Counting distinctions: on the conceptual foundations of Shannon’s information theory

Categorical logic has shown that modern logic is essentially the logic of subsets (or “subobjects”). In “subset logic,” predicates are modeled as subsets of a universe and a predicate applies to an individual if the individual is in the subset. Partitions are dual to subsets so there is a dual logic of partitions where a “distinction” [an ordered pair of distinct elements (u, u′) from the universe U] is dual to an “element”. A predicate modeled by a partition π on U would apply to a distinction if the pair of elements was distinguished by the partition π, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered |U|² pairs from the finite universe. That yields a notion of “logical entropy” for partitions and a “logical information theory.” The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon’s theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon’s theory based on the logical notion of “distinctions.” This paper is dedicated to the memory of Gian-Carlo Rota—mathematician, philosopher, mentor, and friend.     

孟子性善论新探

In Mencius’ theory of the original goodness in human nature, fate is the original source of xing (nature). Heart is the appearance of nature. There are two aspects to nature and heart: ti (form) and yong (function). From the perspective of form, nature is liangzhi (the goodness in conscience) and liangneng (the inborn ability to be good) in human beings and heart is human’s conscience and original heart. From the perspective of function, nature is the four things of benevolence, righteousness, propriety and wisdom, and heart consists in compassion, shame, respect, right and wrong. As the foundation for the theory of the original goodness in human nature, conscience and heart are a combination of human moral instinct, moral rationality and moral volition, whereas moral instinct gradually rises to moral volition and passes through moral rationality. Mencius’ theory of the original goodness in human nature is not a theory of future goodness, but a theory of original goodness. Translated by Wang Bei from Qilu Xuekan 齐鲁学刊(Journal of Qilu), 2006, (4): 16–20     

Roger Swyneshed’s Obligationes: A Logical Game of Inference Recognition?

In [Dutilh Novaes, Medieval-obligations as logical Games of Consistency maintenance, synthese, (2004)], I proposed a reconstruction of Walter Burley’s theory of obligationes, based on the idea that Burley’s theory of obligationes could be seen as a logical game of consistency maintenance. In the present paper, I intend to test the game hypothesis on another important theory of obligationes, namely Roger Swyneshed’s theory. In his treatise on obligationes [edited by P.V. Spade, cf. Spade History and philosophy of Logic 3(1982) 1-32], Swyneshed introduced significant modifications to the general framework of obligationes. To compare the two theories, I apply the same formal apparatus used in the previous paper. It will become patent that Swyneshed’s theory is considerably different from Burley’s, among other reasons because the dynamic aspects that play a major role in the latter are simply not present in the former. My conclusion is that Swyneshed’s version of obligationes is not directed towards consistency maintenance, but rather towards inference recognition, and that it is, from a game-theoretical perspective, less interesting a theory than Burley’s.     

An exposition of Zhou Yi studies in modern Neo-Confucianism

The representatives of modern Neo-Confucianism all greatly value Yi Zhuan and regard it as one of their spiritual resources, and give their own creative interpretations and transformations. Xiong Shili’s ontological-cosmological theory takes “qian yuan” as its center; Ma Yifu has a theory of ontology-cultivation centered on “nature-principle”; Fang Dongmei has a metaphysics of production and reproduction; Mou Zongsan takes the view of “completely knowing the fathomless and understanding transformation” as a moral metaphysics; and in Tang Junyi there is a theory of the harmony of doctrines on Heaven and man in which “the knowledge of divine understanding” is its key concept. They employ modern philosophical concepts and thinking to illustrate the cosmology, ontology, theory of life, theory of human nature, theory of spiritual worlds, axiology and their connections in Zhou Yi. They affirm that the characteristics of Chinese philosophy that are different from Western philosophy consist in a naturalist view of vital life, a harmonious view of totality, an axiological view that values exist in natural universe and the world of fact, the pursuit of Good and Beauty, and intuitive experience of inner world. __________ Translated from Zhou Yi Yanjiu 周易研究 (Zhou Yi Studies), 2004 (4) by Hao Changchi     

A brief explanation of the Chu bamboo slips Hengxian

The discovery of Hengxian and the formation of the category of hengxian are an important recapitulation and creative integration of the theory of the ontological Dao (Tao) in the Pre-Qin period. The cosmology of “self-creating and self-functioning” in Hengxian and the theory of “self-creating and self-evolving” in Liezi and Zhuangzi can be mutually interpreted. It indicates that the theory of transformation of qi entered a quite mature state in the Warring States Period. __________ Translated from Qilu Xuekan 齐鲁学刊 (Qilu Academic Journal), 2005 (1) by Yan Xin     

The ‘Gray’s Elegy’ Argument, and The Prospects for the Theory of Denoting Concepts

