ourselves to a category of possible worlds in the sense above). How does Hanna accept this ? Hanna's argument is that in the schmold world 'gold' has no referent and therefore 'gold is the element with atomic number 79' cannot be false ! Hanna appears to consider GOLD which maintains its identity across worlds, gold2 which is actual-world stuff called 'gold' in the actual world but is replaced by schmold in other worlds, and gold3 which expresses the chemical composition of GOLD or rather of the particular embodiment as gold2, schmold, etc. in a world. He reads 'gold is the element with atomic number 97' as 'gold2 is the element with atomic number 97' and states it to be true across worlds.
One cannot treat the world as a jumble of independent contingent facts rather than a articulate organic finely articulated logical whole. 'Schmold' makes about as much sense as considering a possible world in which for arithmetic 1 + 1 = 3. Thus we cannot accept Hanna's argument above as we cannot accept the concept of schmold except in a sense so artificial (bundle of macroscopic phenomenological properties) which betrays completely the folk-concept-essence of gold.
pp.189 - 191 are dedicated to the well-known puzzles of 'Cicero is Tully' and 'Hesperus is Phosphorus'. Again we recommend the books of Claire Ortiz Hill for a deep yet concise and lucid exposition of this subject. Hanna's audaciously naive (he himself writes 'This may seem a shocking claim') interpretation is that these sentences are a priori and necessary and illustrate the rule $x = x$ from which we can derive, in standard first-order logic, $\square x = x$; and Leibniz's law holds....for all non-modal, non-normative, and more generally non-intensional property (!).
How view is that we are in the presence of a epistemically dynamic revisable proper-name-referenced concept. When we learn these we always have an initial 'tag'. For most people in this case it is 'Cicero' but there is no reason why it could not have been 'Tully'. Under the tag of 'Cicero' we adquire more and more information, including Cicero's tria nomina. We interpret 'Cicero is Tully' as : our concept tagged by 'Cicero' includes the information that the man in question was also known by or named 'Tully' (which was in fact his Roman 'nomen'). This could also work for those whose concept started with the tag 'Tully'.
We hold that 'Hesperus is Phosphorus' (HP) has an entirely different epistemic-semantic-logical type and structure from 'Cicero is Tully'. The meaning of many sentences involves is an non-eliminable way meta-concepts, that is, its meaning can include non-eliminable components which contain the concepts of meaning and reference themselves. In other words: non-eliminable meta-semantic semantics*. Thus (HP) in itself, in its very meaning, is saying that (i) the reference of the terms 'Hesperus' and 'Phosphorus' are the same and (ii) that the intensions of these two terms are different (iii) and that this situation is now part of the concept of 'Hesperus'.
*we have made a similar proposal about the meaning of logical connectives. They are inherently meta-logical because they translate into propositions about truth-values of propositions.
But let us examine on p.190 Hanna's argument that HP is both informative and a priori. Hanna observes that being informative does not mean being a posteriori. For example, if we found a proof of the Goldbach conjecture. We would put it this way: perfect knowledge of the rules of Chess does not imply a perfect knowledge and understanding of all games, tactics, strategies, Chess-puzzles. Many of these can be informative even if they also can be deduced /verified a priori from the rules.
The second paragraph observes that even in the framework in which a necessary a posteriori might be shown to exist we can devise necessary a priori sentences. Hence the existence of such does not entail the destruction of the A-S distinction.
Then Hanna returns yet again to our old friend 'water is H2O' and considers the Kripke-Putnam argument for its necessary a posteriori status. He proposes that this arguments depends on the previous acceptance of scientific essentialism, the doctrine that there exists necessary a posteriori truths about theoretical identitites based on the material constitution of natural kinds. In our view this doctrine is trivial or at most uninteresting because necessary must be read as necessary-in-$C$, and the a posteriority is basically a measure of the incompleteness and insufficiency of the theory. Then on p.191 he considers Putnam's criticism of scientific essentialism which, by the considerations we have put forth above (more than one), cannot be accepted, because of the way 'water' is assumed to have meaning across possible worlds in which causal laws are different. But perhaps Putnam is thinking of a deformation of the actual world in which the basic theory required for the expression H2O still makes sense and yet which some fundamental macroscopic phenomenological properties of H2O no longer hold. But then depending on how we read 'water' the statement becomes quite possibly a priori (depending on the sophistication of the theory) or else completely false (the folk concept 'water' is meaningless in that world) - or true depending on how propositions with non-referencing terms are treated.
