Chris Mortensen | University of Adelaide (original) (raw)
Papers by Chris Mortensen
Notre Dame Journal of Formal Logic, Oct 1, 1997
The question of the interpretation of impossible pictures is taken up. Penrose's account is revie... more The question of the interpretation of impossible pictures is taken up. Penrose's account is reviewed. It is argued that whereas this account makes substantial inroads into the problem, there needs to be a further ingredient. An inconsistent account using heap models is proposed.
Zeno of Elea invented several paradoxes which are justly famous. They amount to interesting and p... more Zeno of Elea invented several paradoxes which are justly famous. They amount to interesting and plausible arguments for obviously false conclusions. This is the characteristic of a good paradox: it promises to be interesting and instructive. To say that Zeno's arguments are ...
Australasian Journal of Philosophy, May 1, 1977
Philosophy East and West, 2007
Philosophy East and West, 2004
Graham Priest (1987) argues that motion must be an inconsistent process. The idea of motion and c... more Graham Priest (1987) argues that motion must be an inconsistent process. The idea of motion and change as inconsistent has a long history, from Heracleitus to Hegel. As a major premise in his proposed account, Priest, following Hegel, argues that an account of motion at a ...
Australasian Journal of Philosophy, Jul 1, 2009
ObituaryChris Mortense
Logique Et Analyse, 2005
... Type: Journal article. Title: It isn't so, but could it be? Author: Mortensen, Chris... more ... Type: Journal article. Title: It isn't so, but could it be? Author: Mortensen, Christian Edward. Citation: Logique et Analyse, 2005; 48 (189-192):351-360. Publisher: Nationaal Centrum voor Navorsingen in de Logica. Issue Date: 2005. ISSN: 0024-5836. ...
Journal of Philosophical Logic, 1978
Topoi-an International Review of Philosophy, May 21, 2019
The paper examines connections between ontology and finance. The ontological debates concerning t... more The paper examines connections between ontology and finance. The ontological debates concerning the role of finance are examined between two opposing schools of thought that can be labelled, very broadly, 'instrumentalist' and 'realist' (analytic-interpretivist). These two schools of thought have had momentous repercussions in understanding what is a good society. Each school defines Nature in particular ways which can be explored using ontology and philosophical insight. Our theoretical investigation aims to accommodate Nature in community financial deliberations. A positive role for government is advocated to finance environmental infrastructure initiatives. For example, precautionary strategies to address climate change must be funded. New roles for finance and government are proposed to align human relationships with Nature. Environmental precautionary principles must be developed in conjunction with finance theory to maintain decent standards of living for all. Reliance on impersonal market forces will not be enough to save the planet given the power of some over the many in the neoliberal arena.
Springer eBooks, 1995
The existence of the inconsistent case of a system of linear equations (or for that matter any sy... more The existence of the inconsistent case of a system of linear equations (or for that matter any system of constraints, not necessarily linear) has been known for a long time, but there has been no attempt to analyse its structure. There would seem to be good reason to do so, if only because the state of affairs might arise in a real life control system (see sections 3 and 4). Using the methods developed so far, it is possible to say something about the structure of solutions to such cases; though it must be confessed that in the end the situation remains less than satisfactory.
