Putnam, Peano, and the Malin Génie: could we possibly bewrong about elementary number-theory?

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others.     

文本结构和时间应激对网页阅读绩效的影响

探讨了文本结构和时间应激对网页阅读绩效的影响效应。采用 2× 3被试间设计 ,自变量为文本结构和阅读时间 ,因变量为找到相关信息的时间及途径的额外节点数。结果发现 ,主效应及交互作用的影响均十分显著。其中 ,当阅读时间为 10和 2 0min时 ,超文本阅读的绩效均显著低于线性文本 ,而在 30min时两者无显著差异 ;对超文本 ,三种阅读时间的效应存在显著差异 ,而对线性材料 ,阅读时间的效应无显著差异。结论 :时间应激对超文本阅读绩效的影响更为明显     

Teaching Genesis: A Present-Day Approach Inspired by the Prophet Nathan

The prophets Nathan (2 Samuel 12:1–15) and John the Baptist (Mark 6:16–28) had comparable tasks before them: to convince their respective kings about the wrongs of taking somebody else's wife and marrying her. Nathan succeeded, while John failed and furthermore lost his life. What made the difference? One possible explanation is that Nathan proceeded in two steps: (1) Tell an interesting, nonthreatening story that nevertheless makes the point at issue; (2) transfer that message to the case at hand. In contrast, John used a direct approach, which raised apprehension, even fear (on the part of Herodias, the woman involved), and led to failure. That lesson has wider applications, as illustrated here for teaching the biblical Genesis narration. The other ingredient in this teaching is relational and contextual reasoning (RCR), the use of which is also indicated for other issues besides teaching Genesis.     

Logic Games are Complete for Game Logics

Game logics describe general games through powers of players for forcing outcomes. In particular, they encode an algebra of sequential game operations such as choice, dual and composition. Logic games are special games for specific purposes such as proof or semantical evaluation for first-order or modal languages. We show that the general algebra of game operations coincides with that over just logical evaluation games, whence the latter are quite general after all. The main tool in proving this is a representation of arbitrary games as modal or first-order evaluation games. We probe how far our analysis extends to product operations on games. We also discuss some more general consequences of this new perspective for standard logic.     

Memory of Past Beliefs and Actions

Two notions of memory are studied both syntactically and semantically: memory of past beliefs and memory of past actions. The analysis is carried out in a basic temporal logic framework enriched with beliefs and actions.     

The Undecidability of Grisin's Set Theory

We investigate a contractionless naive set theory, due to Grisin [11]. We prove that the theory is undecidable.     

Monotonicity in Practical Reasoning

Classic deductive logic entails that once a conclusion is sustained by a valid argument, the argument can never be invalidated, no matter how many new premises are added. This derived property of deductive reasoning is known as monotonicity. Monotonicity is thought to conflict with the defeasibility of reasoning in natural language, where the discovery of new information often leads us to reject conclusions that we once accepted. This perceived failure of monotonic reasoning to observe the defeasibility of natural-language arguments has led some philosophers to abandon deduction itself (!), often in favor of new, non-monotonic systems of inference known as `default logics'. But these radical logics (e.g., Ray Reiter's default logic) introduce their desired defeasibility at the expense of other, equally important intuitions about natural-language reasoning. And, as a matter of fact, if we recognize that monotonicity is a property of the form of a deductive argument and not its content (i.e., the claims in the premise(s) and conclusion), we can see how the common-sense notion of defeasibility can actually be captured by a purely deductive system.     

Toward an Alliance Between the Issue-Processing Approach and Pragma-Dialectical Analysis

On the approach to discussions of policy choices that treats such discussions as instances of issue-processing, the joint use of the logic of questions and the logic of rules gives precise formulation to two sorts of issues. To one sort of issue belong issue-circumscribing questions; to another sort, issues-simplicter, which consist of disjunctions of policy proposals – so many proposed social rules – that are answers, in the case of each disjunction, to a given issue-circumscribing question. Work in pragma-dialectics can take over the issue-processing approach; and by doing so add to the pragma-dialectical repertory further dimensions in the analysis of issues and in protocol-narratives of discussion. The analysis and narratives would now include accounts of how issue-circumscribing questions generate initial standpoints and how discussions sometimes end with compromises between standpoints. Further research questions follow about transformations of issues and the comparison of successive rounds of discussion. A narrative of one period of discussion during `the War on Drugs' in the United States illustrates these points.     

A Reinforcer Pathology perspective on relapse

The Reinforcer Pathology theory proposes conditions under which drugs emerge as excessively preferred reinforcers compared to other available reinforcers among drug users. The theory highlights 2 key variables as important determinants of drug preference: (a) excessive preference for immediate rewards (high discounting of future rewards); and (b) excessive valuation for addictive reinforcers (e.g., drugs). Two iterations of the Reinforcer Pathology theory exist with the latest iteration (i.e., Reinforcer Pathology 2.0) specifying that the temporal window of reinforcer integration (measured by delay discounting) is a determinant of reinforcer value. The 2 iterations of the Reinforcer Pathology theory are described. A novel insight and understanding of abstinence and relapse from a Reinforcer Pathology perspective, limitations, and future directions are discussed. The Reinforcer Pathology theory continues the long-standing efforts to scientifically understand and better define novel concepts and methods to further translational research and improve treatment outcomes. Exploring the complementary relation between the Reinforcer Pathology perspective and other current approaches could have a valuable effect.