Theories aren't Always Intellectual Constructs

  
You seem to have a problem with the word "theory" (that is, Quine's usage of that term). Perhaps if you didn't take the term so intellectually or scientifically.

 
Take a term outside Quine's usage.


Virtually all philosophers of mind use the term "folk psychology". And virtually all these philosophers deem folk psychology to be "theoretical" or a "theory". Folk psychology is a theory upheld by the folk, or the Man on the Street; though that doesn't thereby mean that every member of the folk sat in his or her armchair and devised a theory of mind or even of his own psychology.


Here's Paul M. Churchland on the matter:


"Not only is folk psychology a theory, it is so obviously a theory…The structural features of folk psychology parallel perfectly those of mathematical physics; the only difference lies in the respective domain of abstract entities they exploit - numbers in the case of physics, and propositions in the case of psychology." (From "Eliminative Materialism and the Propositional Attitudes", 1981.)


The theory philosophers call "folk psychology" is more or less inherited. Indeed Churchland thinks that the theory goes back to the ancient Greeks and hasn't really changed much since then. Though it is still, despite its long lineage, a theory. However, it's not an intellectual construct as such; at least not in terms of each individual who adheres (non-cognitively) to it. What it is, despite that, is a scheme of interrelated and mutually supportive concepts, beliefs, truths, etc.


There are numerous such schemes or theories held by many of us without much theoretical, scientific or philosophical hard work on our own part. For example, an individual could accept a huge theory (say, an ideology, religion or philosophical system) without doing much cognitive hard work. The point is, however, that he accepts the theory or is simply born into it. A theory, theoretically, could include only, say, three interlinked and mutually supportive concepts and/or beliefs, etc. And even then they may be accepted as a package-deal and not be knitted together by each individual who accepts them.


Quine's use of the term "posit" (in your example) may put people off a little. But according to Christian theory in the Middle Ages, demons, angels, etc. were posited. According to scientific theory in a previous century phlogiston was posited. According to Aristotelian metaphysics the earth as being the centre of the universe was posited. And today "super strings", numerous particles of various description etc. may simply be posits.


As Quine said in one of your quotes, we can't ever be theory-less. We move around within conceptual schemes (large systems of inter-related theories). We can't achieve a view from Nowhere. Sometimes we may think or feel that we are theory-less (at least in certain respects) simply because we were born into particular theories or conceptual schemes. They now seem almost innate. But they are contingent. (However, certain ways of seeing the world may well be a priori. Say, for example, if one accepts a Kantian position on experience.)

Raymond L. Wilder on the Foundations of Mathematics

From the outside, the early 20th century obsession with the foundations of mathematics may seem strange. It may seem even stranger if we realise what the end result of this obsession was. According to Raymond L. Wilder, the modern mathematicians with


"his most powerful symbolic tools and his powers of abstraction and generalisation have failed the mathematicians in so far as 'explaining' what mathematics is, or in providing a secure 'foundation' and absolutely rigorous methods". (197)


It's quite remarkable that Wilder claims that the modern mathematician has failed to explain what mathematics is considering the fact that even the layman would have a good go at the job.


The question is: Why can’t they explain what mathematics is?


Why is this task so difficult?


Was it Gödel’s results that stopped mathematics from ‘providing a secure foundation’ as well as ‘absolutely rigorous methods’? Is it really the case that the search for foundations, as well as for absolutely rigorous methods, is well and truly over, let alone when Wilder wrote these words in 1968?


From what Wilder says next, it seems as if mathematics not having any foundations, or not being free from all contradictions, may not be such a bad thing. More precisely, he writes that
 
"perfect rigour and absolute freedom from contradictions in mathematics are no more to be expected than are final and exact explanations of natural or social phenomena". (197)


And, of course, in science we don't have "exact explanations of natural and social phenomena" and nor are such things ‘expected’ in science. Is this really the case in mathematics as well? Surely not. Perhaps this conclusion, on Wilder’s part, is simply a result of his materialist, sociological or even Marxist position on the practice and history of mathematics. Surely even these positions accept different standards from maths – indeed, they do.


Again, it is no surprise that Wilder says what he says if he that "the only reality mathematical concepts have is as cultural elements or artefacts" (197). This position seems to go even further than constructivism; though perhaps not as far as the late Wittgenstein.


