scholarly journals Approaching deterministic and probabilistic truth: a unified account

Synthese ◽  
2021 ◽  
Author(s):  
Gustavo Cevolani ◽  
Roberto Festa
Keyword(s):  
General Theory ◽  
Basic Problem ◽  
Truth Approximation ◽  
General Characterization ◽  
Formal Framework ◽  
Relevant Domain

AbstractThe basic problem of a theory of truth approximation is defining when a theory is “close to the truth” about some relevant domain. Existing accounts of truthlikeness or verisimilitude address this problem, but are usually limited to the problem of approaching a “deterministic” truth by means of deterministic theories. A general theory of truth approximation, however, should arguably cover also cases where either the relevant theories, or “the truth”, or both, are “probabilistic” in nature. As a step forward in this direction, we first present a general characterization of both deterministic and probabilistic truth approximation; then, we introduce a new account of verisimilitude which provides a simple formal framework to deal with such issue in a unified way. The connections of our account with some other proposals in the literature are also briefly discussed.

Why Does Rationality Matter?

2017 ◽  
Author(s):  
Ralph Wedgwood
Keyword(s):  
Mental States ◽  
External World ◽  
Dutch Book ◽  
Strong Sense ◽  
General Characterization ◽  
Internal Rationality

Internalism implies that rationality requires nothing more than what in the broadest sense counts as ‘coherence’. The earlier chapters of this book argue that rationality is in a strong sense normative. But why does coherence matter? The interpretation of this question is clarified. An answer to the question would involve a general characterization of rationality that makes it intuitively less puzzling why rationality is in this strong sense normative. Various approaches to this question are explored: a deflationary approach, the appeal to ‘Dutch book’ theorems, the idea that rationality is constitutive of the nature of mental states. It is argued that none of these approaches solves the problem. An adequate solution will have to appeal to some value that depends partly on how things are in the external world—in effect, an external goal—and some normatively significant connection between internal rationality and this external goal.

Practical Steps and Reasons for Action

1997 ◽  
Vol 27 (1) ◽  
pp. 17-45 ◽  
Author(s):  
Philip Clark
Keyword(s):  
Reasons For Action ◽  
Reasons For Belief ◽  
The Real ◽  
General Characterization ◽  
Practical Inference

There is an idea, going back to Aristotle, that reasons for action can be understood on a parallel with reasons for belief. Not surprisingly, the idea has almost always led to some form of inferentialism about reasons for action. In this paper I argue that reasons for action can be understood on a parallel with reasons for belief, but that this requires abandoning inferentialism about reasons for action. This result will be thought paradoxical. It is generally assumed that if there is to be a useful parallel, there must be some such thing as a practical inference. As we shall see, that assumption tends to block the fruitful exploration of the real parallel. On the view I shall defend, the practical analogue of an ordinary inference is not an inference, but something I shall call a practical step. Nevertheless, the practical step will do, for a theory of reasons for action, what ordinary inference does for an inferentialist theory of reasons for belief. The result is a general characterization of reasons, practical and theoretical, in terms of the correctness conditions of the relevant sorts of step.

The Paradoxes of Allais and Ellsberg

1986 ◽  
Vol 2 (1) ◽  
pp. 23-53 ◽  
Author(s):  
Isaac Levi
Keyword(s):  
General Theory ◽  
Rational Choice ◽  
Expected Utility ◽  
John Dewey ◽  
Expected Value ◽  
Human Knowledge ◽  
Numerical Indicator ◽  
Charles Peirce ◽  
Oriented Approach

In The Enterprise of Knowledge (Levi, 1980a), I proposed a general theory of rational choice which I intended as a characterization of a prescriptive theory of ideal rationality. A cardinal tenet of this theory is that assessments of expected value or expected utility in the Bayesian sense may not be representable by a numerical indicator or indeed induce an ordering of feasible options in a context of deliberation. My reasons for taking this position are related to my commitment to the inquiry-oriented approach to human knowledge and valuation favored by the American pragmatists, Charles Peirce and John Dewey. A feature of any acceptable view of inquiry ought to be that during an inquiry points under dispute ought to be kept in suspense pending resolution through inquiry.

scholarly journals The Abel map for surface singularities III: Elliptic germs

2021 ◽  
Author(s):  
János Nagy ◽  
András Némethi
Keyword(s):  
General Theory ◽  
Present Note ◽  
Affine Subspace ◽  
Normal Surface ◽  
Rational Homology ◽  
Surface Singularities ◽  
Abel Map ◽  
Appl Math ◽  
Rational Homology Sphere

