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These are fairly straight forward question to which I have found no answers. Years ago, when I was taking a seminar on Quine, the professor explained Quine's philosophy of science. According to Quine, if I remember correctly, science driven by the principle of having theories with the greatest simplicity possible that cover the highest scope. An example that one of my professor always gave: We could take any outdated scientific theory, say Aristotle's physics for example, and make it work if we add a considerably large number of ad-hoc hypothesis, but the quantity of ad-hoc hypothesis that we may need to add in order to save a scientific theory may increase its complexity to the point that it may be better for it to be replaced altogether.

I believe two conclusions follow from this:

(1) There are no crucial experiments. An experiment never is enough to falsify a theory. This is known as the Duhem-Quine thesis, and it holds that we could change a theory while keeping its "core elements" to adapt it to the results of the experiment that otherwise would falsify the theory.

My professor back then always used the word "core". Scientific theories have a "core" and "exterior" elements, and the theory can be kept keeping its "core" while changing "exterior" elements. The problem is that he could not give a satisfactory answer to what exactly are core and exterior elements in a theory, instead he said I should ask to some professors in philosophy of science, which I did, and I receive no answer since non of them agreed with the Duhem-Quine thesis.

(2) Quine also develops a sort of hierarchy that goes beyond the scientific theory. According to Quine we have "Elements in the world", inside the former we have scientific theories, inside the latter there are mathematical rules, and inside again there are logical rules. This means that changing logical rules would imply changing mathematics and science. In order to create the less possible chaos in the order of things, scientific progress change this from above. Changing the elements in the world seems to have the following meaning: if our scientific theory doesn't apply for some objects in the world we may change the objects in order to keep the scientific theory, for example, if a theory X holds that some elements E should behave in a certain way, but this is shown to be false, elements E', E'', etc. can be constructed of the objects that formerly where known as E, in such way that one of the E's will take the place of the former E. I understand this as a change in the classification of elements required by a theory under new phenomena. It looks like Quine holds a nominalism, but according to Quine it is not a nominalism. How can his thought in this matter be understood if not as a nominalism?

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    Don't know about the second point. The "core" vs "exterior" dichotomy and the part of increasing add-hoc hypotheses eventually leading to the theory being replaced sounds more like Imre Lakatos' views than Quine. – Alexander S King May 2 '17 at 18:09
  • Hi. I did not understand how the second point is supposed to be related to nominalism. – Ram Tobolski May 2 '17 at 20:38
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Both of these questions have to do with Quine's idea that the structure of scientific knowledge is a “web of belief.” The web metaphor suggests that beliefs are connected to one another. The connections can be understood as resulting from how the definition of any term (whether a scientific term or not) can only be given in terms of other terms. So, the web is partly about the connections among beliefs by virtue of the meanings of sentences being connected, in so far as sentences are built from words, and words get their meanings only by relationship to other words and sentences. The connections among beliefs in a web of belief are also justificatory, given how we build beliefs on top of other beliefs.

The semantic (which is to say, related to meaning) and justificatory connections among our beliefs produce a hierarchy, where some sentences are more fundamental than others, in so far as others are based on them. Quine would have us think about these more fundamental beliefs as being at the core of our web of belief. Beliefs about logic and mathematics, for instance, are beliefs one which nearly all other justified beliefs are ultimately based. Laws of nature depend on those more fundamental beliefs, but are only slightly less fundamental. Then, as we build out from this core to the periphery of the web of belief, we find at its edges sentences which depend on many others, but on which few or no other beliefs depend. On the very edge of the web might be beliefs about ordinary observations, like that a donut costs $1.79 at the store nearest me.

This exposes another kind of relationship among the sentences in the web, which might be its most interesting feature. Given the falsification of one of our beliefs, we have options about what to reject. We can reject only the most superficial edge beliefs, or we can reject more fundamental beliefs. We have a general psychological preference for making the most superficial revisions possible to our web of belief, but this is not justified by logic so much as preference. The implication of that is that even mathematical beliefs could in principle be revised in the face of a rejection of a belief about something observable (which is to say that the traditional analytic/synthetic distinction is blurred). If I am told that donuts at the store cost $1.99, my disposition is to give up the belief that I read the sign correctly. I could, however, give up beliefs about the definition of donuts, or the laws of nature, or addition.

I hope this explanation of the relationship between the core and exterior of the web of belief answers most of your questions except the last one about nominalism. One way this is all connected to nominalism is that (against nominalism) Quine believes that there are natural kinds. However, his idea of what a natural kind is is quite weak. Any set of things that share any natural property at all form a natural kind. Given belief in the web of belief, one can make sense of why we might very easily revise what kinds of things (or as you say, elements) we believe exist by adjusting how we lump things together. Ordinarily this sort of acceptance of casually lumping things together into sets might be a sign of being nominalist rather than realist about kinds. But given Quine's weak definition of "kind" it is not, for him.

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