More technically, Wilder expresses his constructivist, Marxist or sociological position on mathematics by elaborating on the notion of a ‘completed infinite’ (198). This sounds like a blatant and direct contradiction. How can any infinite be complete or completed? If it is completed, then surely it's not infinite. What, exactly, does Wilder say on this issue of the completed infinite? -


"For example, an infinite decimal is not something that ‘just goes on and on without end’. It is to be conceived as a completed infinite, just as one conceived of the totality of natural numbers as a completed infinity." (198)


Wilder gives us examples of completed infinities, the infinite decimal and ‘the totality of natural numbers’; though he doesn’t say what such things actually are or what the phrase ‘completed infinite’ means. The following hints at an explanation; though it doesn't help the non-mathematicians much. He writes:


"Symbolically, it may be considered a second-order symbolism, in that it is not susceptible to complete perception, but is only conceptually perceivable." (198)


Do you have a vague idea of what Wilder means by the above? Perhaps it's a kind of ‘direct insight’ or intuition into the nature of completed infinities. It can be conceptually perceived; though not seen – literally or even non-literally.

 

Gödel's Incompleteness Theorem & Leibniz’s Dream

Albert Einstein and Kurt Godel

The mathematician and educator, Morris Kline, once made a rather grand claim about Kurt Gödel’s Incompleteness Theorems when he (in his Mathematics: The Loss of Certainty) said that it

"was a response to Leibniz’s 250-year-old dream of finding a system of logic powerful enough to calculate questions of law, politics, and ethics".

Perhaps Leibniz’s dream had nothing to do with applying logic to the content of law, politics and ethics; but only to the form of the arguments in which these things were expressed. For example, in ethics, logic can't show us “what is good”. However, it can detect good and bad arguments as to what constitutes “the Good”.

Similarly logic can show faulty reasoning in political and legal debate; regardless of the actual content of these debates.

So, in that sense, it's indeed true that logic can be applied to law, politics and ethics – indeed to anything! So just as the premises of a deductive argument needn't be true in order for the argument to be valid; so the content of political, legal and ethical statements doesn't matter to the logician - though what follows from them, logically, does matter him.

Logic can "provide the tools to resolve ethical questions by mere calculation" if it dealt only with form and not with metaphysical, epistemological and semantic content.

In any case, were Gödel’s theorems really a response to Leibniz’s dream? Perhaps it was just Gödel’s way of showing us that, well, an axiomatic system (or mathematics generally) can't be both fully consistent and complete – that’s it (without philosophical knobs on).

Much has been made of Gödel’s theorem by non-mathematicians and by many non-philosophers. Morris Kline expresses much of this here. He writes that we

"might think that Gödel’s proof implies that the rational mind is limited in its ability to understand the universe".

How a result in metamathematics could do that (even in principle), I’m not sure. In any case, the mind, again in principle, must surely be limited in some way or ways. Perhaps that means that it could never understand everything there is to know about an infinite universe. Indeed this is bound to be the case. Only an omniscient mind could know everything there is to know about the universe.

Kline makes this point. He says that

"though the mind may have its limitations, Gödel’s result doesn’t prove that these limitations exist".

What is limited isn't the mind as such; but that "axiomatic systems are limited in how well they can be used to model other types of phenomena". This has nothing to do with the mind of man taken generically! It's to do with axiomatic systems and the modelling of other types of phenomena.

Not only that: the "mind may possess far greater capacities than an axiomatic system or a Turing machine". I would say that of course the mind does actually possess far greater capacities than an axiomatic system or a Turing machine. Evidently! For a start, the mind can create great poems or pieces of music. It has memory, experience, imagination, the ability to dream, create, invent, manipulate the environment and so on. Some of these things Turing machines can do; though many of them they can’t do. And no single axiomatic system or Turning machine can do all the things a human mind can do – not even a deranged or damaged human mind!

Another common supposed result of Gödel’s theorems is to assume that his proof implies a limit to artificial intelligence. Perhaps this is a more feasible idea because it must be about the mathematical limitations of artificial intelligence – and that would be relevant to Gödel’s proof. That is, would an indefinite advance in AI be halted by the result of Gödel’s proof which showed that if a mathematical system (therefore all combined) can't be both complete and fully consistent, then a project that relies on mathematics (that is, AI) will never be both complete and fully consistent? Thus there will be a limit to what AI can do.