Russell’s new theory of denoting phrases introduced in “On Denoting” in Mind 1905 is now a paradigm of analytic philosophy. The main argument for Russell’s new theory is the so-called ‘Gray’s Elegy’ argument, which purports to show that the theory of denoting concepts (analogous to Frege’s theory of senses) promoted by Russell in the 1903 Principles of Mathematics is incoherent. The ‘Gray’s Elegy’ argument rests on the premise that if a denoting concept occurs in a proposition, then the proposition is not about the concept. I argue that the premise is false. The ‘Gray’s Elegy’ argument does not exhaust Russell’s ammunition against the theory of denoting concepts. Another reason Russell rejects the theory is, as he says, that it cannot provide an adequate account of non-uniquely denoting concepts. In the last section of the paper, I argue that even though Russell was right in thinking that the theory of denoting concepts cannot provide an adequate account of non-uniquely denoting concepts, Russell’s new theory does not succeed in eliminating the occurrence of all denoting concepts, as it requires a commitment to the existence of variables that indirectly denote their values. However, the view that variables are denoting concepts is unproblematic once the ‘Gray’s Elegy’ argument is blocked.     

Relational Science: A Synthesis

A synthesis of the two primary theory structures in Robert Rosen’s relational complexity, (1) relational entailment mapping based on category theory as described by Rosen and Louie, and (2) relational holism based on modeling relations, as described by Kineman, provides an integral foundation for relational complexity theory as a natural science and analytical method. Previous incompatibilities between these theory structures are resolved by re-interpreting Aristotle’s four causes, identifying final and formal causes as relations with context. Category theory is applied to introduce contextual entailment algebra needed to complete the synthesis. The modeling relation is represented as a recursive four-cause hierarchy, which is a unit of both whole and part analysis (a ‘holon’) that relates realized and contextual domains of nature as complementary inverse entailments between structure and function. Context is a non-localized domain of distributed potentials (models) for existence, as contrasted with the realized domain of localized interactive and measurable events. Synthesis is achieved by giving modeling relations an algebraic form in category theory and by expanding relational analysis to include contextual entailments. The revised form of analysis is applied and demonstrated to examine Rosen’s M-R diagram, showing that structure–function relations imply adaptive interaction with the environment, and that contextual relations imply three forms of the M-R entailment corresponding with the generally known three forms of life; Archaea, Bacteria, and Eukaryota, which can be represented by their holon diagrams. The result of this synthesis is a consistent foundation for relational science that should have important implications in many disciplines.     

Non-monotonic Probability Theory and Photon Polarization

A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov’s positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov’s theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; yet, many standard theorems are also theorems of the new theory since Kolmogorov’s other axioms are retained. What is of particular interest is that the new theory can accommodate quantum phenomena (photon polarization experiments) while preserving Boolean operations, unlike Kolmogorov’s theory. Although non-standard notions of probability have been discussed extensively in the physics literature, they have received very little attention in the philosophical literature. One likely explanation for that difference is that their applicability is typically demonstrated in esoteric settings that involve technical complications. That barrier is effectively removed for non-monotonic probability theory by providing it with a homely setting in the quantum domain. Although the initial steps taken in this paper are quite substantial, there is much else to be done, such as demonstrating the applicability of non-monotonic probability theory to other quantum systems and elaborating the interpretive framework that is provisionally put forward here. Such matters will be developed in other works.     

Shared structure need not be shared set-structure

Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models. I wish to thank Katherine Brading, Anjan Chakravartty, Steven French, Martin Thomson-Jones, Antigone Nounou, Stathis Psillos, Dean Rickles, Mauricio Suarez and two anonymous referees for valuable comments and criticisms, and Gregory Janzen for editorial suggestions. Research for this paper was funded by a generous SSHRC grant for which I am grateful     

A New Mixed View of Virtue Ethics, Based on Daniel Doviak’s New Virtue Calculus

In A New Form of Agent-Based Virtue Ethics, Daniel Doviak develops a novel agent-based theory of right action that treats the rightness (or deontic status) of an action as a matter of the action’s net intrinsic virtue value (net-IVV)—that is, its balance of virtue over vice. This view is designed to accommodate three basic tenets of commonsense morality: (i) the maxim that “ought” implies “can,” (ii) the idea that a person can do the right thing for the wrong reason, and (iii) the idea that a virtuous person can have “mixed motives.” In this paper, I argue that Doviak’s account makes an important contribution to agent-based virtue ethics, but it needs to be supplemented with a consequentialist account of the efficacy of well-motivated actions—that is, it should be transformed into a mixed (motives-consequences) account, while retaining its net-IVV calculus. This is because I believe that there are right-making properties external to an agent’s psychology which it is important to take into account, especially when an agent’s actions negatively affect other people. To incorporate this intuition, I add to Doviak’s net-IVV calculus a scale for outcomes. The result is a mixed view which accommodates tenets (ii) and (iii) above, but allows for (i) to fail in certain cases. I argue that, rather than being a defect, this allowance is an asset because our intuitions about ought-implies-can break down in cases where an agent is grossly misguided, and our theory should track these intuitions.     

