Do people combine the parity- and five-rule checking strategies in product verification?

The basic question of the present experiment was whether people use a combination of arithmetic problem solving strategies to reject false products to multiplication problems or whether they simply use the single most efficient strategy. People had to verify true and false, five and non-five arithmetic problems. Compared with no-rule violation problems, people were faster with (a) five problems that violated the five rule (i.e., N×5=number with 5 or 0 as the final digit; e.g., 15 × 4=62), (b) problems that violated the parity rule (i.e., to be true, a product must be even if either or both of its multipliers is even; otherwise, it must be odd; 4 × 38=149), and (c) problems that violated both the parity and five rules (e.g., 29 × 5=142). Finally, people were equally fast and accurate when they solved two-rule violation problems than when they solved five-rule violation problems, and faster for those two types of problems than for parity-rule violation problems. Clearly, people use the single most efficient strategy when they reject false product to multiplication problems. This result has implications for our understanding of strategy selection in both arithmetic in particular and human cognition in general. Received: 18 October 1999 / Accepted: 27 January 2000     

Pattern recognition makes search possible: Comments on Holding (1992)

Chase and Simon's chunking theory of expert memory, which emphasizes the role of pattern recognition in problem solving, has attracted much attention in cognitive psychology. Holding advanced a series of criticisms that, taken together, purported to refute the theory. Two valid criticisms – that chunk size and LTM encoding were underestimated – are dealt with by a simple extension of the theory. The remainder of Holding's criticisms either are not empirically founded or are based on a misunderstanding of the chunking theory and its role in a comprehensive theory of skill. Holding's alternative SEEK theory, which emphasizes the role of search, lacks key mechanisms that could be implemented by the type of pattern recognition proposed by Chase and Simon. Received: 3 September 1997 / Accepted: 28 January 1998     

Risk, Rights, and Restitution

In “Imposing Risks,” Judith Thomson gives a case in which, by turning on her stove, she accidentally causes her neighbor’s death. She claims that both the following are true: (1) she ought not to have caused her neighbor’s death; (2) it was permissible for her to turn her stove on. In this paper it is argued that it cannot be that both (1) and (2) are true, that (2) is true, and that therefore (1) is false. How this is so is explained, and the implications of this position regarding the relation between rights and duties is explored.     

The inconceivability of zombies

I argue for the claim that if Lewis’s regularity theory of laws were true, we could not know any positive law statement to be true. Premise 1: According to that theory, for any law statement true of the actual world, there is always a nearby world where the law statement is false (a world that differs with respect to one matter of particular fact). Premise 2: One cannot know a proposition to be true if it is false in a nearby world (the epistemological safety principle). The conclusion that no law statement can be known to be true follows immediately from the two premises.     

Trivalent Semantics and the Vaguely Vague

Michael Tye responds to the problem of higher-order vagueness for his trivalent semantics by maintaining that truth-value predicates are “vaguely vague”: it’s indeterminate, on his view, whether they have borderline cases and therefore indeterminate whether every sentence is true, false, or indefinite. Rosanna Keefe objects (1) that Tye’s argument for this claim tacitly assumes that every sentence is true, false, or indefinite, and (2) that the conclusion is any case not viable. I argue – contra (1) – that Tye’s argument needn’t make that assumption. A version of her objection is in fact better directed against other arguments Tye advances, though Tye can absorb this criticism without abandoning his position’s core. On the other hand, Keefe’s second objection does hit the mark: embracing ‘vaguely vague’ truth-value predicates undermines Tye’s ability to support validity claims needed to defend his position. To see this, however, we must develop Keefe’s remarks further than she does.     

Warrant <Emphasis Type="Italic">does</Emphasis> entail truth

Let ‘warrant’ denote whatever precisely it is that makes the difference between knowledge and mere true belief. A current debate in epistemology asks whether warrant entails truth, i.e., whether (Infallibilism) S’s belief that p is warranted only if p is true. The arguments for infallibilism have come under considerable and, as of yet, unanswered objections. In this paper, I will defend infallibilism. In Part I, I advance a new argument for infallibilism; the basic outline is as follows. Suppose fallibilism is true. An implication of fallibilism is that the property that makes the difference between knowledge and mere belief (which I dub ‘warrant*’) is the conjunctive property being warranted and true. I show that this implication of fallibilism conflicts with an uncontroversial thesis we have learned from reflection on Gettier cases: that nonaccidental truth is a constituent of warrant*. It follows that infallibilism is true. In the second part of the paper, I present and criticize a new argument against infallibilism. The argument states that there are plausible cases where, intuitively, the only thing that is keeping a belief from counting as knowledge is the falsity of that belief. Furthermore, it is plausible that such a belief is warranted and false. So, the argument goes, infallibilism is false. I show that this argument fails.     

A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning

Perhaps the most common criterion for partitioning a data set is the minimization of the within-cluster sums of squared deviation from cluster centroids. Although optimal solution procedures for within-cluster sums of squares (WCSS) partitioning are computationally feasible for small data sets, heuristic procedures are required for most practical applications in the behavioral sciences. We compared the performances of nine prominent heuristic procedures for WCSS partitioning across 324 simulated data sets representative of a broad spectrum of test conditions. Performance comparisons focused on both percentage deviation from the “best-found” WCSS values, as well as recovery of true cluster structure. A real-coded genetic algorithm and variable neighborhood search heuristic were the most effective methods; however, a straightforward two-stage heuristic algorithm, HK-means, also yielded exceptional performance. A follow-up experiment using 13 empirical data sets from the clustering literature generally supported the results of the experiment using simulated data. Our findings have important implications for behavioral science researchers, whose theoretical conclusions could be adversely affected by poor algorithmic performances.     