Notre Dame Journal of Formal Logic, Apr 1, 1986
is foaming at the mouth or John is biting the carpet. John is not foaming at the mouth. Therefore... more is foaming at the mouth or John is biting the carpet. John is not foaming at the mouth. Therefore, John is biting the carpet. Such an instance of Disjunctive Syllogism (DS) is undoubtedly intuitive, but a form of inference which is intuitive is not thereby valid. There are (at least) three positions which can be taken concerning the validity of DS. First: DS is valid, and the "or" in it is the two-valued extensional "or". Thus, the argument form Extensional Disjunctive Syllogism (EDS), i.e., Aw B, ~A/:.B, is valid. Second: EDS is invalid. There is a valid argument form, Intensional Disjunctive Syllogism (IDS), namely A + B,-A/.'.B, where " + " is intensional disjunction. Whenever you have a valid example of DS, it is because it is an instance of IDS. Third: The examples of DS which seem intuitive are often instances of EDS; but this does not make EDS valid, and it is not. Whenever it seems intuitive to infer using EDS, it is because there is an extra assumption, that things are "normal", which ensures the truth of the conclusion and which explains the apparent intuitiveness of EDS. Recently (in [8]), I defended the third of these. Read (in [9]) defended the second. In the course of my argument, I made the further claim that there are precise sufficient conditions for when the truth of the premises of EDS would ensure the truth of the conclusion and that these conditions obtained whenever there was an intuitive example of EDS. Both Read and Burgess ([4], see also his [5] and [6]) understood me to be trying to prove my claim by appeal to the validity of EDS in the metatheory, an appeal which they took to be circular. In Section 2 of this note, I will argue that there is no circularity in my position. In Section 3, I will argue that my position is a stable one, in that no collapse into a generally valid .EDS follows from it. In Section 4, I will briefly respond to some of Burgess's other points from [4]. 2 The appeal to normality We need some definitions. A theory for a logic L is a set of sentences closed under the consequence relation |-L It is useful to consider the situation we find ourselves in when deducing according to "natu
Notre Dame Journal of Formal Logic, 1983
This note is prompted by John Burgess's "Relevance: A Fallacy?" [2], which offers an argument in ... more This note is prompted by John Burgess's "Relevance: A Fallacy?" [2], which offers an argument in favour of the deductive validity of the argument form Disjunctive Syllogism, DS C4,not-,4 or B/.'.B). The kind of argument he gives is not so unusual, and can be encountered around the literature (e.g., [3], p. 666) and not infrequently in the verbal pronouncements of philosophers. The bones of the reply I will give to Burgess can also be found in a number of places and as long ago as 1972 (e.g., [4]-[6]), though I do not think it has been systematically developed anywhere. Since Burgess's argument is representative of a widespread kind of mistake about relevant logics, it is worthwhile to try to say clearly what is wrong with it. Burgess disclaims any attempt to discuss the extensive literature on relevant logics other than Anderson and Belnap's 1975 "masterwork" Entailment. Hence, his argument is best viewed as a piece of internal criticism of that book. However, he makes several remarks which imply fairly clearly that his sights are on more general targets, and are intended to apply to all "self-styled" relevant logicians. Let me therefore concede straight away that in my view Anderson and Belnap's discussion of DS in Entailment is inadequate. It would be rash, however, to draw the conclusion that there is no hope offered within the broad programme loosely classifiable as "relevantist" for shoring up their rejection of DS. Indeed, in view of the well-known Lewis proofs of the irrelevant principle of Ex Falso Quodlibet, there had better be. Burgess says that the issue as far as he is concerned is whether relevant logics "are in better agreement with common sense than classical logic", and *I wish to thank Bob Meyer, Graham Priest, and Stephen Read for helpful comments.
Springer eBooks, 1995
Inconsistent mathematics I Chris Mortensen. p. cm.-(Mathematlcs and ltS appllcations v. 3121 Incl... more Inconsistent mathematics I Chris Mortensen. p. cm.-(Mathematlcs and ltS appllcations v. 3121 Includes bibl iographical references and index.
Trends in Logic, 2019
Dialetheism is the thesis that there are true contradictions. But humans tolerate contradictions ... more Dialetheism is the thesis that there are true contradictions. But humans tolerate contradictions without necessarily believing them to be true. Two sources are (a) contradictions in mathematics, which are dialethic only if one is a realist, non-fictionalist about mathematics (b) contradictory images such as the impossible triangle, which are certainly not true in the real world. This paper explores these ideas, and concludes that impossible figures give us examples of non-dialethic contradictory contents.
Pointing at the Moon, 2009
This chapter explores the limits of the sayable in the context of Zen stories, arguing that the v... more This chapter explores the limits of the sayable in the context of Zen stories, arguing that the very fact that Zen addresses our mode of prereflective engagement with the world-a mode of engagement that is in important ways precognitive-means that much of what Zen has to teach us must be shown, and not said. This language, of course, is redolent of the Tractatus.Chris Mortensenhttp://trove.nla.gov.au/work/3497273
History of Philosophy in Australia and New Zealand, 2014
Inconsistent Mathematics, 1995
Inconsistent Mathematics, 1995
Inconsistent Mathematics, 1995
Notre Dame Journal of Formal Logic, Oct 1, 1997
The question of the interpretation of impossible pictures is taken up. Penrose's account is revie... more The question of the interpretation of impossible pictures is taken up. Penrose's account is reviewed. It is argued that whereas this account makes substantial inroads into the problem, there needs to be a further ingredient. An inconsistent account using heap models is proposed.
