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- Simon Evnine, Old Evidence Again.In Bayesian epistemology, the concept of one proposition’s being evidence for another is explained along the following lines. Given a measure of degrees of confidence, con(...), that conforms to standard probability axioms: (EV) a proposition e is evidence for a proposition h iff con(h|e) is greater than con(h). (Con(h|e) is the degree of confidence in h given e, and is defined as con(h and e)/con(e).) Proposals along these lines, however, have been dogged by what Clark Glymour called the Problem of Old Evidence.[i] (EV) apparently precludes a theory being confirmed by evidence that is already in. For if a potentially evidential proposition, e, is already known, then con(e)=1. One can be subjectively certain of propositions already known to be true. But by definition of con(h|e), where con(e)=1, con(h|e) will always be equal to, and hence never greater than, con(h). Not only does (EV) preclude one from confirming new theories on the basis of information already gathered. Suppose Q is some proposition of which we are now uncertain, but which is evidence for a scientific hypothesis P. That is, con(P|Q) is greater than con(P). If we now devise an experiment to test whether Q, perform the experiment, and become certain that Q, it will no longer count as evidence for P. Thus, if we accept (EV), gathering new evidence to support a theory actually has quite the opposite effect. Gathering the evidence destroys its quality as evidence.
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Abstract Evidence that supports a theory may be available to the scientist who constructs the theory and used as a guide to that construction, or it may only be discovered in the course of testing the theory. The central claim of this essay is that information about whether the evidence was accommodated or predicted affects the rational degree of confidence one ought to have in the theory. Only when the evidence is accommodated is there some reason to believe that the theoretical system was ?fudged? to fit the evidence in a way that weakens support. This weakening is an objective matter, but not one that can be conclusively determined by examining the contents of the theory and its logical relationship to the evidence. Consequently, there is less reason to believe a theory on the basis of that evidence when it is known that the evidence was accommodated than there would be if it was known instead that the same evidence had been predicted.
The burden of this theorem, stated informally, is that when a hypothesis h is maximally independent of the evidence — that is, it goes wholly beyond the evidence —, then the probability p(h, e) increases when the evidence e is weakened; and hence, the weaker is the evidence, the greater is the probabilistic support.
We ought, as far as possible, to take into account the most specific evidence we have. Let us idealize and suppose that at a given point in time my evidence is constituted by my complete qualitative experiential state (QES). Insofar as my QES is more subjectively probable given one hypothesis than given another, my evidence better confirms the first. But which proposition is made more probable when my evidence is better confirmed? Is it that someone has this QES? Or that I have this QES?
Your evidence constrains your rational degrees of confidence both locally and globally. On the one hand, particular bits of evidence can boost or diminish your rational degree of confidence in various hypotheses, relative to your background information. On the other hand, epistemic rationality requires that, for any hypothesis h, your confidence in h is proportional to the support that h receives from your total evidence. Why is it that your evidence has these two epistemic powers? I argue that various proposed accounts of what it is for something to be an element of your evidence set cannot answer this question. I then propose an alternative account of what it is for something to be an element of your evidence set. 1 Introduction 2 The elements of one's evidence set are propositions 3 Which kinds of propositions are in one's evidence set? 3.1 Doxastic accounts of evidence 3.2 Non-doxastic accounts of evidence 4 Elaborating and defending the LIE CiteULike Connotea Del.icio.us What's this?
We ought, as far as possible, to take into account the most specific evidence we have. Let us idealize and suppose that at a given point in time my evidence is constituted by my complete qualitative experiential state (QES). Insofar as my QES is more subjectively probable given one hypothesis than given another, my evidence better confirms the first. But which proposition is made more probable when my evidence is better confirmed? Is it that someone has this QES? Or that I have this QES?
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The ´, or world's con flagration, followed by the restoration of an identical world seems to go against the rationality of the Stoic god. The aim of this paper is to show that Cleanthes, the second head of the School, can avoid this paradox. According to Cleanthes, the con flagration is an inevitable side-effect of the necessary means used by god to sustain the world. Given that this side-effect is contrary to god's sustaining activity, but unavoidable, god's rationality requires the restoration of an identical world once the con flagration subsides. The paper also deals with the relation between Cleanthes and other early Stoics on the topic of con flagration. In particular, Cleanthes' position seems to diff er from Chrysippus'. For in contrast with the Cleanthean god, who causes the con flagration as a side-effect only, the Chrysippean god, according to an in fluential interpretation put forward by Jaap Mansfeld, causes the con flagration as his ultimate cosmological goal.
We prove the following Main Theorem: $ZF + AD + V = L(R) \Rightarrow DC$ . As a corollary we have that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + DC)$ . Combined with the result of Woodin that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + \neg AC^\omega)$ it follows that DC (as well as AC ω ) is independent relative to ZF + AD. It is finally shown (jointly with H. Woodin) that ZF + AD + ¬ DC R , where DC R is DC restricted to reals, implies the consistency of ZF + AD + DC, in fact implies R # (i.e. the sharp of L(R)) exists.
We begin with a subsidiary question: Is reasonable disagreement ever possible? Opposing answers to one and the same question can both be reasonable, of course, if at least one of them is based on evidence that is persuasive but misleading. This much is uncontroversial. In a more interesting case, Pro and Con share all their evidence. Can they still assess the shared evidence differently? Can one affirm what the other denies, though each proceeds reasonably enough? For each to be reasonable, each needs positive justification. Unlike ethics, epistemology repels arbitrariness. Facing a choice between bringing it about that p and bringing it about that not-p, you may have no sufficient reason to prefer either over the other, in which case you might well be free to take your pick. That’s how it is for practical choices or actions. By contrast, with no more reason for believing either a proposition or its negation in preference to the other, you are definitely not free to proceed either way. Here you must withhold, if you are to proceed reasonably at all, epistemically. If two opponents are both to be reasonable, then, each needs a balance of reason favoring his side.[2] But is this compatible with their sharing all of their evidence? Not if any reason they may have, for or against believing, would have to be found in the evidence that they share. We are supposing they share all their evidence. Since the evidence cannot point in two opposite directions at once, Pro and Con cannot each have substantial positive reason for affirming what the other denies. Based on such reasoning, you may well conclude that reasonable disagreement with full disclosure is just impossible. But others will no doubt disagree. Suppose you all pool your evidence, and they remain unimpressed. On one view with substantial support in the literature, if you encounter opposition from an apparent peer, then, absent independent reason to downgrade him, you must lower your confidence, perhaps below the threshold of belief..
Discussion of Simon Evnine, Old evidence again
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