How Not to Apply to College

Samples of letters written by college students are excerpted to demonstrate the deterioration of students' writing skills. The relative unimportance many college students and graduates attach to the art of writing letters of inquiry is emphasized. A checklist is provided to assist students in preparing letters requesting information from colleges and universities.     

How Mathematics Isn't Logic

If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting : nonuniform term substitution in logical sentences. 'Televisions are televisions' and 'TVs are televisions' neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical sentences and their synomic interceptions have identical factual content, which seems to exhaust semantic content. However, intercepting alters syntax by eliminating term recurrence, the sole strictly syntactic means of ensuring necessary term coextension, and thereby syntactically securing necessary truth. Interceptional necessity is lexical, a notational artifact. The denial of interception nonsynonymy and the disregard of term recurrence in logic link with many misconceptions about propositions, logical form, conventions, and metalanguages. Mathematics is distinct from logic: its truth is not syntactic; it is transmitted by synonym substitution; term recurrence has no essential role. The '=' of mathematics is an objectual relation between numbers; the '=' of logic marks a syntactic relation of coreferring terms.     

How Mathematics Propels the Development of Physical Knowledge

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of 5-year-olds. In Experiment 2, 11-year-olds solved problems with feedback. They were encouraged to use math or words to justify their answers. Children who used math developed an understanding superior to most adults, whereas children who used words did not. In Experiment 3, 9-year-olds solved problems with or without prompts to use math. Children encouraged to use math exhibited greater qualitative understanding, even though they were unable to discover metric proportions. The results indicate it is possible to design symbolic experiences to propel the development of physical understanding, thereby relating developmental psychology to instructional theory.     

中国逻辑如何影响中国传统数学(英文)

中国传统数学在中国古代逻辑特别是墨家逻辑的影响下,形成了自己的推理体系,即:以"以类合类"为基本方法,以"类"和"分类"为核心成分,以"推类"为主导推理形式。正是由于这一推理体系,使得中国传统数学在相当长的时期内保持世界的领先地位。因此,我们可以得出这样的结论:中国逻辑不是阻碍了中国传统数学进一步发展的因素,换句话说,中国传统数学所蕴含的逻辑方法并不是阻碍其进一步发展的原因。     

Two Examples of How the History of Mathematics Can Inform Theology

In several of his writings, Bernard Lonergan emphasized the study of mathematics and especially its history as being important for philosophy and theology. In this article, I offer two examples of how the history of mathematics might inform theology. My first example explores the disparities between Euclid's Elements and Aquinas' Summa Contra Gentiles. My second example applies the idea of incompleteness to the “good and necessary consequence” clause of the Westminster Confession of Faith.     

Children Apply Principles of Physical Ownership to Ideas

Adults apply ownership not only to objects but also to ideas. But do people come to apply principles of ownership to ideas because of being taught about intellectual property and copyrights? Here, we investigate whether children apply rules from physical property ownership to ideas. Studies 1a and 1b show that children (6–8 years old) determine ownership of both objects and ideas based on who first establishes possession of the object or idea. Study 2 shows that children use another principle of object ownership, control of permission—an ability to restrict others’ access to the entity in question—to determine idea ownership. In Study 3 , we replicate these findings with different idea types. In Study 4 , we determine that children will not apply ownership to every entity, demonstrating that they do not apply ownership to a common word. Taken together, these results suggest that, like adults, children as young as 6 years old apply rules from ownership not only to objects but to ideas as well.     

继发性的高血压线索来自于基本的临床检查

继发性高血压病因的检出和针对病因的治疗,不仅可以提高高血压的治愈率和控制率,有利于保护靶器官,还可以极大程度地减少医疗资源的浪费。基本的临床检查,如血、尿常规,血浆电解质,血糖,血脂,血尿酸和血清肌酐,可以为继发性高血压的诊断提供重要的线索。     

How Teachers Link Ideas in Mathematics Instruction Using Speech and Gesture: A Corpus Analysis

This research investigated how teachers express links between ideas in speech, gestures, and other modalities in middle school mathematics instruction. We videotaped 18 lessons (3 from each of 6 teachers), and within each, we identified linking episodes—segments of discourse in which the teacher connected mathematical ideas. For each link, we identified the modalities teachers used to express linked ideas and coded whether the content was new or review. Teachers communicated most links multimodally, typically using speech and gestures. Teachers’ gestures included depictive gestures that simulated actions and perceptual states, and pointing gestures that grounded utterances in the physical environment. Compared to links about new material, teachers were less likely to express links about review material multimodally, especially when that material had been mentioned previously. Moreover, teachers gestured at a higher rate in links about new material. Gestures are an integral part of teachers’ communication during mathematics instruction.     

继发性的高血压线索来自于基本的临床检查

继发性高血压病因的检出和针对病因的治疗,不仅可以提高高血压的治愈率和控制率,有利于保护靶器官,还可以极大程度地减少医疗资源的浪费.基本的临床检查,如血、尿常规,血浆电解质,血糖,血脂,血尿酸和血清肌酐,可以为继发性高血压的诊断提供重要的线索.     

How to Read Wittgenstein

"How to Read Wittgenstein" is a discussion of some misinterpretations that arise when Ludwig Wittgenstein's later works are read, not in their historical context, but as though they were written for a generation of philosophers influenced by G.E. Moore and ordinary language philosophy. The criticisms are directed primarily at Oswald Hanfling's "Critical Notice" in Philosophical Investigations 19:2 (April, 1996).     

How to Precisify Quantifiers

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition.     

如何看待科学主义

奇特的美国人,即为人类登月而崇拜科学,又有近一半的人不相信“进化论”,而相信各种各样的超自然现象。     

How to Reid Moore

Moore's 'Proof of an External World' has evoked a variety of responses from philosophers, including bafflement, indignation and sympathetic reconstruction. I argue that Moore should be understood as following Reid on a variety of points, both epistemological and methodological. Moreover, Moore and Reid are exactly right on all of these points. Hence what I present is a defence of Moore's 'Proof', as well as an interpretation. Finally, I argue that the Reid-Moore position is useful for resolving an issue that has recently received attention in epistemology, namely, how is it that one knows that one is not a brain in a vat?     

How to Understand Internalism

Internalism about practical reasons claims that there is a necessary connection between what an agent has reason to do and what he would be motivated to do if he were in privileged or optimal conditions. Internalism is traditionally supported by the claim that it alone can capture two (supposed) conditions of adequacy for any theory of practical reasons, that reasons must be capable of justifying actions, and that reasons must be capable of explaining intentional acts. Robert Johnson ( The Philosophical Quarterly , 49 (1999), pp. 53–71) has argued that versions of internalism which avoid obvious problems nevertheless fail to capture both conditions. I argue that Johnson's criticisms rest upon a misinterpretation of the 'explanatory condition', and I proceed to formulate a version of internalism which will allow practical reasons to have both justificatory and explanatory force.