http://daniel.cohnitz.de/index.php?frege

The Ins and Outs of Mathematical Explanation

Abstract

Proofs of mathematical theorems tell us that the theorem is true, but some proofs go further and tell us why the theorem is true. That is, some, but not all, proofs are explanatory. Call this intra-mathematical explanation. It has been argued that whenever there are physical applications of the theorems in question, we also have mathematical explanations of physical phenomena. Call this extra-mathematical explanation. In this paper I willconsider both intra- and extra-mathematical explanations and discuss why they are of philosophical interest. I will also make some speculative remarks about two promising accounts for a theory of mathematical explanation.

Professor Colyvan is ARC Future Fellow and Professor of Philosophy, President of the Society for Risk Analysis (ANZ), and Director of the Sydney Centre for the Foundations of Science.

Abstract

A physical account of consciousness does not appear convincing. It leaves the explanatory gap between the conscious phenomena and their physical explanation. However, instead of drawing metaphysical conclusions from this perplexity, several philosophers have tried to deflate its significance by explaining the gap intuition as something that stems from our psychological structure.
Fiala, Arico and Nichols have proposed a psychological explanation that presumes a dual-process account of the attribution of consciousness. According to this, conscious states can be ascribed either via the “low road” mechanism that is triggered by the presence of certain cues in the object or via the “high road” mechanism that controls the reflective judgements. In their view, the gap intuition is an outcome of the mismatch between the low and the high road processing. In the lack of sufficient cues, the low road mechanism is not activated and as a result, the high road reasoning remains unsupported by the automatic low road response. This gives rise to the intuition about the explanatory gap.
In my talk, I mainly criticise such an explanation of the gap intuition and briefly outline an alternative psychological account.

Abstract:

Hypostatization, (reification in one of its many senses) or the fallacy of misplaced concreteness refers to an abstraction being “treated as if it were a concrete, real event, or physical entity.”  Hypostatization has occurred when concepts, frameworks, and theories freeze into pictures of reality that cannot be shaken by reality.

There is a natural psychological tendency to assume that every word in language refers to something outside of language. Beliefs about the reality of the things of nature, such as gravity, heat, kinetic force, stones, and water, are usually unproblematic even though, as Kant demonstrated, these beliefs must involve an element of interpretation.  Natural scientists are rarely concerned by the doubts of philosophers as to whether a real world exists.  It is easy to grasp how the things existing in the natural world can kick back at the hypotheses scientists attempt to impose, and render them problematic.

It is understandable that social scientists also tend to view the concepts they use, like political system, elite, social class, interest group, bureaucracy, and capitalism existing as do stones, trees, and thunderstorms.  This commonsense naive realist view of a reality existing independently of our knowledge has deep roots in the human psyche and in language. Few doubt the existence of a social world that can sometimes shatter our false beliefs about it.  Yet it remains unclear just what it is that might kick back at the hypotheses social scientists make about it.  When social scientists set about to study things like governments, markets, or power, they must have some idea of the nature of the things they wish to research.  They make assumptions about the things they intend to investigate and these assumptions play a crucial role in determining what kinds of information to gather and how to gather it.  Yet when the notions of social reality underlying social science research are scrutinized, it becomes clear how tenuous their representation can be.
If there is no clear sense of what is “out there” in the real world, concepts tend to create worlds of their own without protest from reality.  Facts can always be found that fit the concepts.  When a clear notion of social reality is present, that reality can kick back and shatter propositions that are made about it.  This reduces the potential for hypostatization.

This paper will argue that a clear sense of social reality is usually missing in social science research, and that accounts for the widespread tendency to hypostatize.  It will attempt to develop  a remedial approach to hypostatization by suggesting ways of developing an adequate, practical ontology of the social.  Words are not simply labels for things.  Improving our sense  of real social world is the only effective means to combat reification.  Research seeks to discover concrete sources of orderliness in social reality that can serve as objective constraints on the hypotheses the research seeks to impose.

This just came out and was presented to John at his birthday party at the CSLI, Stanford. I’ll teach a seminar based on this book this term. More later…

This year’s Gottlob Frege Lectures in Theoretical Philosophy will be delivered by John Perry. The exact dates are not fixed yet, but it will probably be in the last week of June. These are the topics John will cover:

I. Folk-psychology as an amazing Intellectual Accomplishment

• How our lives depend on our “theory” of mind
• Basic categories:  Feelings, cognitions, ideas
• The “Propositional Attitudes”
• Properties of the PAs
• Causal
• Phenomenological
• How we report and describe them

II.  Three theories of the attitudes

• Frege’s Picture of the attitudes:  agents, times, relations, propositions (The Simple Content Picture).
• Fodor’s Picture of the attitudes: agents, times, and mental representations. (The Simple Representational Picture)
• Representations and contents
• The Complex Picture (Cognitions with Contents)

III.  Self-Locating Belief

• Names, Descriptions and Roles
• Role based-”modes of presentation”.
• Roles and Frege’s picture
• Roles and Fodor’s picture
• Roles and the Complex Picture

IV.  Beliefs about the Self

• Primitive self-belief
• Beliefs about the Self
• Self-notions
• Self-notions, buffers, detached notions
• Lewis’s concept of “self-attribution of properties” confuses primitive self-belief and having beliefs about oneself.

V.  The general theory of Content (Reflexive/Referential Theory)

• Indexical content
• Referential Content
• Network Content and empty names

VI.  Reporting Attitudes

• Traditional Problems
• The Crimmins-Perry Theory
• The Thread Theory

The special issue is edited by Teresa Marques (Lisbon) and Daniel Cohnitz (Tartu).

Papers should be emailed to mariateresamarques@campus.ul.pt or cohnitz@ut.ee no later than

April 1st, 2012.

Submissions must be in English and conform to the submission standards of Erkenntnis (please consult the “instructions for authors” here: http://www.springer.com/philosophy/journal/10670#)

All submissions must be prepared for blind review.

http://daniel.cohnitz.de/index.php?Linguistic-Reality-and-it-Psychological-Basis