How is God-talk logically possible? A sketch for an argument on the logic of ‘God’

In this paper I want to argue for the optimal way to characterise the logical and semantical behaviour of the singular term ‘God’ used in religious language. The relevance of this enterprise to logical theory is the main focus as well. Doing this presupposes to outline the two rivaling approaches of well-definition of singular terms: Kripke’s (“rigid designators”) and Hintikka’s (“world-lines”). ‘God’ as a “rigid designator” is purified from all real-life-language-games of identification and only spells out a metaphysical tag, which favours the view of “anything goes”. Instead, ‘God’ as a “world-line,” plus two ways of quantification, is much more flexible to theological traditions, teachings of the church, religious practices and personal feelings. Thus, it provides a sufficiently well-defined singular term for the purposes of logical theory. The whole sketch is based on Jaakko Hintikka’s logical ideas, mainly on his responses to different authors in PJH. I have systematically omitted direct references to his texts because I have modified considerably his ideas for my own purposes.     

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.     

How to be a structuralist all the way down

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be structuralists all the way down.     

Motivational Cognitivism and the Argument from Direction of Fit

An important argument for the belief-desire thesis is based on the idea that an agent can be motivated to act only if her mental states include one which aims at changing the world, that is, one with a “world-to-mind”, or “telic”, direction of fit. Some cognitivists accept this claim, but argue that some beliefs, notably moral ones, have not only a “mind-to-world”, or “thetic”, direction of fit, but also a telic one. The paper first argues that this cognitivist reply is deficient, for only the “dominant” direction of fit of an attitude is responsible for its character and function. Further, it seems that the dominant direction of fit of an attitude is determined by its psychological mode, and so all beliefs seem to have a dominant thetic direction of fit, and to be motivationally inert. The main part of this paper, however, is devoted to explaining how it is that attitudes, like moral attitudes, can truly have two directions of fit in a way which enables them to be both cognitive and motivational. Reflection on the nature of beliefs suggests that the claim that the dominant direction of fit of an attitude is determined by its psychological mode should be qualified. The reasons beliefs provide draw their authority for the agent – their demanding nature – from the objects represented by these beliefs, and so, it is the beliefs’ content which determine their dominant direction of fit, as far as their role in practical reasoning is concerned. Thus, in the sense relevant to practical reasoning a belief with a normative content does have a dominant telic direction of fit. At the same time, in the sense relevant to its satisfaction conditions a moral belief has a dominant thetic direction of fit, which underlies its classification as a cognitive attitude. Cognitivists, then, can have it both ways.     

Epistemological Challenges to Mathematical Platonism

Since Benacerraf’s “Mathematical Truth” a number of epistemological challenges have been launched against mathematical platonism. I first argue that these challenges fail because they unduely assimilate mathematics to empirical science. Then I develop an improved challenge which is immune to this criticism. Very roughly, what I demand is an account of how people’s mathematical beliefs are responsive to the truth of these beliefs. Finally I argue that if we employ a semantic truth-predicate rather than just a deflationary one, there surprisingly turns out to be logical space for a response to the improved challenge where no such space appeared to exist.     

Minimal Belief Change and the Pareto Principle

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the standard AGM postulates. The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. The Ramsey test is a well-known way of establishing connections between belief revision postulates and axioms for conditionals (“if p, then q”). Pareto-minimal theory change corresponds exactly to three characteristic axioms of counterfactual systems: a theory revision operator that satisfies the Ramsey test validates these axioms if and only if the revision operator is Pareto-minimal. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Dynamic-Logical Perspective on Quantum Behavior

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system.     

The logic of scientific and religious principles

Summary In every domain, the philosopher finds some principle which is unfalsifiable in so far as all experience is interpreted in accordance with it. This principle is tautologous or analytic-within-its domain in that it defines fundamental terms with which it characterizes experiences: Newton’s Laws define “mass” and “the equality of times”; the Principle of the Rectilinear Propagation of LIght defines “light”; the Principle of Evolution defines “adaptation” and “natural selection”; and the Principle of the Conservation of Energy defines “a closed system.” Moreover, each principle is employed as a methodological rule or a tacit imperative to the investigator to interpret experience or to draw inferences in accordance with it. Nevertheless, each principle has empirical content: not only by virtue of its place within its respective domain but also because there are sufficient rules of correspondence which make the statement-form empirically relevant; not only because the principle itself is taken to be true but also because empirical inferences are drawn in accordance with it. To construe these principles as mere counterfactuals would be clearly incorrect. Counterfactuals, as Rescher would characterize them, are “belief-contravening suppositions” because certain beliefs are excluded if one is to be consistent. Although this is certainly true of these principles, the range of beliefs contravened is far larger than those beliefs excluded in mere laws of nature. For, to give up these principles would be to give up explaining the entire domain of experience to which they are applicable.     

