Geoffrey Hellman
Biographic Data
| ID | 1017811 |
|---|---|
| NAME | Geoffrey Hellman |
| GIVEN NAMES | Geoffrey |
| FAMILY NAME | Hellman |
| SIGNATURE | HELLMAN G |
| AFFILIATIONS | Twin Cities Orthopedics |
| ORCID | 0000-0001-5559-4932 |
| VERIFIED | Yes |
| TOTAL WORKS | 21 |
| TOTAL CITATIONS | 40 |
| AUTHOR COUNT | 21 |
| EDITOR COUNT | 0 |
| FIRST PUBLICATION YEAR | 1911 |
| LATEST PUBLICATION YEAR | 2021 |
| H-INDEX | 4 |
Geoffrey Hellman, The Laki volcanic eruption of 1783-1784
Mathematical Structuralism
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of …
Mathematical Structuralism
On Nominalism
Mathematical Constructivism in Spacetime
To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the …
Responses to Maher, and to Kelly, Schulte, and Juhl
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Bayes and Beyond
Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a “protective belt” of auxil…
Mathematics without Numbers
Part 1 The natural numbers and analysis: the modal-structural framework - the hypothetical component the categorical component - an axiom of infinity and a derivation (inspired by Dedekind with help from Frege) justifying the translation scheme justification from within extensions the question of nominalism. Part 2 Set theory: informal principles - many versus one the relevant structures unbounded sentences - Putnam semantics axioms of infinity -…
Toward a modal-structural interpretation of set theory
Epr, Bell, and Collapse
Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of “stochastic“ hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist (“realist”) interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reaso…
Dualling
Realist Principles
We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-à-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empir…
Einstein and Bell
Stochastic Einstein-locality and the Bell theorems
Quantum Logic and the Projection Postulate
This paper explores the status of the von Neumann-Lüders state transition rule (the “projection postulate”) within “real-logic” quantum logic. The entire discussion proceeds from a reading of the Lüders rule according to which, although idealized in applying only to “minimally disturbing” measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effec…
A probabilistic version of the Kochen-Specker no-hidden-variable proof
Physicalism
The Structure of Appearance
Reason and Prediction
Introduction 1. A statement of the problem 2. The analysis of reason 3. The logic of increasing confidence 4. Goodman's paradox 5. Probability and reasons 6. The principle of indifference 7. Successful policies 8. Objectivity and prediction Bibliographical index
The New Riddle of Radical Translation
This paper presents parts of a theory of radical translation with applications to the problem of construing reference. First, in sections 1 to 4 the general standpoint, inspired by Goodman's approach to induction, is set forth. Codification of sound translational practice replaces the aim of behavioral reduction of semantic notions. The need for a theory of translational projection (manual construction on the basis of a finite empirical correlati…
Prof. Hellmann on the Floods of the Oder
Stochastic Einstein-locality and the Bell theorems
Bayes and Beyond
Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a “protective belt” of auxil…
Einstein and Bell
Realist Principles
We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-à-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empir…
Epr, Bell, and Collapse
Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of “stochastic“ hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist (“realist”) interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reaso…
Dualling
Quantum Logic and the Projection Postulate
This paper explores the status of the von Neumann-Lüders state transition rule (the “projection postulate”) within “real-logic” quantum logic. The entire discussion proceeds from a reading of the Lüders rule according to which, although idealized in applying only to “minimally disturbing” measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effec…
Mathematical Constructivism in Spacetime
To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the …
Responses to Maher, and to Kelly, Schulte, and Juhl
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Toward a modal-structural interpretation of set theory
The New Riddle of Radical Translation
This paper presents parts of a theory of radical translation with applications to the problem of construing reference. First, in sections 1 to 4 the general standpoint, inspired by Goodman's approach to induction, is set forth. Codification of sound translational practice replaces the aim of behavioral reduction of semantic notions. The need for a theory of translational projection (manual construction on the basis of a finite empirical correlati…
Prof. Hellmann on the Floods of the Oder
The New Riddle of Radical Translation
This paper presents parts of a theory of radical translation with applications to the problem of construing reference. First, in sections 1 to 4 the general standpoint, inspired by Goodman's approach to induction, is set forth. Codification of sound translational practice replaces the aim of behavioral reduction of semantic notions. The need for a theory of translational projection (manual construction on the basis of a finite empirical correlati…
Reason and Prediction
Introduction 1. A statement of the problem 2. The analysis of reason 3. The logic of increasing confidence 4. Goodman's paradox 5. Probability and reasons 6. The principle of indifference 7. Successful policies 8. Objectivity and prediction Bibliographical index
The Structure of Appearance
A probabilistic version of the Kochen-Specker no-hidden-variable proof
Physicalism
Quantum Logic and the Projection Postulate
This paper explores the status of the von Neumann-Lüders state transition rule (the “projection postulate”) within “real-logic” quantum logic. The entire discussion proceeds from a reading of the Lüders rule according to which, although idealized in applying only to “minimally disturbing” measurements, it nevertheless makes empirical claims and is not a purely mathematical theorem. An argument (due to Friedman and Putnam) is examined to the effec…
Einstein and Bell
Stochastic Einstein-locality and the Bell theorems
Realist Principles
We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-à-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empir…
Dualling
Epr, Bell, and Collapse
Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of “stochastic“ hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist (“realist”) interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reaso…
Toward a modal-structural interpretation of set theory
Mathematics without Numbers
Part 1 The natural numbers and analysis: the modal-structural framework - the hypothetical component the categorical component - an axiom of infinity and a derivation (inspired by Dedekind with help from Frege) justifying the translation scheme justification from within extensions the question of nominalism. Part 2 Set theory: informal principles - many versus one the relevant structures unbounded sentences - Putnam semantics axioms of infinity -…
Responses to Maher, and to Kelly, Schulte, and Juhl
An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content
Bayes and Beyond
Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a “protective belt” of auxil…
Mathematical Constructivism in Spacetime
To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the …
On Nominalism
Mathematical Structuralism
The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of …
Mathematical Structuralism
Geoffrey Hellman, The Laki volcanic eruption of 1783-1784
Philosophy (15 works) · Epistemology (14 works) · Mathematics (12 works) · Computer Science (10 works) · Quantum Mechanics and Applications (7 works) · Physics (6 works) · Mathematical economics (5 works) · Philosophy of science (5 works) · Calculus (dental) (4 works) · Metaphysics (4 works)