Vollkommene Syllogismen und reine Vernunftschlüsse: Aristoteles und Kant. Eine Stellungnahme zu Theodor Eberts Gegeneinwänden. Teil 2

In an earlier article (see J Gen Philos Sci (2010) 41: 341–355) I have compared Aristotle’s syllogistic with Kant’s theory of “pure ratiocination”. “Ratiocinia pura” („reine Vernunftschlüsse“) is Kant’s designation for assertoric syllogisms Aristotle has called ‘perfect’. In Kant’s view they differ from non-pure ratiocinia precisely in that their validity rests only on the validity of the Dictum de omni et nullo (which, however, in Kant’s view can be further reduced to more fundamental principles) whereas the validity of non-pure ratiocinia additionally presupposes the validity of inferences which Kant calls consequentiae immediatae. I have argued that Kant’s view is in some (not in all) essential features in accordance with Aristotle’s view concerning perfect syllogisms and certainly leading to a tenable and interesting logical theory. As a result I have rejected not only the interpretation of Aristotle adopted by Theodor Ebert, but also the objections he has raised against Kant’s logical theory. As far as Aristotle is concerned, Ebert has attempted to defend his position in the first part of his reply to my article published in J Gen Philos Sci (2009) 40: 357–365, and I have argued against this defence in issue 1 of the J Gen Philos Sci (2010) 41: 199–213 (cf. Ebert’s answer in the same issue pp. 215–231). In the following discussion I deal with Eberts defence of his criticism of Kant published in the second part of his reply to my article (see J Gen Philos Sci (2009) 40: 365–372). I shall argue, that Kant’s principle ‘nota notae est nota rei ipsius’ and his use of technical vocabulary stand up to the objections raised by Ebert. His attempts to prove that Kant’s logical theory is defective are based on several misinterpretations.     

Depiction and plastic perception. A critique of Husserl’s theory of picture consciousness

In this paper, I will present an argument against Husserl’s analysis of picture consciousness. Husserl’s analysis of picture consciousness (as it can be found primarily in the recently translated volume Husserliana 23) moves from a theory of depiction in general to a theory of perceptual imagination. Though, I think that Husserl’s thesis that picture consciousness is different from depictive and linguistic consciousness is legitimate, and that Husserl’s phenomenology avoids the errors of linguistic theories, such as Goodman’s, I submit that his overall theory is unacceptable, especially when it is applied to works of art. Regarding art, the main problem of Husserl’s theory is the assumption that pictures are constituted primarily as a conflict between perception/physical picture thing and imagination/picture object. Against this mentalist claim, I maintain, from a hermeneutic point of view, that pictures are the result of perceptual formations [Bildungen]. I then claim that Husserl’s theory fails, since it does not take into account what I call “plastic perception” [Bildliches Sehen], which plays a prominent role not only within the German tradition of art education but also within German art itself. In this connection, “plastic thinking” [Bildliches Denken] was prominent especially in Klee, in Kandinsky, and in Beuys, as well as in the overall doctrine of the Bauhaus. Ultimately, I argue that Husserl’s notion of picture consciousness and general perceptive imaginary consciousness must be replaced with a more dynamic model of the perception of pictures and art work that takes into account (a) the constructive and plastic moment, (b) the social dimension and (c) the genetic dimension of what it means to see something in something (Wollheim).

What Things <Emphasis Type="Italic">Still</Emphasis> Don’t Do

This paper praises and criticizes Peter-Paul Verbeek’s What Things Do (2006). The four things that Verbeek does well are: (1) remind us of the importance of technological things; (2) bring Karl Jaspers into the conversation on technology; (3) explain how technology “co-shapes” experience by reading Bruno Latour’s actor-network theory in light of Don Ihde’s post-phenomenology; (4) develop a material aesthetics of design. The three things that Verbeek does not do well are: (1) analyze the material conditions in which things are produced; (2) criticize the social-political design and use context of things; and (3) appreciate how liberal moral-political theory contributes to our evaluation of technology.     