“Assertion” and intentionality

Robert Stalnaker argues that his causal-pragmatic account of the problem of intentionality commits him to a coarse-grained conception of the contents of mental states, where propositions are represented as sets of possible worlds. Stalnaker also accepts the “direct reference” theory of names, according to which co-referring names have the same content. Stalnaker’s view of content is thus threatened by Frege’s Puzzle. Stalnaker’s classic paper “Assertion” is intended to provide a response to this threat. In this paper, I evaluate Stalnaker’s claim that the causal-pragmatic account of intentionality commits one to a coarse-grained conception of the contents of mental states, and argue that the apparatus laid out in “Assertion” is not sufficiently comprehensive to account for all versions of Frege’s Puzzle.     

A Coherence Theory of Truth in Ethics

Quine argues, in “On the Nature of Moral Values” that a coherence theory of truth is the “lot of ethics”. In this paper, I do a bit of work from within Quinean theory. Specifically, I explore precisely what a coherence theory of truth in ethics might look like and what it might imply for the study of normative value theory generally. The first section of the paper is dedicated to the exposition of a formally correct coherence truth predicate, the possibility of which has been the subject of some skepticism. In the final two sections of the paper, I claim that a coherence theory in ethics does not reduce the practice of moral inquiry to absurdity, in practice as well as in principle.     

The enduring scandal of deduction

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed.     

Coherent choice functions under uncertainty

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.     

经验基础与知识确证

Whether empirical givenness has the reliability that foundationalists expect is a point about which some philosophers are highly skeptical. Sellars took the doctrine of givenness as a “myth,” denying the existence of immediate perceptual experience. The arguments in contemporary Western epistemology are concentrated on whether sensory experience has conceptual contents, and whether there is any logical relationship between perceptions and beliefs. In fact, once the elements of words and conceptions in empirical perception are affirmed, the logical relationship between perceptual experience and empirical belief is also affirmed. This relationship takes place through perceptual experience acting as evidence for beliefs. The real problem lies in how one should distinguish between the different relationships with perception of singular beliefs and of universal beliefs, and in how singular beliefs can provide justification for universal beliefs. __________ Translated from Zhongguo Shehui Kexue 中国社会科学 (Social Sciences in China), 2007, (1): 65–75     

Scientific Realism: Old and New Problems

Scientific realism is a doctrine that was both in and out of fashion several times during the twentieth century. I begin by noting three presuppositions of a succinct characterization of scientific realism offered initially by the foremost critic in the latter part of the century, Bas van Fraassen. The first presupposition is that there is a fundamental distinction to be made between what is “empirical” and what is “theoretical”. The second presupposition is that a genuine scientific realism is committed to their being “a literally true story of what the world is like”. The third presupposition is that there are methods for justifying a belief in the empirical adequacy of a theory which do not also suffice to justify beliefs in its literal truth. Each of these presuppositions raises a number of problems, some of which are quite old and others rather newer. In each case, I briefly review some of the old problems and then elaborate the newer problems.     

