A Logic for Reasoning about Relative Similarity

A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.     

Whiteheadian Societies and Peirce's Law of Mind: Actuality and Potentiality in the Cosmic Process

Abstract

A more suitable philosophical position to counter the claims of scientific materialism re the nature of physical reality can possibly be found in combining the metaphysics of A.N. Whitehead and C.S. Peirce. Peirce postulated a habit-forming tendency or inbuilt potentiality of the cosmic process as a whole to move over time toward ever greater organization and more complex structure. But he is vague on how “the law of the mind” applies to nature below the level of human self-awareness. Whitehead's notion of actual entities (momentary self-constituting subjects of experience) as the “final real things of which the world is made up” logically allows for some primitive form of subjectivity with the requisite potentiality for habit-formation at all levels of existence and activity within nature. In addition, Whitehead's notion of structured societies made up of subsocieties with a “regnant” subsociety seems philosophically to justify the new emphasis on bottom-up rather than top-down causation in the emergence of more complex levels of existence and activity within the life-sciences.     

Considering too few alternatives: The mental model theory of extensional reasoning

When solving a simple probabilistic problem, people tend to build an incomplete mental representation. We observe this pattern in responses to probabilistic problems over a set of premises using the conjunction, disjunction, and conditional propositional connectives. The mental model theory of extensional reasoning explains this bias towards underestimating the number of possibilities: In reckoning with different interpretations of the premises (logical rules, mental model theoretical, and, specific to conditional premises, conjunction and biconditional interpretation) the mental model theory accounts for the majority of observations. Different interpretations of a premise result in a build-up of mental models that are often incomplete. These mental models are processed using either an extensional strategy relying on proportions amongst models, or a conflict monitoring strategy. The consequence of considering too few possibilities is an erroneous probability estimate akin to that faced by decision makers who fail to generate and consider all alternatives, a characteristic of bounded rationality. We compare our results to the results published by Johnson-Laird, Legrenzi, Girotto, Legrenzi, and Caverni [Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]–88 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. doi:10 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1037 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]/0033 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]-295X Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].106 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].1 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].62 Johnson-Laird, P., Legrenzi, P., Girotto, V., Legrenzi, M., &; Caverni, J. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88. doi:10.1037/0033-295X.106.1.62[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], and we observe lower performance levels than those in the original article.     

Chances and frequencies in probabilistic reasoning: rejoinder to Hoffrage,Gigerenzer, Krauss,and Martignon

Do individuals unfamiliar with probability and statistics need a specific type of data in order to draw correct inferences about uncertain events? Girotto and Gonzalez (Cognition 78 (2001) 247) showed that naive individuals solve frequency as well as probability problems, when they reason extensionally, in particular when probabilities are represented by numbers of chances. Hoffrage, Gigerenzer, Krauss, and Martignon (Cognition 84 (2002) 343) argued that numbers of chances are natural frequencies disguised as probabilities, though lacking the properties of true probabilities. They concluded that we failed to demonstrate that naive individuals can deal with true probabilities as opposed to natural frequencies. In this paper, we demonstrate that numbers of chances do represent probabilities, and that naive individuals do not confuse numbers of chances with frequencies. We conclude that there is no evidence for the claim that natural frequencies have a special cognitive status, and the evolutionary argument that the human mind is unable to deal with probabilities.     

Children's understanding of human and super-natural mind

Barrett, Richert, and Driesenga [Barrett, J. L., Richert, R. A., & Driesenga, A. (2001). God's beliefs versus mother's: The development of nonhuman agents concepts. Child Development, 72(1), 50–65] have suggested that children are able to conceptualize the representational properties held by certain super-natural entities, such as God, before they achieve representational understanding of the human mind. The two experimental conditions of the present study aimed at cross-checking the above suggestion. One hundred and twenty children aged from 3 to 7 years were involved in both conditions. In the first, a modified perspective-taking and appearance-reality task, similar to that adopted in Barrett et al.'s study, was used. The task in the second addressed another aspect of representational understanding of the human mind, that is, the early emerging of the rule that knowledge is constrained by perception. The results of the study showed that younger children systematically treat God as a human protagonist regarding the representational properties they possess. Moreover, it was found that children are able to reason, accurately, about God's representational properties, only upon reaching their 5th year of age, when their representational understanding of the human mind becomes stable and robust.     

Quine’s Eliminativism and the Crystal Spheres

Quine’s eliminativist theory has largely been ignored by the philosophical community. This is highly regrettable because Quine’s theory is probably close to correct. Now, the probable correctness of Quine’s theory has an important consequence since, according to the theory, there are no mental entities (events, states, phenomena, properties, etc.) nor do such entities play any role in a scientific account of the relevant phenomena. But the hundreds or probably thousands of publications that deal with issues such as mental causation, the nature of qualia, supervenience of the mental, or multiple realizability, presume the existence of, or at least attribute a positive role to, mental entities. The probable correctness of Quine’s theory therefore suggests that all these publications are worthless and reading them is a waste of time just as reading studies about how crystal spheres can move planets is considered nowadays a waste of time.

The Myth of Reductive Extensionalism

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the ontology of such phenomena is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion.

儒家文化对当前中国心理健康服务实践的影响

心理健康服务是以心理学的理论和方法为主导来维护与促进人们心理健康的活动。它与个人的心理因素和社会文化因素有必然联系, 中国心理健康服务植根于中国文化的土壤之中, 它本身就是文化的产物。而儒家文化作为中国社会的主流文化, 它在中国心理健康服务过程中具有表征、构建、指导、唤起功能; 对心理健康服务者和被服务者的人格、应对方式以及服务态度和行为产生直接和间接影响。中国心理健康服务模式与儒家文化传统的关系问题实际上涉及的是心理健康服务与文化的普遍性与特殊性问题。构建适合中国文化土壤的心理健康服务体系需要研究儒家文化传统对心理健康服务模式的观念、理论及实践操作层面的作用和影响。     

Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities

Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. STATEMENT OF MODAL PLATONISM. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.