Let us move on to p.191 The Kripke-Putnam argument based on the existence of the contingent a priori. We have said enough about the type of sentences exemplified by WL, CA and WM and the problems of the arguments related to them presented on the last paragraph of p.191. So we will only discuss (SM). Suppose on uses a stick S as the standard meter bar. Then 'S is 1 meter at time $t_0$' is claimed to be both a priori and contingent, because the stick 'could have been longer or shorter than a meter at $t_0$'. Now the problem here is that any region of space and time, hence every specific individual in the world (such as the stick S) cannot be given an absolute determinative description (we discussed this in the example of how we could not give the coordinates of our solar system).
Thus the notion of 'meter' is bound up with indefinable spatio-temporal location or identity. Thus 'meter' is still a folk-concept, dynamic, revisable, relative, referentially incomplete... Thus, rigorously speaking, all our physical units are anthropocentric. Why should Mary's concept of 'myself' in itself contain the information sufficient to point out Mary as a space-time individual in all the vastness of the universe ? Such notions are like functions which may take arguments but which in themselves do not contain information or specification of any particular arguments. Thus 'meter' is like a function which takes as argument the true absolute specification of Paris (unknown to us) and gives as result the stick S. As such we agree with Hanna that SM is in nowise contingent. Let us now analyse Hanna's argument on pp. 192-194.
Again Hanna introduced in a rather wordy way, the distinction between between a mere linguistic expression and a proposition. This seems rather pointless (except to justify that there can be more than one reading of SM) as it has been expounded before. Also we do not understand how Hanna justifies that any linguistic expression has at least two meanings or interpretations. If this were so we would have to fix the two possible meanings of an expression by means of two further expressions. But then each of these would likewise in turn have two possible meanings which we would have to fix in turn through two more expressions. Thus we could potentially be lead to an infinite regress and total ambiguity of a given expression.
Hanna then argues that SM has a purely analytic a priori reading of the form 'the current president is the president' or more generally of the logical truth $F(\iota x.F(x))$ and that the contingent reading based on rigid designators it not tenable. It seems to us that 'stick S' and 'meter' are indeed like proper names in that they are inherently relative and point to what is to us indefinable space-time regions (the actual stick and its length across reasonable deformations of the actual world). And yet the relationship between 'stick S' and 'meter' remains invariant (whenever they make sense) - for this follows from the intentional structure involved, the invariant intensional relation between the stick S and the term 'meter' across possible worlds for which they make sense. This is very different from the interpretation: 'Zaphod is 1 meter long' so in this we are totally in agreement with Hanna's argument.
(9) pp. 195-198. Here Hanna considers the logic of indexicals. Kaplan claimed that 'I am here now' and 'I am, I exist' are both a priori and contingent. But, counters Hanna (in agreement with Kripke), this is an a priori statement based on indexical reference not on meaning and hence not a priori. Indeed these sentences can be given two divergent interpretations, one a priori and necessary, another contingent and a posteriori. For our own part, we think that the this is only the tip of the iceberg of the vast undiscovered realm of the meaning of the term 'I'. A phenomenological introspective analysis reveals that Hanna is indeed correct, in the most usual sense of 'I am here now' the term 'I' has far greater semantic richness than a mere 'indexical' pointing at its reference, in fact, it has a host of meta-semantic components which completely justify Hanna's definitely non-contingent reading. Being here is part of the meaning of 'I' in this sentence, for how could I use this term 'I' without being here ? Indeed the indexicals 'here' and 'now' would seem to involve and depend in an essential way on the 'I', on mind-stuff, on self-stuff, on consciousness.
After these critical preliminaries the rest of chapter 4 is dedicated to the expounding of the 'The Content-and-Rationality Theory of the Analytic Distinction and Modal Dualism' which we will conveniently abbreviate to CRTASDaMD. p.198 section 4.6, Back to Kant ! All Over Again is a small preface to the lengthy section 4.7. Now some remarks on what Hanna holds to be the five goals of Kant's original A-S distinction theory.
