Abstraction and generalization are two processes of reasoning that have a special role in the construction of scientific theories and models. They have been important parts of the scientific method ever since the nineteenth century. A philosophical and historical analysis of scientific practices shows how abstraction and generalization found their way into the theory of the logic of science of the nineteenth-century philosopher Charles S. Peirce. Our case studies include the scientific practices of Francis Galton and John Herschel, (...) who introduced composite photographs and graphical methods, respectively, as technologies of generalization and thereby influenced Peirce’s logic of abstraction. Herschel’s account of generalization is further supported by William Whewell, who was very influential on Peirce. By connecting Herschel’s scientific technology of abstraction to Peirce’s logical technology of abstraction—namely, diagrams—we highlight the role of judgments in scientific observation by hypostatic abstractions. We also relate Herschel’s discovery-driven logic of science and Peirce’s open-ended diagrammatic logic to the use of models in science. Ultimately, Peirce’s theory of abstraction is a case of showing how logic applies to reality. (shrink)

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal‐based generalization (CBG) view included effects of an existing feature’s base rate (Experiment 1), the direction of the causal relations (Experiments (...) 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to‐be‐generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes. (shrink)

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

This paper will introduce the notion of a naming convention and use this paradigm to both develop a new version of the Second Incompleteness Theorem and to describe when an axiom system can partially evade the Second Incompleteness Theorem.

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let <A> be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to <A> and <antiA>, and one corresponding to neutral (indeterminate) <neutA> (also denoted <neutroA>) between the opposites}, which may (...) or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra is an algebra which has at least one NeutroOperation or one NeutroAxiom (axiom that is true for some elements, indeterminate for other elements, and false for the other elements). A Partial Algebra is an algebra that has at least one Partial Operation, and all its Axioms are classical (i.e. axioms true for all elements). Through a theorem we prove that NeutroAlgebra is a generalization of Partial Algebra, and we give examples of NeutroAlgebras that are not Partial Algebras. We also introduce the NeutroFunction (and NeutroOperation). (shrink)

Inductive generalization asserts that what obtains in known instances can be generalized to all. Its original form is enumerative induction, the earliest form of inductive inference, and it has been elaborated in various ways, largely with the goal of extending its reach. Its principal problem is that it supplies no intrinsic notion of strength of support so that one cannot tell if the generalization has weak or strong support.

In many domains of biology, explanation takes the form of characterizing the mechanism responsible for a particular phenomenon in a specific biological system. How are such explanations generalized? One important strategy assumes conservation of mechanisms through evolutionary descent. But conservation is seldom complete. In the case discussed, the central mechanism for circadian rhythms in animals was first identified in Drosophila and then extended to mammals. Scientists' working assumption that the clock mechanisms would be conserved both yielded important generalizations and served (...) as a heuristic for discovery, especially when significant differences between the insect and mammalian mechanism were identified. †To contact the author, please write to: Department of Philosophy and Interdisciplinary Programs in Science Studies and Cognitive Science, 0119, University of California, San Diego, La Jolla, CA 92093‐0119; e‐mail: [email protected]. (shrink)

In his essay “Pragmatism and Humanism,” William James recalls a friend’s disappointment that the “prodigious star-group” known as the Big Dipper “should remind us Americans of nothing but a culinary utensil.”1 Such, presumably, is the fault of generalization, though James himself is less than specific in illustrating the occasional parity of varied perspectives. For example, he posits two identical equilateral triangles, one inverted and overlapping the other, and notes, “You can treat the adjoined figure as a star, as two (...) big triangles crossing each other, as a hexagon with legs set up on its angles, as six equal triangles hanging together by their tips, etc.”. What he does not say is that the design.. (shrink)

This paper surveys the literature on m singer's book "generalization in ethics", And focuses on a problem not previously discussed: the significance of the "ceteris paribus" clause. Previous literature has pointed out the problem involved in singer's collective use of the term 'everyone', But the precise nature of the difficulty is not made clear until the issue of the ceteris paribus clause is considered. We argue that singer's argument cannot be useful in moral deliberation, Because it is not possible (...) to isolate on a particular individual who has an obligation, To see if one's own case is similar. (shrink)

We argue that confusability between items should be distinguished from generalization between items. Shepard's data concern confusability, but the theories proposed by Shepard and by Tenenbaum & Griffiths concern generalization, indicating a gap between theory and data. We consider the empirical and theoretical work involved in bridging this gap. [Shepard; Tenenbaum & Griffiths].

