The Positivists were on the right track, but they seem to have insisted on 'verification', which is far stronger a test than required.

All that is necessary is enough empirical evidence to give the concepts being discussed some minimal plausibility, roughly comparable to that of the other concepts being jointly considered.

Every sphere investigating 'external reality', ie not based on axiomatic/deductive processes.

All one can aim for is to be able to assign a degree of confidence in each bit of raw empirical data, which is going to inevitably have a degree of fuzziness, and use the techniques of Bayesian Analysis to calculate rigorously the consequent likelihood of a conclusion based on those inputs. For a hypothesis which matches reality well, this will produce a high figure for 'degree of confidence', or likelihood of 'truth'.

For deductive systems, such as logic and math, the raw input assessments of confidence would be for the initial axioms or starting assumptions, and how closely they are assumed to match 'reality'. This would only apply to the assessment of the truth value of any conclusions as applied to the 'real world', domains beyond that of the deductive system itself. In an elementary example, the confidence we can have in the results of elementary arithmetic would depend on our confidence in the input figures, such as our confidence that there really are N items in that collection which we are multiplying by some other figure.

This is at least the way we should be going - rather than pursuing the futile, recursive attempt to 'prove' anything about reality, we need to tighten up the management and assessment of uncertainty.

Remember, Gödel showed that rigorously deductive systems can have well-formed statements which are inherently undecideable, so conclusions in such systems are either totally true (in the context of the axioms) or totally undecidable. IOW the confidence within such systems is either 100% or zero.

Inductive, probability-based systems allow a continuum of confidence levels.

EDIT:

So in the 'God talk' context, we apply likelihood levels, rather than saying a God statement either has meaning or is meaningless. We assess its 'meaningfulness', based on all our personal experience and judgement. and go from there.

Science, like any other coherent discipline, employs logic and math, as essential tools of analysis. But it also relies on experiment, observation and measurement, and the hypothesis, testing, and modification to iteratively converge on an (hopefully) ever-closer approximations to the 'truth'. That is most definitely NOT an axiomatic/deductive process. That extension takes it beyond the limitations of purely axiomatic/deductive processes, which is my point there.

You seem to have a blind spot on this point.

Simple - you just have to analyse it a bit more. Don't treat it as all or nothing.

'God-talk' may have some vaguely coherent elements, along with much which is pretty close to being 'meaningless'. You then need to dig into it and point out (with arguments) the bits, the aspects, which are clearly indefensible, while acknowledging the parts which have some basis, although not necessarily in the way the Theist would like to acknowledge.

I agree that induction is fundamental to Science, which is another way of saying that induction is fundamental to gaining actual knowledge... and the inductive process is NOT an axiomatic/deductive system, which was your initial assertion. Induction also employs logic, as does any serious area of investigation and argument. Science of course goes beyond pure induction in its extended process of testing and hypothesis forming.

Deductive processes cannot discover any new information not already implicit in the axioms and/or initial assumptions, whereas induction is fundamentally based on observation, which means it is continually gathering new information.

Induction is better described as a form of reasoning, rather than logic, since typical examples given as demonstrations of induction, in the same syllogistic form as basic logic, are not sound, IMHO.

For example: (from the Wikipedia article)

All observed crows are black.

Therefore:

All crows are black.

That is not how inductive reasoning works. The conclusion has to be expressed in probabilities. It would have to include, at least, an assessment of what proportion of all possible crows have been observed. The process would then involve likelihoods being assigned to various possible conclusions. In the simplest case one would assign a probability to the conclusion that 'All crows are black', which is the way science employs induction.

And yes, Science has some initial assumptions, call them axioms if you like. That assumption you referred to would be common to every area of formal and informal knowledge. It probably follows from the definition of knowledge.

Again you are not taking on board my argument that the fact that some discipline relies on some more elementary domain such as logic, does not make it a form of that domain, unless it relies exclusively on that domain. This is most definitely not the case with science. 

The fact that all philosophical discussion relies on the rules of language grammar does not make philosophy a branch of grammar.

Induction depends on basic logic AND observation AND probabaility theory.

Science depends on Induction AND math AND experimental design AND independent replication of observations and experiments AND peer review.

You could say with some validity that all those areas really depend on logic and some really fundamental assumptions. But if you are going then to conclude that Science is 'just' a form of logic, that would be like saying that Biology is 'just' a branch of Physics, since they both ultimately depend on the behavior of sub-atomic particles.

