Human Cognitive Closure and Mysterianism: Reply to Kriegel

In this paper, I respond to Kriegel’s criticism of McGinn’s mysterianism (the thesis that humans are cognitively closed with respect to the solution of the mind-body problem). Kriegel objects to a particular argument for the possibility of human cognitive closure and also gives a direct argument against mysterianism. I intend to show that neither the objection nor the argument is convincing.     

A Significant ‘False Perception’ of Wittgenstein’s Draft on Mind’s Eye

If we read the Tractatus logico-philosophicus according to the decimal numbering of its propositions, we may understand, finally, the section about the self and the limits of language and world. Proposition 5.64 follows 5.63 (not 5.634); 5.634 follows 5.633 (not 5.6331); and so on. Thus, it becomes clear that the picture of the visual field (TLP 5.6331) cannot be what scholars have always quoted and discussed, i.e. a draft of an eye inside its field of sight. Actually, Wittgenstein’s original drafts depict (to criticise it) the ordinary way of representing the visual field. Following him, the field of vision is ‘without limits’; it does not have a form that implies the existence of an eye, as far as the phenomenological experience does not have a form that implies the existence of an ‘I’. As a result, the current reproductions of the 5.6331 image must be rectified, and all references to this similitude should be radically amended.     

Trivial Languages

I here present and defend what I call the Triviality Theory of Truth (TT), to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth (IT). A specific formulation of (TT) is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for (TT) specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with (TT) as I understand it. Finally, I consider a normative reading of their objection and offer a response.     

Solving Linear Boundary Value Problems Via Non-commutative Gröbner Bases

A new approach for symbolically solving linear boundary value problems is presented. Rather than using general-purpose tools for obtaining parametrized solutions of the underlying ODE and fitting them against the specified boundary conditions (which may be quite expensive), the problem is interpreted as an operator inversion problem in a suitable Banach space setting. Using the concept of the oblique Moore—Penrose inverse, it is possible to transform the inversion problem into a system of operator equations that can be attacked by virtue of non-commutative Gröbner bases. The resulting operator solution can be represented as an integral operator having the classical Green’s function as its kernel. Although, at this stage of research, we cannot yet give an algorithmic formulation of the method and its domain of admissible inputs, we do believe that it has promising perspectives of automation and generalization; some of these perspectives are discussed.     

Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the finite simple group classification

Davenport’s Problem asks:What can we expect of two polynomials,over Z,with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport,Lewis and Schinzel.By bounding the degrees,but expanding the maps and variables in Davenport’s Problem,Galois stratification enhanced the separated variable theme,solving an Ax and Kochen problem from their Artin Conjecture work.Denef and Loeser applied this to add Chow motive coefficients to previously introduced zeta functions on a diophantine statement.By restricting the variables,but leaving the degrees unbounded,we found the striking distinction between Davenport’s problem over Q,solved by applying the Branch Cycle Lemma,and its generalization over any number field,solved by using the simple group classification.This encouraged Thompson to formulate the genus 0 problem on rational function monodromy groups.Guralnick and Thompson led its solution in stages.We look at two developments since the solution of Davenport’s problem.Stemming from MacCluer’s 1967 thesis,identifying a general class of problems,including Davenport’s,as monodromy precise.R(iemann)E(xistence)T(heorem)’s role as a converse to problems generalizing Davenport’s,and Schinzel’s (on reducibility).We use these to consider:Going beyond the simple group classification to handle imprimitive groups,and what is the role of covers and correspondences in going from algebraic equations to zeta functions with Chow motive coefficients.     

The Problem of Emotional Significance

What does it mean to say that an emotional response fits the situation? This question cannot be answered simply by specifying the core relational theme (loss or risk, say) associated with each emotion: we must also explain what constitutes an emotionally significant loss or risk. It is sometimes suggested that emotionally significant situations are those that bear on the subject’s interests or concerns. I accept that this claim is plausible for some emotional responses, and I propose a particular way of interpreting it. I suggest that, for many emotions, emotional significance is determined by the subject’s likes and dislikes – that is, settled dispositions to find a certain situation pleasant or distressing. I contrast this account with other preference-based accounts and with an account that appeals to the subject’s interests. I argue that we should prefer the likes-based account to these rival views.     

A killer theorem

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The mathematical ethicist

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

A subprime lending market primer

Opening a copy of TheMathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Mangum,P.I.

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway —a mathematical journal, or what? ” Or you may ask, “Where am I? ” Or even “Who am I? ” This sense of disorientation is at its most acute when you open to Colin Adams ’s column. Relax. Breathe regularly. It ’s mathematical, it ’s a humor column, and it may even be harmless.     

This theorem is big

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Rumpled stiltskin

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Journey to the center of mathematics

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The Math fall fashion preview

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Trial and error

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?“ Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

More from the mathematical ethicist

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column.Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

The three little pigs

Opening a copy ofThe Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column.Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

Dynamic pricing for perishable items with costly price adjustments

Dynamic pricing is widely adopted in inventory management for perishable items, and the corresponding price adjustment cost should be taken into account. This work assumes that the price adjustment cost comprises of a fixed component and a variable one, and attempts to search for the optimal dynamic pricing strategy to maximize the firm’s profit. However, considering the fixed price adjustment cost turns this dynamic pricing problem to a non-smooth optimal control problem which cannot be solved directly by Pontryagin’s maximum principle. Hence, we first degenerate the original problem into a standard optimal control problem and calculate the corresponding solution. On the basis of this solution, we further propose a suboptimal pricing strategy which simultaneously combines static pricing and dynamic pricing strategies. The upper bound of profit gap between the suboptimal solution and the optimal one is obtained. Numerical simulation indicates that the suboptimal pricing strategy enjoys an efficient performance.     

Williams college student course survey form: Instructor modified version

Opening a copy of The Mathematical Intelligenceryou may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Colin Adams’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be harmless.     

运输问题的合作对策求解方法

产地间或销地间往往存在竞争,在这种情况下,使用运输问题最优化方法是不合理的。因此,从个体理性的视角提出运输问题的合作对策求解方法,方法将运输问题看作是一个博弈问题,各个产地或销地是博弈的局中人,求解其纳什均衡与纳什讨价还价解。在此基础上,说明了运输问题的非合作形式是一个指派问题,并证明指派问题的最优解是一个纳什均衡点。接着,通过实验验证运输问题的最优解是一个纳什讨价还价解,满足产地或销地的自身利益。在此基础上,针对纳什讨价还价解不唯一的问题,从决策者的视角给出最大可能激励成本的计算方法。最后,为弥补纳什讨价还价解不唯一及纳什讨价还价解不允许出现子联盟的缺陷,给出运输收益分配或成本分摊的Shapely值计算方法。