RECONSTRUCTION OF EPSILON-MACHINES IN PREDICTIVE FRAMEWORKS AND DECISIONAL STATES

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided utility or pay-off function. The utility function encodes some a priori knowledge external to the system, it quantifies how bad it is to make mistakes. The intrinsic underlying structure of the system is modeled by an epsilon-machine and its causal states. The decisional states form a partition of the lower-level causal states that is defined according to the higher-level user's knowledge. In a complex systems perspective, the decisional states are thus the "emerging" patterns corresponding to the utility function. The transitions between these decisional states correspond to events that lead to a change of decision. The new REMAPF algorithm estimates both the epsilon-machine and the decisional states from data. Application examples are given for hidden model reconstruction, cellular automata filtering, and edge detection in images.

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‘With a Philosophical Eye’: the role of mathematical beauty in Kant’s intellectual development

Canadian Journal of Philosophy ◽

10.1080/00455091.2014.974468 ◽

2014 ◽

Vol 44 (5-6) ◽

pp. 759-788

Author(s):

Courtney David Fugate

Keyword(s):

Intellectual Development ◽

A Priori ◽

Underlying Structure ◽

A Priori Knowledge ◽

Early Analysis ◽

Historical Explanation ◽

Mathematical Beauty ◽

Synthetic A Priori ◽

Priori Knowledge

This paper shows that Kant’s investigation into mathematical purposiveness was central to the development of his understanding of synthetic a priori knowledge. Specifically, it provides a clear historical explanation as to why Kant points to mathematics as an exemplary case of the synthetic a priori, argues that his early analysis of mathematical purposiveness provides a clue to the metaphysical context and motives from which his understanding of synthetic a-priori knowledge emerged, and provides an analysis of the underlying structure of mathematical purposiveness itself, which can be described as unintentional, but also as objective and unlimited.

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Seeing, Knowing, and Doing

10.1093/oso/9780197503508.001.0001 ◽

2020 ◽

Author(s):

Robert Audi

Keyword(s):

Practical Reasoning ◽

Practical Knowledge ◽

A Priori ◽

Human Action ◽

A Priori Knowledge ◽

Rational Action ◽

Reasons For Action ◽

Discriminative Response ◽

Rich Information ◽

Priori Knowledge

This book provides an overall theory of perception and an account of knowledge and justification concerning the physical, the abstract, and the normative. It has the rigor appropriate for professionals but explains its main points using concrete examples. It accounts for two important aspects of perception on which philosophers have said too little: its relevance to a priori knowledge—traditionally conceived as independent of perception—and its role in human action. Overall, the book provides a full-scale account of perception, presents a theory of the a priori, and explains how perception guides action. It also clarifies the relation between action and practical reasoning; the notion of rational action; and the relation between propositional and practical knowledge. Part One develops a theory of perception as experiential, representational, and causally connected with its objects: as a discriminative response to those objects, embodying phenomenally distinctive elements; and as yielding rich information that underlies human knowledge. Part Two presents a theory of self-evidence and the a priori. The theory is perceptualist in explicating the apprehension of a priori truths by articulating its parallels to perception. The theory unifies empirical and a priori knowledge by clarifying their reliable connections with their objects—connections many have thought impossible for a priori knowledge as about the abstract. Part Three explores how perception guides action; the relation between knowing how and knowing that; the nature of reasons for action; the role of inference in determining action; and the overall conditions for rational action.

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How Reality is Reasonable

10.1093/oso/9780198810384.003.0006 ◽

2018 ◽

Author(s):

Donald C. Williams

Keyword(s):

A Priori ◽

A Priori Knowledge ◽

Dimensional Manifold ◽

The World ◽

Being There ◽

Ways Of Being ◽

Fundamental Entity ◽

Spatiotemporal Relations ◽

Priori Knowledge

This chapter begins with a systematic presentation of the doctrine of actualism. According to actualism, all that exists is actual, determinate, and of one way of being. There are no possible objects, nor is there any indeterminacy in the world. In addition, there are no ways of being. It is proposed that actual entities stand in three fundamental relations: mereological, spatiotemporal, and resemblance relations. These relations govern the fundamental entities. Each fundamental entity stands in parthood relations, spatiotemporal relations, and resemblance relations to other entities. The resulting picture is one that represents the world as a four-dimensional manifold of actual ‘qualitied contents’—upon which all else supervenes. It is then explained how actualism accounts for classes, quantity, number, causation, laws, a priori knowledge, necessity, and induction.

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How Do We Know that We’re Not Brains in Vats?

10.1093/oso/9780199564477.003.0007 ◽

2018 ◽

Author(s):

Keith DeRose

Keyword(s):

Epistemic Justification ◽

A Priori ◽

A Priori Knowledge ◽

Conservative Approach ◽

Contingent Fact ◽

Brains In Vats ◽

Priori Knowledge

In this chapter the contextualist Moorean account of how we know by ordinary standards that we are not brains in vats (BIVs) utilized in Chapter 1 is developed and defended, and the picture of knowledge and justification that emerges is explained. The account (a) is based on a double-safety picture of knowledge; (b) has it that our knowledge that we’re not BIVs is in an important way a priori; and (c) is knowledge that is easily obtained, without any need for fancy philosophical arguments to the effect that we’re not BIVs; and the account is one that (d) utilizes a conservative approach to epistemic justification. Special attention is devoted to defending the claim that we have a priori knowledge of the deeply contingent fact that we’re not BIVs, and to distinguishing this a prioritist account of this knowledge from the kind of “dogmatist” account prominently championed by James Pryor.

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