First goal: Kant wanted to use his A-S distinction to justify that there are two kinds of mental content: concepts and intuitions. But 'concepts' and 'intuitions' are both likewise transcendental concepts not actual mental contents all of which - to Kant - involve both in an inseparable way. Thus speaking of 'mental content' is a little bit misleading - and more so to speak of 'intensional content'. Thus the term 'autonomous essentially non-conceptual contents' appears to be un-Kantian.
Second goal: the text reads : ' where a "possible world" is just a complete consistent set of different conceivable ways the actual world could have been'. This does not make much sense. Perhaps we should read "possible worlds" in lieu of "possible world", that is, Hanna is defining a possible world as a conceivable way in which the actual world could have been. This is not much of a definition for it is replacing the modal notion 'possible' with the notion of 'could have been'. Indeed the whole affair appears dubiously circular. Our approach however makes use of a set of reasonable 'worlds' and a 'deformation' relation between them and so does not appeal directly, at least, to any modal notion.
Third goal: Kant wanted to explain the difference between two kinds of necessity, (i) those of logic and conceptual analysis and (ii) those of mathematics, science and metaphysics.
But who can tell where logic ends and mathematics begins...this itself in an extremely important question which has not been settled. As seen above with reject Hanna's characterization of the logic of the analytic as monadic first-order logic and instead argue that such a logic must be at least as strong as monadic second-order logic so as to be computationally complete. Even in the realm of variants of second-order logic substantial portions of mathematics can be captured. This state of affairs suggests that this 'modal dualism' is not as clearly defined as Hanna would have it. p.199 Indeed the idea that mathematics flows from 'immanent structures of things in the manifestly real world' and 'represented by formal autonomous essentially non-conceptual contents' appears to be quite questionable. It would be interesting to examine this problem in the light the work of Jules Vuillemin on 'Kant's intuitionism'. In Schopenhauer's radical modification of Kant's theory, the entire causal-spatio-temporal world (conceived as representation) is generated without any aid of, or necessary connection to, concepts. And yet by some remarkable power of the mind, concepts can be drawn out of this intuitive world, as if they were Aristotelically immanent, part of its "structure" in Hanna's own term.
p.199 4.7 The huge section expounding CRTASDaMD. p.200 Hanna's goal it argue for point (1) that CRTASDaMD provides an adequate explanation of the A-S distinction which supports Kant's Pitchfork and Modal Dualism. The latter are stated to have been already argued for by Hanna in previous books. What he wants to do here is to is to show that CRTASDaMD confirms and vindicates them, in the spirit of a sound inference to the best philosophical explanation - or as a transcendental explanation. If this is not viciously circular it is viciously unclear. Let us go through the 8 steps of CRTASDaMD.
Steps 1 and 2 involve chapter 2 of the book and will be analyzed in a separate post. Step is Kantian non-conceptualism. pp.201-202 offers a long-winded definition which involves a large dosage of common-sense realism. Apparently the aim is to characterize a certain content X of perception termed 'essentially non-conceptual'. Not surprisingly such a content X has to be 'not a conceptual content' of a 'minded animal subject' causally related to some material being B in its environment, etc. And yet by (iii) B can be the 'minded animal subject' itself ! So apparently material being B is to be taken as being having a material component.