The 10-Item Positive and Negative Affect Schedule for Children, Child and Parent Shortened Versions: Application of Item Response Theory for More Efficient Assessment

The Positive and Negative Affect Schedule for Children (PANAS-C/P; child and parent versions) yield positive affect (PA) and negative affect (NA) scales that are clinically useful for identifying youth with anxiety and mood problems. Despite the advantages that item response theory (IRT) offers relative to classical test theory with respect to shortening test instruments, no studies to date have applied IRT methodology to the PANAS-C/P scales. In the present study, we thus applied IRT methodology using a school-based development sample (child sample: N = 799; parent sample: N = 553) and developed a shortened 5-item PA scale (joyful, cheerful, happy, lively, proud) and a 5-item NA scale (miserable, mad, afraid, scared, sad) for the sake of simultaneously increasing the assessment efficiency of the PANAS-C/P scales while improving the psychometric properties of the scales. The reduced PA and NA child scales classified relevant diagnostic groups in a separate clinic-referred validation sample (N = 662) just as well as the original PANAS-C child scales and may be used to help identify youth with internalizing disorders in need of mental health services.     

A New Form of Agent-Based Virtue Ethics

In Morals From Motives, Michael Slote defends an agent-based theory of right action according to which right acts are those that express virtuous motives like benevolence or care. Critics have claimed that Slote’s view— and agent-based views more generally— cannot account for several basic tenets of commonsense morality. In particular, the critics maintain that agent-based theories: (i) violate the deontic axiom that “ought” implies “can”, (ii) cannot allow for a person’s doing the right thing for the wrong reason, and (iii) do not yield clear verdicts in a number of cases involving “conflicting motives” and “motivational over-determination”. In this paper I develop a new agent-based theory of right action designed to avoid the problems presented for Slote’s view. This view makes morally right action a matter of expressing an optimal balance of virtue over vice and commands agents in each situation to improve their degree of excellence to the greatest extent possible.     

Mentalist evidentialism vindicated (and a super-blooper epistemic design problem for proper function justification)

Michael Bergmann seeks to motivate his externalist, proper function theory of epistemic justification by providing three objections to the mentalism and mentalist evidentialism characteristic of nonexternalists such as Richard Feldman and Earl Conee. Bergmann argues that (i) mentalism is committed to the false thesis that justification depends on mental states; (ii) mentalism is committed to the false thesis that the epistemic fittingness of an epistemic input to a belief-forming process must be due to an essential feature of that input, and, relatedly, that mentalist evidentialism is committed to the false thesis that the epistemic fittingness of doxastic response B to evidence E is an essential property of B–E; and (iii) mentalist evidentialism is “unmotivated”. I object to each argument. The argument for (i) begs the question. The argument for (ii) suffers from the fact that mentalist evidentialists are not committed to the consequences claimed for them; nevertheless, I show that there is, in the neighborhood, a substantive dispute concerning the nature of doxastic epistemic fittingness. That dispute involves what I call “Necessary Fittingness”, the view that, necessarily, exactly one (at most) doxastic attitude (belief, or disbelief, or suspension of judgment) toward a proposition is epistemically fitting with respect to a person’s total evidence at any time. Reflection on my super-blooper epistemic design counterexamples to Bergmann’s proper function theory reveals both the plausibility of Necessary Fittingness and a good reason to deny (iii). Mentalist evidentialism is thus vindicated against the objections.     

Proxytypes and Linguistic Nativism

Prinz (Perceptual the Mind: Concepts and Their Perceptual Basis, MIT Press, 2002) presents a new species of concept empiricism, under which concepts are off-line long-term memory networks of representations that are ‘copies’ of perceptual representations – proxytypes. An apparent obstacle to any such empiricism is the prevailing nativism of generative linguistics. The paper critically assesses Prinz’s attempt to overcome this obstacle. The paper argues that, prima facie, proxytypes are as incapable of accounting for the structure of the linguistic mind as are the more traditional species of empiricism. This position is then confirmed by looking in detail at two suggestions (one derived from recent connectionist research) from Prinz of how certain aspects of syntactic structure might be accommodated by the proxytype theory. It is shown that the suggestions fail to come to terms with both the data and theory of contemporary linguistics.     

Benti, practice and state: On the doctrine of mind in the four chapters of Guanzi

“Xin 心 (Mind)” is one of the key concepts in the four chapters of Guanzi. Together with Dao, qi 气 (air, or gas) and de 德 (virtue), the four concepts constitute a complete system of the learning of mind which is composed of the theory of benti 本体 (root and body), the theory of practice and the theory of spiritual state. Guanzi differentiates the two basic layers of mind—the essence and the function. It tries to attain a state of accumulated jing 精 (essence, anima) and nourished qi, in which qi is concentrated in a miraculous way, through a series of methods of mind cultivation and nurturing, including being upright, calm, tranquil and moderate, and to concentrate the mind and intention. The doctrine of mind of the four chapters of Guanzi influenced Daoism and Confucianism and is a key link in the history of Chinese thought. It is a prelude to the merger of Confucianism, Daoism and Buddhism.