Such relationships are best described by a hierarchy of categories, recognizing that the study of complex reality is best pursued by breaking up domains of study in such a way that more fundamental domains such as Physics formulate 'laws' describing the collective behaviour of aggregations of the fundamentals that it studies.

This allows another discipline such as Chemistry to concentrate on studying the behaviour of molecules without having to take into account the properties of quarks.

I already agreed that logic is essential to Science, but surely it is also an essential component of virtually every other discipline or domain of thinking worth taking seriously.

So what is your point?

Wittgenstein was not a positivist, but he influenced them

I think you making a very 'hair-splitting' distinction.

I do see a distinction between the simplistic version of "inductive logic" as in that quoted example, and the more sophisticated version employed by Science.

As to your apparent objection to my saying that Science 'employs' logic/induction/whatever, rather than is 'based on', I think you are reading something odd into that.

I am just trying to emphasise that the essence of what makes Science what it is, is NOT logic, or even induction (certainly not the most simplistic version) - virtually all other serious discourse employs/uses/applies (pick what verb you are most comfortable with) basic Logic, and I don't think Science is the only domain which applies some form of induction.

I beleive one could do science without a lot of the things one see as necessary to science, such as peer-review, falsification, etc. IMHO the two non-negotiables are reproducibility and empirical induction. Without these two, then science is impossible. The more "sophisticated" version obviously assumes the more "simplistic" version. "Employs" seems to imply that science is somehow independent of logic, or that logic is subservient to science.

The more sophisticated version of induction does not include the simplistic version, it corrects it, by replacing true/false conclusions with probability assessments.

Logic is an essential tool of science, as is math.

On case it wasn't clear it was this response of yours

which I thought was somewhat 'hair-splitting'.

On another point, I personally feel that, in speaking of forming models of reality, which are really models of the perceived and measured behavior of 'real' entities, I am specifically avoiding making any assumptions about the ultimate nature of reality. I am avoiding making any claims that our theories accurately describe 'reality', just that the behavior and attributes they describe can be mapped quite closely to reality as perceived.

I am finding it increasingly difficult not to see your thought patterns as showing all the worst sort of outmoded misconceptions I would expect from someone immersed in the medieval (or older) thinking that goes with traditional metaphysical and other philosophical world-views. You combine an obsession with categories with a very confusing application of those categories. Sorry...

And to me, Metaphysics, Epistemology, and Ontology (I don't think you actually mentioned that one, but I always associate it with Epistemology), as formal domains of 'knowledge' and study, or however you want to characterize them in a formal sense, are utterly devoid of real insights into existence and whatever passes for reality, and worse than a waste of time to actually study. But that should be no surprise to you by now...

I specifically enclosed the word 'reality' in quotes to signal that I was not assuming any specific interpretation of the word, but maybe you don't react to that punctuation in that way.

I intentionally did not mention ontology to avoid confusion.

Also, I did not really know what you meant by the quotes.

A word such as 'God' can be meaningless in the sense that it lacks any coherent definition, while its usage reveals something about the thoughts of the user.

There is no conflict in that quote.

Neither should there be any problem in reading the second quote - we can look at both, at all aspects of a claim. Primarily of course the content of the claim, but if that is hard to verify, we can take into consideration what we know of the claimant, but of course this normal provides much weaker grounds for any level of acceptance of the claim.

You really need to be a bit more subtle in your reading of what people say if you are to have a hope of understanding the full import of the words people utter.

Surely you understand this? Are these rhetorical questions, where you are trying to make some point, or are you truly this confused on these things?

EDIT: It really does seem, based on many of your posts, that you really do "just lack the ability to understand" much of what people say? Or perhaps it is time to rethink your approach of trying to fit everything into a relatively neat category.

Of course, even though we would say it's impossible for something that's undefined to be 'thought of', christians create a powerful anthropomorphic-father god in their heads and then they believe their personal god projection exists. One of the most unusual things christians insist is that god is love. You'd have to assume they mean that god is the personification of selfless human love which dies to save children, etc. Love could arguably be seen to be our great quality despite the fact other animals will die to protect their young and must feel a hot surge of something other than anger to drive them to do it. Mother grizzlies for instance. Father wolves. It's a strange thing for the big monkey to believe, that an all-powerful universe creating deity is the personification of primate brain juice.