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Popper believed that scientific knowledge is obtained through conjectures and refutations; the refutation of Newton's theory by Einstein is an example. He also believed that in this way science becomes gradually closer to the truth. But it is not clear to me how he maintained this view within the conjecture-refutation framework.

To understand the role of truth in Popper's philosophy of science I wonder: What would become of it if the notion of approaching the truth was given up? Would it make his philosophy pragmatist (or instrumentalist)? Many times they seem similar to me in various respects, except of course for the idea of truth or of getting closer to the truth.

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    Popper redefined what "getting closer to the truth" means by introducing in Conjectures and Refutations a formal notion of verisimilitude ("truthlikeness") in terms of "truth content", see SEP. Roughly, a theory is "more truthlike" if it entails more true sentences. "The account has a couple of disastrous consequences... a falsehood is never more worthwhile than a worthless logical truth... no false theory is closer to the truth than any other". There were many attempts at a more palatable measure of verisimilitude after Popper. – Conifold Nov 21 '17 at 1:00
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    "giving up the notion of truth?" I do not think so: the "method" of Conjectures and Refutations is aimed at rejecting theories that do not "fit" with facts. These theories are empirically confunted, i.e. false. And it is hard to understand the notion of false withiut that of true. – Mauro ALLEGRANZA Nov 21 '17 at 12:47
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    @MauroALLEGRANZA, thank you. Sorry, I must have not expressed myself clearly enough, for related or meant to relate to giving up on the idea of getting closer to the truth. Falsifying theories of course requires truth values (i.e. {true,false}). The question then is what happens if avoiding postulating as did Popper that our theories getting closer to the Truth via conjectures-refutations. I think I try to find out what is the main difference between Popper and Pragmatists (or instrumentalists). – L.M. Student Nov 21 '17 at 19:44
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    @Conifold, thank you. I am aware of his somewhat vague attempts to ground his fallibilism within a realism framework. I think I try to understand what is the core of the difference between Popper and his Pragmatists and Instrumentalists rivals, for many times they seem similar to me in various respects except of course for the idea of truth or of getting closer to truth. And I wondered if without this idea Popper would have had a kind pragmatist philosophy. – L.M. Student Nov 21 '17 at 20:32
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One can be a pragmatist (albeit, perhaps, not an instrumentalist) even without giving up the idea of approaching the truth. Popper was not the first philosopher who tried to reconcile radical fallibilism with a form of realism. Many ideas of scientific methodology associated with him, including the "hypothetico-deductive method" and falsification, were developed decades earlier by the founder of pragmatism, Peirce, see SEP on Peirce's logic of science. Quine also advocated a form of fallible realism, albeit less robust than Peirce's, or even Popper's. Quine is sometimes called a "logical pragmatist", but this is using "pragmatism" broadly. Like Popper, he was more influenced by positivists than by classical pragmatists (Peirce, James and Dewey), but he was more of a pragmatist than Popper, who remained much closer to positivist optimism about the reach of formalization and the theory/observation distinction. It is unclear how much Popper, positivists or even Quine were familiar with Peirce's works, their publication stretched over decades after his death.

A common theme to such reconciliations is that reality is posited as hypothetical with its features determined through some form of inference to the best explanation. Roughly, positing the ontology of our best scientific theories as real/existing best explains their empirical success (Peirce adds that Humean empiricist view of laws of nature defeats science as an explanatory enterprise, an ethical point touching on intellectual values). What is also common to Peirce and Popper (but not Quine) are the partitioning of reality into different kinds of existence, and the idea of convergence of scientific knowledge to "the truth". Peirce had an ontology of acting laws and relations, both inside and outside the "subject", underlying the derivative objects, both concrete and abstract, existent and real-possible, and Popper had his three worlds. According to Germino:

"“World 1” represents physical objects and states; it is the “total world of the materialists.” “World 2” consists of states of consciousness and subjective knowledge. “World 3” represents the “whole world of culture,” or knowledge in the “objective sense”... Popper calls the third world the realm of “epistemology without a knowing subject. Not surprisingly, Popper attempts to positivitize, as it were, the contents of his third world, calling it the realm of “objective knowledge.”"