We wonder how Hanna would classify the statement 'material beings exist outside the mind'. Does he take his common sense realism of the 'manifestly real world' as an ontological and epistemic given ? Anyhow the articulation of 2 looks suspiciously like the introduction of naturalistic, anthropological elements into logic...something that goes far beyond evidence. Also there seems to be some vicious circularity involved in the appeal to 'minded' subjects, i.e. rational subjects. Isn't the whole point to explicate rationality ? Again it would be far better to engage with the meticulous and detailed analysis of concepts, intensions, meanings, expressions, intuitions, etc. found in Husserl's Logical Investigations which may well hold to key to a rigorous and satisfactory version of the A-S distinction. See also the work of Rosado Haddock. Here is Husserl's definition of analyticity which should be considered in the light of the work of Lotze and Bolzano:
Analytic laws are unconditionally general laws (and, thus, free from any explicit or implicit postulation of individual existence), which contain no other concepts except formal [ones], [and] thus, when we go back to the primitives, nothing other than formal properties. In comparison with the analytic laws, there are their particularizations, which originate by means of the introduction of material concepts, and eventually of thoughts postulating individual existence…. As in general, particularizations of laws produce necessities, so particularizations of analytic laws [produce] analytic necessities. What one calls ''analytic propositions'' are usually analytic necessities. [Logische Untersuchungen II, U. III, § 12]
Analytically necessary propositions, so we can define them, are such propositions, which are completely independent from the material peculiarity of their objectualities (determined or conceived in undetermined generality) and from the eventual factuality of the case, from the validity of the eventual postulation of existence; thus, propositions, that allow being completely formalised and [being] considered as special cases or empirical applications of the formal or analytic laws validly obtained by means of such a formulation. In an analytic proposition it must be possible to replace any material content with the void form something, while completely preserving the logical form of the proposition, and eliminate each postulation of existence by means of passing to the corresponding form of judgement of ''unconditional generality'' or lawfulness. [Logische Untersuchungen II, U. III, § 12]
See the discussion in chapter 12 of Rosado Haddock's Against the Current (Ontos Verlag, 2012). Mathematical statements are allegedly analytic according to Husserl's definition whilst, according to Rosado Haddock 'all bachelors are unmarried' is not. We do not agree. The definition of 'bachelor' is a man who is not and has never been married. Thus this sentence is saying that \[ \forall (a: man)(\forall( w: woman)(t \leq t_0: time) \neg married(a,w,t) \rightarrow \neg \exists (w:woman) married(a, w, t_0)) \] This is a purely formal, logical truth. Also, as we discussed above, consideration of this sentence across possible worlds is either trivial or nonsense or illogical. We will discuss the other objection about metalogical truths on another occasion. Husserls analytic laws recall polymorphic/dependent type theory, in particular types of the form $\forall (A,B:Type) A \vee B \leftrightarrow B \vee A$. While regional ontologies suggest continuous variation, homotopies, within specific types conceived as spaces.
We speculate that the analytic/synthetic division is related to the fundamental division between (i)logic, abstract algebra, discrete mathematics, recursion theory and (ii) geometry, topology, analysis and differential equations. One difference its that (ii) involves greater cardinalities, has a relationship to intuition in particular that of continuity, has different styles of proofs and conceptual architecture, is more directly related to applied science. And yet both (i) and (ii) share the same 'necessity' and potential a priority. The very notion of causality seems intimately connected to that of continuity and differentiability and hence non-enumerable cardinalities. Differential equations offer an example of a space of possibilities, phase space, a set of 'possible worlds' which is based on topological concepts and actually makes sense. The same goes for the calculus of variations - and it is perhaps no coincidence that this was the subject of Husserl's PhD thesis. What is most interesting is modern mathematics apparent realization of Kant's concept of schematism through the various functors between (i) and (ii), for instance the geometric realization functor (or taking the spectrum) and the extraction of algebraic invariants from spaces. How does our previous computationalist concept of analyticity relate to this division ?
The synthetic a priori is the realm of continuous, smooth, analytic and allied categories, fundamental to all natural science. It is the realm of 'abstract' objects - but nevertheless having a profound component of intuition (sp. continuity) - immanent in 'concrete' objects, limning their structure. The analytic a priori is the realm of 'concepts' in the Fregean sense, the realm of logic, computer science, linguistics. These are closer to consciousness, to the mind, yet we could also class them as a kind of 'abstract' object, pace Frege. It is the realm of the mental, the living experience in cognition, the mysterious unconquerable realm of schematism mediating between the last two realms, perhaps even 'constituting' objects or being 'filled' by objects, which eludes both logic and mathematics, and gives rise to confusion, a quagmire of linguistic equivocation. Of course we can posit intensions as abstract objects in their own right, but these are not concrete lived mental intentions. To make progress in philosophy, and to understand the varied realms of objects, their cognition, and the mystery of the mental, we must approach the realm of the self. It is worth considering and exploring if a suitable flexible and high-level formal framework might be valuable in this project, without, of course, turning the realm of self naively into a domain of objects or ordinary concepts. We must consider the possibility that the realm of self determines, constitutes or is somehow involved with all these different realms of objects, or offers unique knowledge and insight into their nature, constitution, relationship, origin, ultimate meaning, validity, etc.
Addendum 15th October: what does it mean for a formal system to express or represent a total computable function ? Must examine Gödel's philosophy of analyticity, reducible proofs and system $T$.