Shepard's exponential law provides a functional explanation of generalization. The account complements the more common mechanistic models. The elegant and powerful analyses answer one of Tinbergen's (1963) four whys of behavior: a benefit conferred on the animal by generalizing in this way. A complete account might address evolutionary and developmental questions in addition to mechanistic and functional ones. [Shepard].

We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and "halts" in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known "limit lemma" due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of (...) this result, we give a recursion theoretic analysis of clopen determinacy: there is a correlation given between the height α of a well-founded tree corresponding to a clopen game $A \subseteq \omega^\omega$ and the Turing degree of a winning strategy f for one of the players--roughly, f can be chosen to be recursive in 0 α and this is the best possible (see § 4 for precise results). (shrink)

According to the simple proposal, a predicate is rigid iff it signifies the same property across the different possible worlds. The simple proposal has been claimed to suffer from an over-generalization problem. Assume that one can make sense of predicates signifying properties, and assume that trivialization concerns, to the effect that the notion would cover any predicate whatsoever, can be overcome. Still, the proposal would over-generalize, the worry has it, by covering predicates for artifactual, social, or evaluative properties, such (...) as 'is a knife,' 'is a bachelor,' or 'is funny.' In defense, it is argued that rigidity for predicates as characterized plays the appropriate theoretical role, and that the contention that "unnatural" properties are not to be rigidly signified is ungrounded. (shrink)

This paper defines the form of prior knowledge that is required for sound inferences by analogy and single-instance generalizations, in both logical and probabilistic reasoning. In the logical case, the first order determination rule defined in Davies (1985) is shown to solve both the justification and non-redundancy problems for analogical inference. The statistical analogue of determination that is put forward is termed 'uniformity'. Based on the semantics of determination and uniformity, a third notion of "relevance" is defined, both logically and (...) probabilistically. The statistical relevance of one function in determining another is put forward as a way of defining the value of information: The statistical relevance of a function F to a function G is the absolute value of the change in one's information about the value of G afforded by specifying the value of F. This theory provides normative justifications for conclusions projected by analogy from one case to another, and for generalization from an instance to a rule. The soundness of such conclusions, in either the logical or the probabilistic case, can be identified with the extent to which the corresponding criteria (determination and uniformity) actually hold for the features being related. (shrink)

A concise proof of Bell's theorem on the necessary nonlocality of any theory which models individual measurements in correlated quantum mechanical systems is presented. A family of inequalities is derived which may be applied to a broad class of correlated systems to test the assumption of locality.

We offer a defense of one aspect of Paul Horwich’s response to the Liar paradox—more specifically, of his move to preserve classical logic. Horwich’s response requires that the full intersubstitutivity of ‘ ‘A’ is true’ and A be abandoned. It is thus open to the objection, due to Hartry Field, that it undermines the generalization function of truth. We defend Horwich’s move by isolating the grade of intersubstitutivity required by the generalization function and by providing a new reading (...) of the biconditionals of the form “ ‘A’ is true iff A.”. (shrink)

We clarify Bohr’s interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.

In Process and Reality (1929) and subsequent writings, A.N. Whitehead builds on the success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis. He holds that the proper generalization of the meaning of the function shows that it is primarily to be defined in terms of many-to-one mapping activity, which he terms 'creativity'. This allows him to generalize the range of the function, so that it constitutes a universal ontology of construction or (...) 'process'. He analyzes the concept of God in terms of functional mapping to structure, and he defines finite entities as iterative 'occasions' of mapping activity. He thus challenges the widespread logical-analytical view that the connectives and variables of a function in its different instantiations are merely numerically different, and he develops a fallibilist theory of activity as essentially serial in nature. (shrink)

Écriture sans écriture, critique sans discours : il s’agit de traquer et de faire ressortir l’obsession du « projet » et de son idéologie dans la trame d’un appel à contrats doctoraux. Ctrl+B chaque fois (et elles sont très nombreuses) où le petit mot est réitéré.