I argue against theories that attempt to reduce scientific representation to similarity or isomorphism. These reductive theories aim to radically naturalize the notion of representation, since they treat scientist's purposes and intentions as non-essential to representation. I distinguish between the means and the constituents of representation, and I argue that similarity and isomorphism are common but not universal means of representation. I then present four other arguments to show that similarity and isomorphism are not the constituents of (...) scientific representation. I finish by looking at the prospects for weakened versions of these theories, and I argue that only those that abandon the aim to radically naturalize scientific representation are likely to be successful. (shrink)
This paper investigates the interpretation of counterfactual conditionals. The main goal of the paper is to provide an account of the semantic role of similarity in the evaluation of counterfactuals. The paper proposes an analysis according to which counterfactuals are treated as predications “ de re ” over past situations in the actual world. The relevant situations enter semantic composition via the interpretation of tense. Counterfactuals are treated as law-like conditionals with de re predication over particular facts. Similarity (...) with respect to particular facts is ensured by the semantics of tense in interaction with the modal, while the modal itself is responsible for invoking laws. In the paper, various arguments are provided to support a local view of similarity over the global approach found in semantics along the line of Lewis’s and Stalnaker’s. Arguments are also provided tying the evaluation of similarity to the interpretation of tense. Finally, arguments are provided to show that in key cases, the approaches make comparable predictions. (shrink)
A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...) the grounds that the benefits outweigh the costs every time, the decision-maker therefore reveals intransitive preferences, since once she has taken it this large number of times, she would prefer to return to the situation in which she had never taken the action at all. We defend transitivity against two versions of this argument: one in which it is assumed that taking the action one more time never has any perceptible cost, and one in which it is assumed that the cost of taking the action, though (sometimes) perceptible, is so small as to be outweighed at every step by the significant benefit. We argue that the description of the choice situation in the first version involves a contradiction. We also argue that the reasoning used in the second version is a form of similarity-based decision-making. We argue that when the consequences of using similarity-based decision-making are brought to light, rational decision-makers revise their preferences. We also discuss one method that might be used in performing this revision. (shrink)
Anything is similar to anything, provided the respects of similarity are allowed to be gerrymandered or gruesome, as Goodman observed.2 But similarity in non-gruesome or—as I shall say—genuine respects is much less ecumenical. Colors, it seems, provide a compelling illustration of the distinction as applied to similarities among properties.3 For instance, in innumerable gruesome respects, blue is more similar to yellow than to purple. But in a genuine respect, blue is more similar to purple than to yellow (genuinely (...) more similar, as I shall sometimes put it). (shrink)
In this paper I will examine two responses to the argument from marginal cases; the argument from kinds and the similarity argument. I will argue that these arguments are insufficient to show that all humans have moral status but no animals do. This does not prove that animals have moral status but it does shift the burden of proof onto those who want to maintain that all humans are morally considerable, but no animals are.
A summary of recent experimental results shows that entanglement can be generated more easily than before, and that there are improved chances for its persistence. An eminent finding of Generalised Quantum Theory is the insight that the notion of entanglement can be extended, such that, e.g., psychological or psychophysical problem areas can be included, too. First, a general condition for entanglement to occur is given by the term ‘common prearranged context’. A formalised treatment requires a quantitative definition of the (...) class='Hi'>similarity or dissimilarity between two complex structures which takes their internal structures into account. After some specific remarks on distance, metrics, and semi-metrics in mathematics, a procedure is described for setting up a similarity function with the required properties. This procedure is in analogy with the two-step character of measurement and with the well-known properties of perspective notions. A general methodology can be derived for handling perspective notions. Finally, these concepts supply heuristic clues towards a formalised treatment of the notions of ‘meaning’ and ‘interpretation’. (shrink)