AbstractThe present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, 2019; Nagy and Némethi in Adv Math 371:20, 2020; Nagy and Némethi in Pure Appl Math Q 16(4):1123–1146, 2020). Besides the general theory, by the study of specific families we wish to show the power of this new method. Indeed, using the general theory of Abel maps applied for elliptic singularities in this note we are able to prove several key properties for elliptic singularities (e.g. the statements of the next paragraph), which by ‘old’ techniques were not reachable. If $$({\widetilde{X}},E)\rightarrow (X,o)$$ ( X ~ , E ) → ( X , o ) is the resolution of a complex normal surface singularity and $$c_1:{\mathrm{Pic}}({\widetilde{X}})\rightarrow H^2({\widetilde{X}},{\mathbb {Z}})$$ c 1 : Pic ( X ~ ) → H 2 ( X ~ , Z ) is the Chern class map, then $${\mathrm{Pic}}^{l'}({\widetilde{X}}):= c_1^{-1}(l')$$ Pic l ′ ( X ~ ) : = c 1 - 1 ( l ′ ) has a (Brill–Noether type) stratification $$W_{l', k}:= \{{\mathcal {L}}\in {\mathrm{Pic}}^{l'}({\widetilde{X}})\,:\, h^1({\mathcal {L}})=k\}$$ W l ′ , k : = { L ∈ Pic l ′ ( X ~ ) : h 1 ( L ) = k } . In this note we determine it for elliptic singularities together with the stratification according to the cycle of fixed components. E.g., we show that the closure of any $$W(l',k)$$ W ( l ′ , k ) is an affine subspace. For elliptic singularities we also characterize the End Curve Condition and Weak End Curve Condition in terms of the Abel map, we provide several characterization of them, and finally we show that they are equivalent.

scholarly journals On complete objects in the category of T0 closure spaces

2003 ◽  
Vol 4 (1) ◽  
pp. 25 ◽  
Author(s):  
D. Deses ◽  
Eraldo Giuli ◽  
E. Lowen-Colebunders
Keyword(s):  
General Theory ◽  
Complete Lattices ◽  
Closure Spaces

<p>In this paper we present an example in the setting of closure spaces that fits in the general theory on “complete objects” as developed by G. C. L. Brümmer and E. Giuli. For V the class of epimorphic embeddings in the construct Cl<sub>0</sub> of T<sub>0</sub> closure spaces we prove that the class of V-injective objects is the unique firmly V-reflective subconstruct of Cl0. We present an internal characterization of the Vinjective objects as “complete” ones and it turns out that this notion of completeness, when applied to the topological setting is much stronger than sobriety. An external characterization of completeness is obtained making use of the well known natural correspondence of closures with complete lattices. We prove that the construct of complete T<sub>0</sub> closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.</p>

scholarly journals Teorías y actitudes escépticas en la Antigüedad

1970 ◽  
Author(s):  
Juan A. García González
Keyword(s):  
Greek Philosophy ◽  
General Characterization

RESUMENSe expone en este trabajo una panorámica del escepticismo antiguo, en sus tres fromas más notables: pirronismo, probabilismo y fenomenismo. Después se procede a una caracterización general del escepticismo y se glosa la interpretación hegeliana del mismo.PALABRAS CLAVEESCEPTICISMO, FILOSOFÍA GRIEGAABSTRACTIt is exposed in this work a panoramic of the old scepticism, in their three more remarkable forms: pirronism, probabilism and phenomenism. The you proceeds to a general characterization of the scepticism and is glossed the interpretation hegeliana of the scepticism.KEYWORDSSCEPTICISM, GREEK PHILOSOPHY

scholarly journals Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory

2020 ◽  
pp. 352-382
Author(s):  
Wilfried Sieg
Keyword(s):  
Proof Theory ◽  
Incompleteness Theorem ◽  
Mathematical Structures ◽  
General Characterization ◽  
Mathematical Structuralism ◽  
Mathematical Experience

Mathematical structuralism is deeply connected with Hilbert and Bernays’s proof theory and its programmatic aim to ensure the consistency of all of mathematics. That aim was to be reached on the basis of finitist mathematics. Gödel’s second incompleteness theorem forced a step from absolute finitist to relative constructivist proof-theoretic reductions. This mathematical step was accompanied by philosophical arguments for the special nature of the grounding constructivist frameworks. Against that background, this chapter examines Bernays’s reflections on proof-theoretic reductions of mathematical structures to methodological frames via projections. However, these reflections are focused on narrowly arithmetic features of frames. Drawing on broadened meta-mathematical experience, this chapter proposes a more general characterization of frames that has ontological and epistemological significance. The characterization is given in terms of accessibility: domains of objects are accessible if their elements are inductively generated, and principles for such domains are accessible if they are grounded in our understanding of the generating processes.

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