Zeno of Elea invented several paradoxes which are justly famous. They amount to interesting and p... more Zeno of Elea invented several paradoxes which are justly famous. They amount to interesting and plausible arguments for obviously false conclusions. This is the characteristic of a good paradox: it promises to be interesting and instructive. To say that Zeno's arguments are ...
Australasian Journal of Philosophy, May 1, 1977
Philosophy East and West, 2007
Philosophy East and West, 2004
Graham Priest (1987) argues that motion must be an inconsistent process. The idea of motion and c... more Graham Priest (1987) argues that motion must be an inconsistent process. The idea of motion and change as inconsistent has a long history, from Heracleitus to Hegel. As a major premise in his proposed account, Priest, following Hegel, argues that an account of motion at a ...
Australasian Journal of Philosophy, Jul 1, 2009
ObituaryChris Mortense
Logique Et Analyse, 2005
... Type: Journal article. Title: It isn't so, but could it be? Author: Mortensen, Chris... more ... Type: Journal article. Title: It isn't so, but could it be? Author: Mortensen, Christian Edward. Citation: Logique et Analyse, 2005; 48 (189-192):351-360. Publisher: Nationaal Centrum voor Navorsingen in de Logica. Issue Date: 2005. ISSN: 0024-5836. ...
Journal of Philosophical Logic, 1978
Topoi-an International Review of Philosophy, May 21, 2019
The paper examines connections between ontology and finance. The ontological debates concerning t... more The paper examines connections between ontology and finance. The ontological debates concerning the role of finance are examined between two opposing schools of thought that can be labelled, very broadly, 'instrumentalist' and 'realist' (analytic-interpretivist). These two schools of thought have had momentous repercussions in understanding what is a good society. Each school defines Nature in particular ways which can be explored using ontology and philosophical insight. Our theoretical investigation aims to accommodate Nature in community financial deliberations. A positive role for government is advocated to finance environmental infrastructure initiatives. For example, precautionary strategies to address climate change must be funded. New roles for finance and government are proposed to align human relationships with Nature. Environmental precautionary principles must be developed in conjunction with finance theory to maintain decent standards of living for all. Reliance on impersonal market forces will not be enough to save the planet given the power of some over the many in the neoliberal arena.
Springer eBooks, 1995
The existence of the inconsistent case of a system of linear equations (or for that matter any sy... more The existence of the inconsistent case of a system of linear equations (or for that matter any system of constraints, not necessarily linear) has been known for a long time, but there has been no attempt to analyse its structure. There would seem to be good reason to do so, if only because the state of affairs might arise in a real life control system (see sections 3 and 4). Using the methods developed so far, it is possible to say something about the structure of solutions to such cases; though it must be confessed that in the end the situation remains less than satisfactory.