In “Backward Causation and the Stalnaker–Lewis Approach to Counterfactuals,” Analysis 62:191–7, (2002), Michael Tooley argues that if a certain kind of backward causation is possible, then a Stalnaker–Lewis comparative world similarity account of the truth conditions of counterfactuals cannot be sound. In “Tooley on Backward Causation,” Analysis 63:157–62, (2003), Paul Noordhof argues that Tooley’s example can be reconciled with a Stalnaker–Lewis account of counterfactuals if the comparative world similarity relation on which the Stalnaker–Lewis account relies is allowed to (...) be antecedent-relative. In this paper I show that taking comparative world similarity to be antecedent-relative results in a formal semantics which is a comparative world similarity semantics in name only. (shrink)
The partitions of a given set stand in a well known one-to-onecorrespondence with the equivalence relations on that set. We askwhether anything analogous to partitions can be found which correspondin a like manner to the similarity relations (reflexive, symmetricrelations) on a set, and show that (what we call) decompositions – of acertain kind – play this role. A key ingredient in the discussion is akind of closure relation (analogous to the consequence relationsconsidered in formal logic) having nothing especially to (...) do with thesimilarity issue, and we devote a final section to highlighting some ofits properties. (shrink)
I call anti-resemblism the thesis that independently of any contextual specification there is no determinate fact of the matter about the comparative overall similarity of things. Anti-resemblism plays crucial roles in the philosophy of David Lewis. For instance, Lewis has argued that his counterpart theory is anti-essentialist on the grounds that counterpart relations are relations of comparative overall similarity and that anti-resemblism is true. After Lewis committed himself to a form of realism about natural properties he maintained that (...) anti-resemblism is true about the relations of overall similarity that enter his counterpart theory and his analysis of counterfactuals. However, in this article I argue that Lewis’s account of degrees of naturalness for properties combined with his modal realism entails that anti-resemblism is false. The Lewisian must amend Lewis’s system if she aims to benefit from the alleged virtues of anti-resemblism. I consider two ways of amending it, neither of which is a free lunch. (shrink)
In this paper I present some difficulties for Lewis’s and similar theories of counterfactuals, and suggest that the problem lies in the notion of absolute similarity. In order to explain the problem, I discuss the relation between Lewis’s and Goodman’s theory, and show that the two theories are not related in the way Lewis thought they were.
This study shows how precise simple analytical solutions for the generalized Dirac equation with repulsive vector and attractive energy-dependent Lorentz scalar potentials, position-dependent mass potential, and a tensor interaction term can be obtained within the framework of both similarity transformation and the asymptotic iteration methods. These methods yield a significant improvement over existing approaches and provide more plausible and applicable ways in explaining the pseudospin symmetry’s breaking mechanism in nuclei.
This article examines the role of similarity in the hybridization of concepts, focusing on hybrid products as an applied test case. Hybrid concepts found in natural language, such as singer songwriter, typically combine similar concepts, whereas dissimilar concepts rarely form hybrids. The hybridization of dissimilar concepts in products such as jogging shoe mp3 player and refrigerator TV thus poses a challenge for understanding the process of conceptual combination. It is proposed that models of conceptual combination can throw light on (...) the judged future success and desirability of hybrid products in general. The composite prototype model proposes two stages of conceptual combination. In the first stage, the concepts are aggregated into an additive hybrid, simply by forming the union of the two sets of attributes. In the second stage, any conflicting attributes are identified and resolved, often with the introduction of emergent attributes, resulting in an integrative hybrid. Across four studies that varied the similarity and type of hybrid products, similar and integrative hybrids were valued more than dissimilar and additive hybrids. Critically, though, dissimilar hybrids were also highly valued if they were integrative. Results supported the two stages proposed by the composite prototype model, and implications for other models of hybrid formation are discussed. (shrink)
We suggest to define objective probabilities by similarity-weighted empirical frequencies, where more similar cases get a higher weight in the computation of frequencies. This formula is justified intuitively and axiomatically, but raises the question, which similarity function should be used? We propose to estimate the similarity function from the data, and thus obtain objective probabilities. We compare this definition to others, and attempt to delineate the scope of situations in which objective probabilities can be used.
