There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject (...) and predicate classes and their complement classes are non-empty for all the propositions we admit. I briefly indicate the room for continued controversy over how properly to interpret Aristotle?s statements regarding these inferences, but find some plausibility in the views of Manley Thompson and A.N.Prior that Aristotle had in mind a particular arrangement of existential import unfamiliar to most contemporary logicians. (shrink)

When Peter Strawson subtitled the most celebrated book in ordinary language philosophy, Individuals, ‘An essay in descriptive metaphysics’, he shocked mainly for having reintroduced ‘metaphysics’ into intellectually respectable English a quarter-century after A.J. Ayer had consigned it to the logical positivists' index of forbidden philosophical words . Few at the time appreciated the import of the modifiers ‘descriptive’ and its opposite, ‘revisionary’. Now, another half century on, philosophers have come around to Bertrand Russell's original view that both the ordinary language (...) philosophy Strawson championed and the ideal scientific language philosophy Ayer championed offer alternative metaphysical visions. The remaining question of philosophical interest is what hangs in the balance between a descriptive and revisionary approach to metaphysics – or, for that matter, any branch of philosophy. This paper critically examines the currently dominant descriptive approach from a revisionary standpoint, initially relying on the terms Strawson uses to frame the distinction, and then moving outward to consider its implications for our understanding of the history of modern philosophy, especially the ‘naturalist’ sensibility that has been especially influential in analytic social epistemology. (shrink)

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the premises, (...) it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

Four ordering systems have been used most frequently in taxonomy: (1) special purpose classifications, (2) downward classifications (identification schemes), (3) upward or grouping classifications (traditional), and (4) Hennigian phylogenetic systems. The special properties of these four systems are critically evaluated. Grouping classifications and phylogenetic systems have very different objectives: the former the documentation of similarity and closeness of relationship, the latter of phylogeny. Both are legitimate ordering systems.

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...) than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes. (shrink)

On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...) clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice. (shrink)

One way to determine the quality and pace of change in a science as it undergoes a major transition is to follow some feature of it which remains relatively stable throughout the process. Following the chosen item as it goes through reinterpretation permits conclusions to be drawn about the nature and scope of the broader change in question. In what follows, this device is applied to the change which took place in logic in the mid-nineteenth century. The feature chosen as (...) the focal point is the categorical syllogism. (shrink)

This paper is about the mode of being of names. The paper begins by explaining why the joke is on commentators who see Lewis Carroll's White Knight as applying the use/mention distinction. Then it argues that the real problem with the distinction is that the idea that names are used to mention what they name depends on mistakenly conceiving of language as existing autonomously; and that philosophers have this conception because they fail to appreciate what they are doing when they (...) philosophise about language. This failure also explains why philosophers mistakenly think of any manifestation of a name as a (physical) token. (shrink)

ArgumentA growing cross-disciplinary literature has acknowledged the importance of verbal-visual interaction in the creation and communication of scientific texts. I contend that the proper understanding of these texts must flow from a hermeneutic model that takes verbal-visual interaction seriously, one that is firmly grounded in cognitive constraints and affordances. The model I propose has two modules, one for perception, derived from Gestalt psychology, the other for cognition, derived from Peirce's semiotics. I apply this model to an important but largely neglected (...) text in the history of nineteenth-century science, Charles Lyell'sThe Geological Evidences of the Antiquity of Man, and to two accounts by well-respected historians of science, both of the same key discovery in quantum physics. In doing so, I hope to demonstrate the advisability of incorporating the exegetical practices my model entails into the everyday practices of historians of science. (shrink)

According to the traditional account Mendel's paper on pea hybrids reported a study of inheritance and its laws. Hence, Mendel came to be known as The Father of Genetics. This paper demonstrates that, in fact, Mendel's objective in his research was finding the empirical laws which describe the formation of hybrids and the development of their offspring over several generations. Having found these laws (and not the laws of inheritance that he is generally credited with) he proposed a theoretical scheme (...) involving the formation of germinal and pollen cells in hybrids and their combination in fertilization competent to explain why his laws took the form that they did. Mendel's research shows a pattern of development closely paralleling the stages of empirical investigation beginning at the level of qualitative description in common language rising through four levels of increasing abstraction and culminating in a fifth level, his simple mechanical theory. This mechanism met all the tests that a theory of this type must pass. In that respect Mendel was highly successful and this success might be the reason why he did not push his theory to a higher level, a sixth level involving the use of particulate determiners; despite this fact, Mendel was credited with having taken exactly that step. (shrink)

Logical psychologism is the position that logic is a special branch of psychology, that logical laws are descriptíons of experience to be arrived at through observation, and are a posteriori.The accepted arguments against logical psychologism are effective only when directed against this extreme version. However, the clauses in the above characterization are independent and ambiguous, and may be considered separately. This separation permits a reconsideration of less extreme attempts to tie logic to psychology, such as those defended by Mill and (...) Boole. It also provides the basis for a reexamination of the relationship between logic and psychology, and raises the possibility of a deeper investigation into the nature of logic itself. (shrink)

Simpson's Paradox is introduced and analysed via the mishaps of a researcher who at first falls afoul of the traps Simpson-reversals can set, and then he learns to exploit those traps to advantage. (Note: An error in the treatment of the Sure Thing Principle is corrected in "Simpson's Paradox: A Logically Benign, Empirically Treacherous Hydra").

Summary In the attempt to understand science, definition is not much of a help. Due to the ever growing complexity of science, no unique and universally valid set of defining criteria is available. Hence, certain distinctions are resorted to: science is both a body of tested knowledge and a method of inquiry. The latter, in turn, consists of two phases: discovery and confirmation. The writer argues that it is mainly in respect of its method that science can best be characterized (...) and distinguished from other types of inquiry. (shrink)

We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum likelihood estimator for a (...) probability weight on such a generalized sample space, given absolute frequency data.As a first example, we discuss an estimation problem with censured data that classically admits only biased ad hoc estimators.Next, we derive an explicit solution of the maximum likelihood estimation problem for a large class of experiments that arise from various kids of compositions of sample spaces. We identify the (categorical) direct sum of sample spaces as a representation of “free choice,” and the (categorical) direct product as a representation of “randomization.”Finally, we apply the foregoing discussion to the case of multiple classification experiments in order to show that there is no Simpson's paradox if the difference between free choice and randomization is recognized in the structure of the experiment.A comparison between our new estimator and the “usual” calculation can be summarized as follows: Pooling the data over one classification factor in the “usual” way in fact destroys or ignores the information contained in it, whereas our proposed maximum likelihood estimator is a proper marginal over this factor that “averages out” the information contained in it. The estimators agree with each other in the case of proportional sample sizes. (shrink)