Russell's Principia: Paradox, Axiom Systems & Set Theory

Russell's Paradox 
Bertrand Russell’s paradox wasn't taken as some little pleasurable game or puzzle. It "forced logicians to recast set theory and logic in a different way". Why was that? Because it kept ‘creeping in’ to set theory and logic generally. Despite that, logicians wanted to "still retain the bulk of what was useful and descriptive in the original systems" (326).

It was largely as a result of Russell’s Paradox, and the desire to create a solid foundation for mathematics, that Russell himself and Whitehead wrote the Principia Mathematica. At the heart of this book we can say is

"his first full-scale attempt to describe all of mathematics as a formal axiomatic system – an organisation of mathematical ideas based on a small number of statements assumed to be true".

No doubt this too was influenced by the success and structure of Euclid’s geometrical system as well as by the work of Frege, Cantor and others.

Axiomatic Systems

At the core of an axiomatic system is a short list of simple statements called axioms. What do they do? They're combined in specifically defined ways to derive a much larger set of statements called theorems... 

No. No, what are axioms? Not what do they do.

Anyway, forget the axioms themselves, what about the axiom system or systems to which they belong? What are they? More to the point, what did Russell and Whitehead want from their axiomatic system or systems? Take these examples:

i) A system powerful enough to derive sophisticated statements about mathematics as theorems.

ii) A system that avoided all inconsistencies, such as Russell’s Paradox.

iii) A system which could show that all possible mathematical truths could be derived as theorems.

Number iii) is quite amazing. A single system from which all possible mathematical truths could be derived as theorems. Would that have really been just a single axiomatic system rather than a collection of systems?

It can now be said that "their system also eliminated paradoxes of self-reference, such as Russell’s Paradox" (326). Perhaps this isn't surprising since it was his own paradox he was trying to counteract. However, the writer goes onto say

"whether the Principia Mathematica could avoid all inconsistencies and provide a method to derive all of mathematics remained to be seen". (326)

According to Gödel, I thought that this proved to be impossible. However, the writer only talks about eliminating all ‘inconsistencies’. Perhaps that is achievable. After all, Gödel’s proof shows that we can't have both overall consistency and overall completeness. So perhaps in Russell and Whitehead’s case we do have total consistency, without completeness. Clearly Principia Mathematica didn't and couldn't deliver both consistency and completeness!

In retrospect we can now say that even

"though the axiom set of the Principia did solve the problem of Russell’s Paradox, in practice it was awkward, so it didn’t catch on with mathematicians". (327)

Set Theory

This was something that the young Quine realised in those early days. However, a different set of axioms solved the same problem. This well-known and important set of axioms is called the Zermelo-Frankel axioms (ZF axioms). It solved the problem of Russell’s Paradox and other problems of self-reference by "distinguishing sets from more loosely defined objects known as classes" (327).

How did these axioms do that?

I think that primarily it was a case of Frankel’s Foundation Axiom which showed that sets can never have other sets as members. Perhaps Russell’s Theory of Types and Tarski’s ideas about meta-languages and object-languages are also connected to the solution of Russell’s Paradox and other self-referential paradoxes. In any case, today

"the words set theory usually refers to one of several versions of set theory based in the ZF axioms". (327)

E.O. Wilson against Analytic Philosophers

Some philosophers think that some scientists have a naïve and simplistic view of reduction - and indeed of much else - in science. Especially when it comes to the complexities of causation, which they see as their own pet subject. It's not surprising, then, that E.O. Wilson gets a lot of flack from philosophers. Wilson is not, after all, a philosopher. More relevantly when it comes to reduction and causation, he's not an analytic philosopher. It's interesting, then, to see what Wilson himself thinks about these inevitable criticisms from (analytic) philosophers. 

In his book Consilience, he writes:

"'The subject I address they consider their own, to be expressed in their language, their framework of formal thought. They will draw this indictment: conflation, simplism, ontological reductionism, scientism and other sins made official by the hissing suffix. To which I plead guilty, guilty, guilty.’" 

E.O. Wilson cites all the jargon one would expect analytic philosophers to use when criticising not just scientists, but also all non-analytic philosophers. (Sometimes also when criticising other analytic philosophers.)