Notre Dame Journal of Formal Logic, Apr 1, 1986
is foaming at the mouth or John is biting the carpet. John is not foaming at the mouth. Therefore... more is foaming at the mouth or John is biting the carpet. John is not foaming at the mouth. Therefore, John is biting the carpet. Such an instance of Disjunctive Syllogism (DS) is undoubtedly intuitive, but a form of inference which is intuitive is not thereby valid. There are (at least) three positions which can be taken concerning the validity of DS. First: DS is valid, and the "or" in it is the two-valued extensional "or". Thus, the argument form Extensional Disjunctive Syllogism (EDS), i.e., Aw B, ~A/:.B, is valid. Second: EDS is invalid. There is a valid argument form, Intensional Disjunctive Syllogism (IDS), namely A + B,-A/.'.B, where " + " is intensional disjunction. Whenever you have a valid example of DS, it is because it is an instance of IDS. Third: The examples of DS which seem intuitive are often instances of EDS; but this does not make EDS valid, and it is not. Whenever it seems intuitive to infer using EDS, it is because there is an extra assumption, that things are "normal", which ensures the truth of the conclusion and which explains the apparent intuitiveness of EDS. Recently (in [8]), I defended the third of these. Read (in [9]) defended the second. In the course of my argument, I made the further claim that there are precise sufficient conditions for when the truth of the premises of EDS would ensure the truth of the conclusion and that these conditions obtained whenever there was an intuitive example of EDS. Both Read and Burgess ([4], see also his [5] and [6]) understood me to be trying to prove my claim by appeal to the validity of EDS in the metatheory, an appeal which they took to be circular. In Section 2 of this note, I will argue that there is no circularity in my position. In Section 3, I will argue that my position is a stable one, in that no collapse into a generally valid .EDS follows from it. In Section 4, I will briefly respond to some of Burgess's other points from [4]. 2 The appeal to normality We need some definitions. A theory for a logic L is a set of sentences closed under the consequence relation |-L It is useful to consider the situation we find ourselves in when deducing according to "natu
Notre Dame Journal of Formal Logic, 1983
This note is prompted by John Burgess's "Relevance: A Fallacy?" [2], which offers an argument in ... more This note is prompted by John Burgess's "Relevance: A Fallacy?" [2], which offers an argument in favour of the deductive validity of the argument form Disjunctive Syllogism, DS C4,not-,4 or B/.'.B). The kind of argument he gives is not so unusual, and can be encountered around the literature (e.g., [3], p. 666) and not infrequently in the verbal pronouncements of philosophers. The bones of the reply I will give to Burgess can also be found in a number of places and as long ago as 1972 (e.g., [4]-[6]), though I do not think it has been systematically developed anywhere. Since Burgess's argument is representative of a widespread kind of mistake about relevant logics, it is worthwhile to try to say clearly what is wrong with it. Burgess disclaims any attempt to discuss the extensive literature on relevant logics other than Anderson and Belnap's 1975 "masterwork" Entailment. Hence, his argument is best viewed as a piece of internal criticism of that book. However, he makes several remarks which imply fairly clearly that his sights are on more general targets, and are intended to apply to all "self-styled" relevant logicians. Let me therefore concede straight away that in my view Anderson and Belnap's discussion of DS in Entailment is inadequate. It would be rash, however, to draw the conclusion that there is no hope offered within the broad programme loosely classifiable as "relevantist" for shoring up their rejection of DS. Indeed, in view of the well-known Lewis proofs of the irrelevant principle of Ex Falso Quodlibet, there had better be. Burgess says that the issue as far as he is concerned is whether relevant logics "are in better agreement with common sense than classical logic", and *I wish to thank Bob Meyer, Graham Priest, and Stephen Read for helpful comments.
Springer eBooks, 1995
Inconsistent mathematics I Chris Mortensen. p. cm.-(Mathematlcs and ltS appllcations v. 3121 Incl... more Inconsistent mathematics I Chris Mortensen. p. cm.-(Mathematlcs and ltS appllcations v. 3121 Includes bibl iographical references and index.
Trends in Logic, 2019
Dialetheism is the thesis that there are true contradictions. But humans tolerate contradictions ... more Dialetheism is the thesis that there are true contradictions. But humans tolerate contradictions without necessarily believing them to be true. Two sources are (a) contradictions in mathematics, which are dialethic only if one is a realist, non-fictionalist about mathematics (b) contradictory images such as the impossible triangle, which are certainly not true in the real world. This paper explores these ideas, and concludes that impossible figures give us examples of non-dialethic contradictory contents.
Pointing at the Moon, 2009
This chapter explores the limits of the sayable in the context of Zen stories, arguing that the v... more This chapter explores the limits of the sayable in the context of Zen stories, arguing that the very fact that Zen addresses our mode of prereflective engagement with the world-a mode of engagement that is in important ways precognitive-means that much of what Zen has to teach us must be shown, and not said. This language, of course, is redolent of the Tractatus.Chris Mortensenhttp://trove.nla.gov.au/work/3497273
History of Philosophy in Australia and New Zealand, 2014
Inconsistent Mathematics, 1995
Inconsistent Mathematics, 1995
Inconsistent Mathematics, 1995