The focus of this paper is two-fold. First, similarities generated from six semantic models were compared to human ratings of paragraph similarity on two datasets—23 World Entertainment News Network paragraphs and 50 ABC newswire paragraphs. Contrary to findings on smaller textual units such as word associations (Griffiths, Tenenbaum, & Steyvers, 2007), our results suggest that when single paragraphs are compared, simple nonreductive models (word overlap and vector space) can provide better similarity estimates than more complex models (LSA, Topic (...) Model, SpNMF, and CSM). Second, various methods of corpus creation were explored to facilitate the semantic models’ similarity estimates. Removing numeric and single characters, and also truncating document length improved performance. Automated construction of smaller Wikipedia-based corpora proved to be very effective, even improving upon the performance of corpora that had been chosen for the domain. Model performance was further improved by augmenting corpora with dataset paragraphs. (shrink)
We deal with the approach, initiated by Rubinstein, which assumes that people, when evaluating pairs of lotteries, use similarity relations. We interpret these relations as a way of modelling the imperfect powers of discrimination of the human mind and study the relationship between preferences and similarities. The class of both preferences and similarities that we deal with is larger than that considered by Rubinstein. The extension is made because we do not want to restrict ourselves to lottery spaces. Thus, (...) under the above interpretation of a similarity, we find that some of the axioms imposed by Rubinstein are not justified if we want to consider other fields of choice theory. We show that any preference consistent with a pair of similarities is monotone on a subset of the choice space. We establish the implication upon the similarities of the requirement of making indifferent alternatives with a component which is zero. Furthermore, we show that Rubinstein's general results can also be obtained in this larger class of both preferences and similarity relations. (shrink)
Primate inferior temporal (IT) cortex is thought to contain a high-level representation of objects at the interface between vision and semantics. This suggests that the perceived similarity of real-world objects might be predicted from the IT representation. Here we show that objects that elicit similar activity patterns in human IT tend to be judged as similar by humans. The IT representation explained the human judgments better than early visual cortex, other ventral stream regions, and a range of computational models. (...) Human similarity judgments exhibited category clusters that reflected several categorical divisions that are prevalent in the IT representation of both human and monkey, including the animate/inanimate and the face/body division. Human judgments also reflected the within-category representation of IT. However, the judgments transcended the IT representation in that they introduced additional categorical divisions. In particular, human judgments emphasized human-related additional divisions between human and nonhuman animals and between man-made and natural objects. Human IT was more similar to monkey IT than to human judgments. One interpretation is that IT has evolved visual feature detectors that distinguish between animates and inanimates and between faces and bodies because these divisions are fundamental to survival and reproduction for all primate species, and that other brain systems serve to more flexibly introduce species-dependent and evolutionarily more recent divisions. (shrink)
Case-based reasoning has played an important role in legal reasoning systems. As one criteria for similarity of cases, temporal relationsamong affairs in legal cases should be compared. Thus far in many legalreasoning systems, cases have been described as sequences of pointwiseevents, or at best, simple time intervals, and they have been related bypredicates such as before, after, while,and so on. However, such relations may depend on each implementer'spersonal view, and also require much labor to write down by hand. In (...) this paper, we first propose a classification of affair types by their temporal features, and according to those types, we propose several assumption rules that prescribe the temporal relations between affair types. The temporal relations are automatically generated by these rules. Thereafter, we discuss how thesetemporal relations work in the comparison of similarity of cases. Inthe process of comparison, inadequate temporal relations need to beamended. For this purpose, we introduce revision rules, that refute theresults of assumption rules. (shrink)
The notion of order as a universal and fundamental conceptual category is discussed as being based on sets of similar differences and different similarities. A discussion of relationships between order and disorder is followed by a proposal for a mathematical theory based on non-ordinality which could also have relevance for indistinguishables in physics.
Berit Brogaard and Joe Salerno (2008) have defended the validity of counterfactual hypothetical syllogism (CHS) within the Stalnaker-Lewis account. Whenever the premisses of an instance of CHS are non-vacuosly true, a shift in context has occurred. Hence the standard counterexamples to CHS suffer from context failure. Charles Cross (2011) rejects this argument as irreconcilable with the Stalnaker-Lewis account. I argue against Cross that the basic Stalnaker-Lewis truth condition may be supplemented in a way that makes (CHS) valid. Yet pace Brogaard (...) and Salerno, there are alternative ways of spelling out the basic truth condition which are standard in most debates; and given these ways, the counterexamples to CHS are successful. (shrink)
Logic’s historically central mission has been to provide formally precise descriptions of logical consequence. This was done with two broad expectations in mind. One was that a pre-theoretically recognizable concept of consequence would be present in the ensuing formalization. The other was that the formalization would be mathematically mature. The first expectation calls for conceptual adequacy. The other calls for technical virtuosity. The record of the past century and a third discloses a tension between the two. Accordingly, logicians have sought (...) a reasoned, if delicate, rapprochement, one in which each expectation would be given its due, but well-short of free sway. Recent developments have imperiled this perestroika. One is logic’s massive and often rivalrous pluralism, and the cheapening relativism to which it beckons. This is exacerbated by the long-acknowledged part that the formal representations of logic distort the logical particles of natural language. The present paper discusses what might be done about this. (shrink)