For example, "conflation, simplism, ontological reductionism, scientism and other sins". That is, they're accusing all of us (not just scientists) of not being analytic philosophers. Of daring not to talk about ‘conditionals’ and ‘possible worlds’. Of daring not to read at least five papers a month on causation and possible worlds. Of daring not to use "their language, their framework of formal thought" because they truly believe that there's only way of attaining the truth – their way. That there's only one way of being logical – their way. That there's only one way of being rational – their way. And that there's only one way of being philosophical – their way. Anything else is sneered at and criticised for "conflation, simplism, ontological reductionism, scientism and other sins".

The sin, for example, of not reading Synthese, Analysis or Mind. Of not using the sign for the conditional or schematising one’s writing in a pseudo-scientific manner. Of not being up to date with normativity or what Ted Sider said last week. And so on.

So no wonder Wilson "pleads guilty, guilty, guilty". He can't do anything else. No one outside the Analytic Academy can plead anything else but "guilty" to not being an analytic philosopher or writing analytic-philosophy prose.

All I can say is: What’s wrong with ‘ontological reductionism’? What’s wrong with ‘scientism’? Indeed, what’s wrong with simplicity and a bit of ‘conflation’? There may be things wrong with these things. However, in large parts of the Analytic Academy it's simply assumed that reductionism, scientism and the rest are wrong. After all, Wittgenstein and whomever told us that they're wrong.

The real reason - or one main reason - why some analytic philosophers accuse E.O. Wilson of all these things may be because they've "not kept up" with science. Wilson writes:

"It appears to me that professional philosophers have not kept up with the foundational disciplines of neuroscience, behavioural genetics, and evolutionary biology, and as a result have surrendered their franchise to the scientists. The scientists, not the philosophers, now address most effectively the great questions of existence, the mind, and the meaning of the human condition. This surrender seems to be permanent, and professional philosophers have begun a diaspora into other vital and challenging disciplines that include theoretical neuroscience, evolutionary theory, intellectual history and bioethics."

However, in many cases, especially in England rather than America, analytic philosophers were never up to date when it came to science. They probably weren’t even up to date with Newton.

For example, the "ordinary language" and "linguistic" philosophers (as well as some "analytic metaphysicians" today) championed their ignorance of science and said that no scientific findings had any effect on philosophical fundamental problems or truths. That is, philosophy is an essentially a priori discipline which can't be touched by science or its findings. Of course, the Americans and the logical positivists thought otherwise.

All of this, of course, may be a massive generalisation on Wilson’s part. Surely not all philosophers (certainly not philosophers of science) are ignorant of contemporary science. What about Dennett, Churchland, van Fraassen, Putnam, Quine, Fodor and all the rest? They're far from being ignorant of science. Many of them are (or were) mathematicians and logicians. In any case, how up-to-date is up-to-date? After all, philosophers aren't scientists: they're, well, philosophers. Of course, there will be gaps in their knowledge – sometimes large gaps. That’s why they're philosophers and not scientists. If they knew as much as scientists, then they would probably be scientists instead of philosophers.

Wilson also says that scientists

"now address most effectively the great questions of existence, the mind, and the meaning of the human condition".

The "meaning of the human condition" doesn’t sound like a fit subject for science. Perhaps my view is prejudiced or perhaps things have changed in science and its ambit has enlarged somewhat – especially in the advent of "inter-disciplinary research".

And what does Wilson mean by "the great questions of existence"? This sounds like metaphysics or even ontology – surely not a fit subject for any science. And, yes, scientists may well study the mind; though only by reducing it to the physical, or behavioural, or functional, or the computational. Then they'll be studying something that is scientifically respectable. However, will they be studying the mind or consciousness if they leave out, for instance, qualia or the first-person perspective?

Is it true that philosophers 

"have begun a diaspora into… theoretical neuroscience, evolutionary theory, intellectual history and bioethics"? 

Or is it really a case of philosophers becoming more interdisciplinary and therefore using the findings of theoretical neuroscience, evolutionary theory, etc. in their philosophy? That's not the same thing at all.

Steven Stitch and rest are still philosophers who happen to use - and indeed depend upon - the findings and sometimes the methods of science. However, they're still philosophers – interdisciplinary ones!

Philosophers have always been interested in science and indeed up-to-date. Think of Aristotle, Descartes, Leibniz, J.S. Mill, Russell, Quine, Carnap and all the rest. Indeed, science even provided the philosophers with some of their own problems, as in the case of scepticism about the external world in Descartes’ case.