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Karl Popper is mostly known for his falsification principle. I'm very familiar with his account and I understand it well. I've heard multiple times that there are some real issues with this account and that there are many problems with it. I've googled that and I've read something or two about the criticisms provided by later philosophers like Lakatos.

My question is, What are the real problems that face Popper's account?

both explanations and resources to read about those difficulties are welcomed.

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The fact that a theory is not a model to begin with. The fact, also, that theories are based on metaphysics principles that cannot be proven right but neither false. The fact that one can also complexify models of a given theory to obtain good predictions yet shitty explanation. The fact that it is also non trivial to link experimentations with models (both upward and downward modelization problems), etc etc.

See this answer Newtons law saved by ad-hoc hypothesis? for more details.

edit: Let me give more details about the upward and downward modelization problems. Given a theory T, a model M of such theory, the downward modelization problem stipulates that it is by no mean trivial to say that an experimentation "in real life" is indeed an instantiation of M. That is, how to "produce" (with a good amount of certainty) the model M by an experiment E, and claim that what one is indeed measuring is M within T? Couldn't E' be a more faithful realization of M, or is it even possible to realize M with some experiment?

The upward modelization problem is the reciprocal. Given an experiment E (with some data, hypothesis and so on), how to modelize it with a model M within T? How to be sure that M is indeed the "best model" describing E within T, and that M' wouldn't be better or more relevant? That is, what does "better model" means when one is trying to fit experimental data? Certainly, elegance and simplicity is more important than no error with high complexity and bunches of free parameters.

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    I'm not getting the direct connection between this and falsifiability as a criterion for demarcating scientific hypotheses..
    – Dave
    Aug 31 '15 at 15:21
  • Simple: falsifiability is not at all trivial to define, so it's whole popper philosophy that is fucked up.
    – sure
    Aug 31 '15 at 16:21
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You say you are very familiar with Popper's ideas, and yet you say his main contribution was the "falsification principle". This is false, as was pointed out by Popper himself in the introduction to "Realism and the Aim of Science". Popper's greatest contributions to epistemology was providing an alternative to the idea that theories ought to be justified ("Realism and the Aim of Science", Chapter I), tying epistemology to evolution (see "Objective Knowledge" by Popper, or "Evolutionary Epistemology, Rationality, and the Sociology of Knowledge" edited by Radnitzky and Bartley), and some stuff about epistemology in political philosophy, explained in "The Open Society and Its Enemies". So you seem to have overstated your familiarity with Popper.

Lakatos made up a load of stuff about Popper's alleged positions that have nothing to do with his actual positions. For Lakatos' criticisms and Popper's reply, see "The Philosophy of Karl Popper" edited by Schilpp, and the introduction to "Realism and the Aim of Science".

The best improvements on Popper have been proposed by David Deutsch (see his books "The Fabric of Reality" and "The Beginning of Infinity") and Elliot Temple:

http://curi.us/1595-rationally-resolving-conflicts-of-ideas.

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    Strictly speaking, the OP said "mostly known for his falsification principle", which is a true description of what most people first think of.
    – Dave
    Aug 31 '15 at 13:54

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