Online research in philosophy

Counterexamples are constructed for the theory of rational choice that results from a direct application of classical decision theory to ordinary actions. These counterexamples turn on the fact that an agent may be unable to perform an action, and may even be unable to try to perform an action. An alternative theory of rational choice is proposed that evaluates actions using a more complex measure, and then it is shown that this is equivalent to applying classical decision theory to "conditional policies" rather than ordinary actions.

Actions for which we are responsible constitute our engagement with the world as rational agents. What is the relationship between such actions and our capacities for rational agency? I take this to be a question about responsibility in a particular use of that term, which I shall call ‘responsibility2’. We are not responsible2 for all our intentional actions (actions under hypnosis, for example), but we can nevertheless be responsible2 for actions we do not adequately control, for negligent actions, and for non-intentional omissions. Appreciating this helps show that familiar principles of responsibility are false: those which delimit responsibility to intentional actions or to actions and outcomes under our control. In the attempt to fashion an alternative principle, cases of negligence prove pivotal. We hold ourselves and others responsible2 for conduct within our respective ‘domains of secure competence’, (i.e. that within which we are confident of doing what we set ourselves to do, barring events which defeat our competence), even when actions within that domain fail. The significance of this practice of holding ourselves and others responsible2 lies in the way it maintains our sense of who we are and of how we are related to the world in which we act.1.

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers.

Contemporary democracy has given primacy to thought. Building up institutions on thought and reasoned discourse excludes out human actions derived not from thought that one thinks. Ordinary life is visited by emotion and passion. Such actions of unknown origin are captured best in the drama. Indian theory and practice of drama and the poetics offer communion between the performer and the viewer. Blissful relish of the actions and the dialogues lift up the banal actions from the ordinary to a state beyond simple event. Relishing thus resides in cognition. Drama in theory and in its practice thus offers foundation to institutions that could embrace independent actions as well. In relish there is cognition and reasoning alone cannot lay claim. Folk life and folk actions thus could be emancipatory.

Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis of ourgeneral concept of an effective procedure; mundane procedures and Turing machine procedures are different kinds of procedure. Moreover, the same sequence ofparticular physical action can realize both a mundane procedure and a Turing machine procedure; it is sequences of particular physical actions, not mundane procedures, which enter the world of mathematics. I conclude by discussing whether genuinely continuous physical processes can enter the world of real numbers and compute real-valued functions. I argue that the same kind of correspondence assumptions that are made between non-numerical structures and the natural numbers, in the case of Turing machines and personal computers, can be made in the case of genuinely continuous, physical processes and the real numbers.

Abstract   A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets , eight , as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. Content Type Journal Article Pages 1-38 DOI 10.1007/s11098-011-9779-1 Authors Friederike Moltmann, IHPST (Paris1/ENS/CNRS), Paris, France Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

Abstract   A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets , eight , as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. Content Type Journal Article Pages 1-38 DOI 10.1007/s11098-011-9779-1 Authors Friederike Moltmann, IHPST (Paris1/ENS/CNRS), Paris, France Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

All tools have their advantages and disadvantages and for all tools there are times when they are appropriate and times when they are not. Formal tools are no exception to this and systems of numbers are examples of such formal tools. Thus there will be occasions where using a number to represent something is helpful and times where it is not. To use a tool well one needs to understand that tool and, in particular, when it may be inadvisable to use it and what its weaknesses are. However we are in an age that it obsessed by numbers. Governments spend large amounts of money training its citizens in how to use numbers and their declarative abstractions (graphs, algebra etc.) We are surrounded by numbers every day in: the news, whether forecasts, our speedometers and our bank balance. We are used to using numbers in loose, almost “conversational” ways – as with such concepts as the rate of inflation and our own “IQ”. Numbers have become so famliar that we no more worry about when and why we use them than we do about natural language. We have lost the warning bells in our head that remind us that we may be using numbers inappropriately. They have entered (and sometimes dominate) our language of thought. Computers have exasperbated this trend by making numbers very much easier to store/manipulate/communicate and more seductive by making possible attractive pictures and animations of their patterns. More subtley, when thought of as calculating machines that can play games with us and simulate the detail of physical systems, they suggest that everything comes down to numbers. For this reason it is second nature for us to use numbers in our social simulations and we frequently do so without considering the consequences of this choice. This paper is simply a reminder about numbers: a call to remember that they are just another (formal) tool; it recaps some of the conditions which indicate when a number is applicable and when it might be misleading; it looks at some of the dangers and pitfalls of using numbers; it considers some examples of the use of numbers; and it points out that we now have some viable alternatives to numbers that are not any less formal but which may be often preferable.

Erwin Schroedinger and Werner Heisenberg were the originators of two approaches, known respectively as “wave mechanics” and “matrix mechanics”, to what is now called “quantum mechanics’ or “quantum theory”. The two approaches appear to be extremely different, both in their technical forms, and in their philosophical underpinnings. Heisenberg arrived to his theory by effectively renouncing the idea of trying to represent a physical system, such as a hydrogen atom for example, as a structure in space-time, but by instead, following the lead of Einstein’s 1905 theory of relativity, representing only empirically observable properties, such as the transition amplitudes between the stationary states of the atom. These amplitudes can be arranged in square arrays of numbers. In Heisenberg’s scheme these arrays, and other like them, are combined according to certain rules that were later recognized by Max Born to be the rules of matrix multiplication. The whole scheme is abstract and mathematical, and avoids using any space-time picture of what is going on at the atomic level. Schroedinger, on the other hand, represented the electron in an atom by a cloudlike wave surrounding the nucleus. This is a space-time structure that, superficially at least, is more in line with the classical physical theories of the eighteenth and nineteenth centuries.