Room for a view: on the metaphysical subject of personal identity

Sydney Shoemaker leads today’s “neo-Lockean” liberation of persons from the conservative animalist charge of “neo-Aristotelians” such as Eric Olson, according to whom persons are biological entities and who challenge all neo-Lockean views on grounds that abstracting from strictly physical, or bodily, criteria plays fast and loose with our identities. There is a fundamental mistake on both sides: a false dichotomy between bodily continuity versus psychological continuity theories of personal identity. Neo-Lockeans, like everyone else today who relies on Locke’s analysis of personal identity, including Derek Parfit, have either completely distorted or not understood Locke’s actual view. Shoemaker’s defense, which uses a “package deal” definition that relies on internal relations of synchronic and diachronic unity and employs the Ramsey–Lewis account to define personal identity, leaves far less room for psychological continuity views than for my own view, which, independently of its radical implications, is that (a) consciousness makes personal identity, and (b) in consciousness alone personal identity consists—which happens to be also Locke’s actual view. Moreover, the ubiquitous Fregean conception of borders and the so-called “ambiguity of is” collapse in the light of what Hintikka has called the “Frege trichotomy.” The Ramsey–Lewis account, due to the problematic way Shoemaker tries to bind the variables, makes it impossible for the neo-Lockean ala Shoemaker to fulfill the uniqueness clause required by all such Lewis style definitions; such attempts avoid circularity only at the expense of mistaking isomorphism with identity. Contrary to what virtually all philosophers writing on the topic assume, fission does not destroy personal identity. A proper analysis of public versus perspectival identification, derived using actual case studies from neuropsychiatry, provides the scientific, mathematical and logical frameworks for a new theory of self-reference, wherein “consciousness,” “self-consciousness,” and the “I,” can be precisely defined in terms of the subject and the subject-in-itself.     

Death and design: The terror management function of teleological beliefs

Humans have a tendency to endorse teleological beliefs about the world. According to terror management theory, teleological or purposeful beliefs about the world help people cope with the awareness of mortality. Though research is generally consistent with this assertion, it has not been directly tested. Three studies tested and supported the notion that teleological beliefs about the world serve a terror management function. In “Study 1”, experimentally elevated teleological beliefs reduced death-thought accessibility. In “Studies 2 and 3”, mortality salience increased teleological beliefs, even if this resulted in judgment errors. Alternative explanations were tested and did not account for the findings.     

True Objects and Fulfilments Under Assumption in the Young Husserl

In the year 1894, Husserl had not been already contaminated by Bolzano’s realism. It was then that he conceived a theory of assumptions in order to “save an existence” for mathematical objects. Here we would like to explore this theory and show in what way it represented a convincing alternative to realistic ontology and its counterpart: the correspondence theory of truth. However, as soon as he designed it, Husserl shoved away all the implications for his theory of assumptions, and merely abandoned it. We would also like to consider the wrong reasons for this renouncement, which undoubtedly have to do with the dichotomy between signification and perception in his elaboration of phenomenology.     

“Critique” immanent in “practice”: New Frankfurt School and American pragmatism

As a result of a new understanding of the relation between theory and practice, the “New Frankfurt School,” with Jürgen Habermas as its major representative, highly values the philosophical tradition of American pragmatism, in contrast to the first generation Critical Theorists represented by Max Horkheimer. In Habermas, the idea of “critique” is, both substantially and methodologically, closely connected with the idea of “praxis” in the following senses: communicative action, rational argumentation, public discussion and political culture. “Critique” is thus found to be immanent in “praxis”; or, a la Horkheimer, pragmatism turns out to be a “critical philosophical analysis” without “falling back upon objective reason and mythology.” __________ Translated from Huadong Shifan Daxue Xuebao 华东示范大学学报 (Journal of Huadong Normal University), 2001 (5), with minor modifications     

Prospective teachers’ beliefs about students’ goal orientations: A carry-over effect of prior schooling experiences?

This study examined the relationship between prospective teachers’ (N = 166) retrospective perceptions of their own past achievement goals and their current beliefs about students’ goal orientations and achievement behaviors. Results of hierarchical regression analysis provide correlation evidence in support of a “carry-over effect” of prospective teachers’ past goal orientations on their current beliefs about students. Specifically, prospective teachers’ were found to believe that their future students will pursue goal orientations analogous to their own past goal orientations. In addition, prospective teachers’ explanations for why students might engage in or avoid achievement-directed behaviors were examined. Regardless of past goal orientation, “internal motives” (e.g., improvement and self-satisfaction) represented the most frequent explanation offered by prospective teachers for why students engage in achievement behaviors. Prospective teachers with past performance-approach goals were significantly more likely to view avoidance as a sign of “laziness,” whereas those with past performance-avoidant goals were more likely to view avoidance as resulting from a “lack of confidence and support.” Implications for subsequent research are discussed.     

Category-specified Value Statements

A value statement such as “she is a good teacher” is categoryspecified, i.e., the criteria of evaluation are specified as those that are applicable to a given category, in this case the category of teachers. In this study of categoryspecified value statements, certain categories are identified that cannot be used to specify value aspects. Special attention is paid to categories that are constituted by functional characteristics. The logical properties of value statements that refer to such categories are shown to differ significantly from the corresponding properties in social choice theory.