Spatial orientation by mental transformation

Across three experiments, college students read narratives describing two-dimensional horizontal, sagittal, or coronal environments, each with seven objects in surrounding directions (at 45° angles). Then they responded from memory to questions about which objects were in specific directions. The distributions of error rates and response times were compared with distributions predicted by a mental transformation model and two verbal-spatial decoding and retrieval models. The data fit the predictions of a modified mental transformation model (mental transformation plus 180° exception) better than the predictions of either verbal-spatial model. This was true even though the environment was presented narratively rather than perceptually, and it was true for both the vertical planes in addition to the more typical horizontal plane. Received: 8 August 1997 / Accepted: 2 June 1998     

Philosophy, the “unknown knowns,” and the public use of reason

There are not only true or false solutions, there are also false questions. The task of philosophy is not to provide answers or solutions, but to submit to critical analysis the questions themselves, to make us see how the very way we perceive a problem is an obstacle to its solution. This holds especially for today’s public debates on ecological threats, on lack of faith, on democracy and the “war on terror”, in which the “unknown knowns”, the silent presuppositions we are not aware of, determine our acts.     

Mistaking the instance for the rule: A critical analysis of the truth-table evaluation paradigm

Many studies probe for interpretations of < if A then C> by having people evaluate truth-table cases (<A and C>, < A and not-C>, < not-A and C>, < not-A and not-C>) as making the rule true or false, or being irrelevant. We argue that a single case can never prove a general rule to be true, as philosophy of science has taught any researcher. Giving participants the impossible “true” option would therefore bias results away from this response. In Experiment 1 people judged instead whether cases make a rule false, do not make the rule false, or are irrelevant to the rule. The experimental group (N = 44) showed a significant increase in not-false responses compared with true responses of the control group (N = 39). In Experiments 2 and 3 the experimental groups judged whether cases make a rule true, corroborate it (i.e., make the rule more plausible, but neither true nor false), make it false, or are irrelevant. There was a significant reduction of irrelevant responses as compared to the default true/false/irrelevant task for the control groups. Even < A and C> cases were often no longer considered to make an < if A then C> rule true and were correctly judged to corroborate (vs. verify) rules. Results corroborate our conceptual analyses of the unsuitable “true” response option and put into question arguments that hinge on the presumed likelihood by which people consider truth contingencies to make a rule “true”.     

Darwin and moral realism: survival of the iffiest

This paper defends moral realism against Sharon Street’s “Darwinian Dilemma for Realist Theories of Value” (this journal, 2006). I argue by separation of cases: From the assumption that a certain normative claim is true, I argue that the first horn of the dilemma is tenable for realists. Then, from the assumption that the same normative claim is false, I argue that the second horn is tenable. Either way, then, the Darwinian dilemma does not add anything to realists’ epistemic worries.     

Using story contexts to bias children’s true and false memories

The effects of embedding standard Deese/Roediger-McDermott (DRM) lists into stories whose context biased interpretation either toward or away from the overall themes of the DRM lists on both true and false recognition were investigated with 7- and 11-year-olds. These biased story contexts were compared with the same children’s susceptibility to false memory illusions using the standard DRM list presentation paradigm. The results showed the usual age effects for true and false memories in the standard DRM list paradigm, where 11-year-olds exhibited higher rates of both true and false recognition compared with the 7-year-olds. Importantly, when DRM lists were embedded in stories, these age effects disappeared for true recognition. For false recognition, although developmental differences were attenuated, older children were still more susceptible to false memory illusions than younger children. These findings are discussed in terms of current theories of children’s false memories as well as the role of themes and elaboration in children’s memory development.     

Mental multiplication and working memory

This paper is concerned with the role of working memory resources in mental multiplication. In two experiments a dual-task paradigm was used. In the first experiment neutral tapping was contrasted to three modalityspecific secondary tasks: Irrelevant speech and articulatory suppression were used to disrupt the phonological loop and a visuo-spatial tapping was used to disrupt the visuo-spatial sketchpad. Multiplication sums needed to be solved mentally and results needed to be spoken aloud. Sums varied in difficulty (easy, e.g., 3 x 4 =, difficult, e.g., 8 x 17 =). Results from the first experiment revealed declines in performance on difficult sums under articulatory suppression but no interference effect for easy sums. To investigate the role of central executive processes, a second experiment extended the range of interference conditions to a central executive interference task (random letter generation). Now articulatory suppression and random generation caused a decrease of performance on difficult sums. In addition, performance on easy sums was negatively impacted by random letter generation as well. We infer that solving complex multiplication sums demands phonological loop and central executive processes, whereas retrieving numerical facts in solving simple multiplication sums requires only central executive processes. We found no evidence of modality-specific access to numerical facts stored in long-term memory.     

When it hurts to be misled: A Stroop-like effect in a simple addition production task

In four experiments, subjects saw simple addition equations (e.g., 3 + 4 = 9) and produced the sums while ignoring the presented answer. If the presented answer was false, subjects took longer to produce the sum, as compared with when the presented answer was true (Experiment 1), when there was no answer presented (blanks; Experiment 2), when a letter was presented (Experiment 3), and when a symbol was presented (Experiment 4). The results suggest that subjects were unable to ignore the presented answers, which raises problems for theories of arithmetic verification (i.e., deciding whether 3 + 4 = 9 is true or false) that claim that subjects verify equations by first producing the sum and then comparing the produced sum with the presented answer. Our results are more compatible with theories that claim that in verification and production, an arithmetic knowledge base is used in different ways.