The aim of this article is to discuss the idea that the notion of topos could become the future mathematics of AI, by giving more emphasis to geometric forms, compared to the currently mainstream approach, which favors numbers through statistical procedures. AI engineers are looking for theories that can formalize the basic elements that shape their daily work, as well as the basic operations that structure how the human brain works. The notion of topos could contribute largely to satisfying these (...) two main aspirations of AI engineering. The article is a part of a questioning on the nature of intelligence and supposedly intelligent machines. In this respect, it would be useful to enrich the approach that assimilates the topos as a kind of bridge that removes all the inessential aspects of things to be connected to keep an common essence that associates mathematical things. One of the most promising avenues from the archeology of the discourse on the topos is the reading by meaning. This art of reading well gives rise to the notion of conceptual strata which shows that the things to be connected have a layered configuration. What seems insignificant –in view of a supposed essence– through one conceptual stratum, might seem important through another, even capital. Rather than calling something ‘insignificant’, a consistent relativism of ‘insignificant for’ would be more appropriate, according to the conceptual stratum considered. (shrink)

Isabelle Stengers’ thinking is sensitive, limpid, and complex. Her vision of living worlds is based on the philosophy of becoming and multiplicity. Becoming refers to a living change and therefore to an absence of permanence and natural laws to which we must adapt. Multiplicity refers to several regimes of truth, several types of reason, several modes of existence. Her knowledge universe is made up of several sets of beings and things where thought navigates fluidly between the fields of study. A (...) torrent of freedom that opens up new avenues for overcoming confinement and expanding action. This exploration of the ecology of practices provides the opportunity to address economic life, beyond the confines of academic discipline, as an open field that should be constantly widened through investigation by establishing the conditions of existence. (shrink)

Listening, seeing and reading Gilles Deleuze has had an influence on my thinking more than most of the economic writings I have consulted over the past quarter of a century. This discovery and furtherance of knowledge enriched my reflection and also allowed me to go beyond the general philosopher, as a philosopher opening the way to new horizons. It makes the researcher aware that the most important thing is not the philosopher man but the man philosopher, i.e. the one who (...) writes something that touches a human being at his deepest level and concerns him in his life every day. New generations of economists should meditate on this by going beyond the chapel quarrels coming from the Schumpeterian dichotomy 'science versus ideology'. To quote one of Deleuze's main ideas, no thinking against anything has been important over a long period; what counts are thoughts for something new that affect people's lives, and which are produced with rigor. This opens the way to a thought for life and not against life, which is in line with the progress of research in methodology, where it is a question of giving more importance to social ontology as a level of analysis and not focusing solely on epistemology in the narrowest sense. (shrink)

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Anthony Price's recent book presents a contextualist approach to practical rationality. Price develops his proposal in four chapters. In the first one , he outlines a contextual account of the validity of practical inferences. This chapter deals with logicism. Logicism assumes that ‘there is a form of rationality within practical thinking that connects with the logical validity of a practical entailment’ . Price argues that although the principles of logic are ‘invariant and universal’ , their relevance in evaluating a practical (...) inference is constrained by contextual factors related to the teleology of practical thinking and by the functional role of intentions in guiding our behaviour.In the second chapter , Price argues that the content of A's remark to B – ‘I must put in another 20p’, while both stand together on an underground platform in front of a dispenser – must be interpreted contextually, i.e. as referring to a particular end of A for which she needs to put in …. (shrink)

Analytic philosophers have a tendency to forget that they are human beings, and one of the reasons that P. F. Strawson’s 1962 essay, “Freedom and Resentment”, has been so influential is that it promises to bring discussions of moral responsibility back down to earth. Strawson encouraged us to “keep before our minds...what it is actually like to be involved in ordinary interpersonal relationships”, which is, after all, the context in which questions about responsibility arise in the first place. In this (...) essay I explore what we can learn about ordinary interpersonal relationships from three works of literature – Shakespeare’s King Lear, Jane Austen’s Persuasion, and Graham Greene’s The End of the Affair. My intention is to try to heed Strawson’s advice without imposing upon the data any particular theoretical agenda, and my hope is that the data collected will prove useful for future theorizing about responsibility. (shrink)

With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.

Work in the setting of the recursively enumerable sets and their Turing degrees. A set X is low if X', its Turning jump, is recursive in $\varnothing'$ and high if X' computes $\varnothing''$ . Attempting to find a property between being low and being recursive, Bickford and Mills produced the following definition. W is deep, if for each recursively enumerable set A, the jump of $A \bigoplus W$ is recursive in the jump of A. We prove that there are no (...) deep degrees other than the recursive one. Given a set W, we enumerate a set A and approximate its jump. The construction of A is governed by strategies, indexed by the Turning functionals Φ. Simplifying the situation, a typical strategy converts a failure to recursively compute W into a constraint on the enumeration of A, so that $(W \bigoplus A)'$ is forced to disagree with Φ(-; A'). The conversion has some ambiguity; in particular, A cannot be found uniformly from W. We also show that there is a "moderately" deep degree: There is a low nonzero degree whose join with any other low degree is not high. (shrink)

Comparative study of the Mimamsa philosophy of Kumārila Bhaṭṭa and Prabhākaramiśra, 7th century philosophers.