The thorniest issue, that both Peirce and Popper struggled with, was to reconcile the historical and cultural dependence of fallible knowledge with postulated mind independence of the "objective" reality that it is supposed to "approximate". And here their paths diverge.

Their ontologies are very different, and so is the idea of "approximation". Popper mostly followed in the footsteps of logical positivists by looking for measures of corroboration and approximation such as degree of verisimilitude, "truthlikeness". The more true sentences a theory entails the more truthlike it is, see SEP's Truthlikeness. Even aside from unpleasant formal consequences (no falsehood can be as close to the truth as a logical truth, a triviality, and no false theory is closer to the truth than any other) Popper's account uncritically imports the notion of truth itself. It seems at times that he wanted to keep the traditional correspondence truth, common to "folk philosophy" of scientists, along with the falsificationist epistemology. Peirce was much more sensitive to Kantian problems that such a mix poses for a realist. Particularly, to unifying conceptual accounts of diverse cognizing subjects into a single reality, and describing subject's interaction with it, see What are the similarities/differences between how Kant thinks 'noumenon' limits understanding compared to C.S. Peirce?

This caused his much greater departures from the correspondence truth since for Peirce "objective knowledge", being an abstraction, is not of a kind with reality itself, a living acting entity interacted with by a living acting subject. This is the core of Peirce's pragmatism, which is absent in Popper and is somewhat subdued in Quine. Peirce builds an additional epistemological superstructure of habits of action and concepts as conditional forks in them, a pragmatist semantics, and an elaborate theory of signs, his semiotic, to connect abstractions to reality through action and reaction and account for what is now called the problem of intentionality. This is absent in positivists, but then they were not realists, but it is also absent in Popper, whose attempt to cash in "convergence to truth" via formal measures was not very successful. In fairness, many find Peirce's justification of mind independence and convergence to the truth to also be a stretch, but at least he paints a more plausible picture of cognitive processes and epistemic growth.

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If by “giving up the notion of truth” you mean giving up the correspondence theory of truth – truth as correspondence between the world and our observations/concepts, then to relinquish truth as the goal/aim of [empirico-rational; scientific] inquiry, while preserving such inquiry itself a valid instrument for acquiring fruitful “knowledge” (fruitful though corrigible beliefs -- with predictive value capable of being falsified), as required by Popperian science, then a pragmatic instrumentalism would seem to be its only alternative epistemology. Remember, incidentally, that Popper believed that the logical analysis of scientific knowledge is not so much concerned with questions of fact as with questions of justification or validity.

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Popper believed that scientific knowledge is obtained through conjectures and refutations - the refutation of Newton's theory by Einstein is an example. He also believed that in this way science becomes gradually closer to truth. But it is not clear to me how he maintained this view within the conjecture - refutation framework.

You can get closer to truth, but you never have any guarantee that you are getting closer to truth. This is because any judgement you make is fallible and so could be mistaken. Popper is a more consistent falliblist than most philosophers. Rather you have to decide what positions to by proposing solutions and criticising those solutions with respect to whether the problem is actually solved. This involves having an explanation of how the solution is supposed to work - an account of what is happening in reality to make it work. David Deutsch was clearer about this in "The Fabric of Reality" chapter 1,3 and 7 and "The Beginning of Infinity" chapters 1, 2, 10 and 12.

To understand the role of truth in Popper's philosophy of science I wonder what would become of it if the notion of approaching the truth was given up? Would it make his philosophy pragmatist (or instrumentalist)? Many times they seem similar to me in various respects, except of course for the idea of truth or of getting closer to truth.

The idea of truth is so central to Popper's worldview that nothing would be left if you removed it. Ideas that have survived criticism might be true. Those that have not survived criticism aren't true. That's the only information you can have about the truth or lack thereof of an idea, see

fallibleideas.com/yes-or-no-philosophy

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