Uses of the language of mathematics

Katarina Maksimovic

doi:10.2298/theo1601024m

Uses of the language of mathematics

Theoria Beograd ◽

10.2298/theo1601024m ◽

2016 ◽

Vol 59 (1) ◽

pp. 26-41

Author(s):

Katarina Maksimovic

Keyword(s):

Intuitionistic Logic ◽

Imperative Logic ◽

The Way

In this paper I criticise the dogma that asserting and naming are the most important language uses in the language of mathematics. I present the later Wittgenstein and the intuitionists as the most eminent challengers of the dogma showing that both have to offer valuable arguments against it. Inspired by Kolmorov?s interpretation of intuitionistic logic I examine the connection between intuitionistic logic and imperative logic. Along the way I offer a solution to J?rgensen?s Dilemma rejecting another dogma, the dogma based on the belief that there could not be a deduction in which premises and conclusion are something other than propositions.

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An intuitionistic logic for preference relations

Logic Journal of IGPL ◽

10.1093/jigpal/jzz013 ◽

2019 ◽

Vol 27 (4) ◽

pp. 434-450 ◽

Cited By ~ 1

Author(s):

Paolo Maffezioli ◽

Alberto Naibo

Keyword(s):

Intuitionistic Logic ◽

Preference Relation ◽

Order Logic ◽

First Order Logic ◽

Strict Preference ◽

Preference Relations ◽

First Order ◽

Weak Preference ◽

The Way

AbstractWe investigate in intuitionistic first-order logic various principles of preference relations alternative to the standard ones based on the transitivity and completeness of weak preference. In particular, we suggest two ways in which completeness can be formulated while remaining faithful to the spirit of constructive reasoning, and we prove that the cotransitivity of the strict preference relation is a valid intuitionistic alternative to the transitivity of weak preference. Along the way, we also show that the acyclicity axiom is not finitely axiomatizable in first-order logic.

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Self-sacrifice for in-group's history: A diachronic perspective

Behavioral and Brain Sciences ◽

10.1017/s0140525x18001796 ◽

2018 ◽

Vol 41 ◽

Cited By ~ 2

Author(s):

Maria Babińska ◽

Michal Bilewicz

Keyword(s):

Clinical Psychology ◽

Historical Events ◽

Emotional Events ◽

Reciprocal Process ◽

The Way

AbstractThe problem of extended fusion and identification can be approached from a diachronic perspective. Based on our own research, as well as findings from the fields of social, political, and clinical psychology, we argue that the way contemporary emotional events shape local fusion is similar to the way in which historical experiences shape extended fusion. We propose a reciprocal process in which historical events shape contemporary identities, whereas contemporary identities shape interpretations of past traumas.

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What is the purpose of cognition?

Behavioral and Brain Sciences ◽

10.1017/s0140525x19001626 ◽

2020 ◽

Vol 43 ◽

Cited By ~ 1

Author(s):

Aba Szollosi ◽

Ben R. Newell

Keyword(s):

Infinite Number ◽

Human Cognition ◽

The Way

Abstract The purpose of human cognition depends on the problem people try to solve. Defining the purpose is difficult, because people seem capable of representing problems in an infinite number of ways. The way in which the function of cognition develops needs to be central to our theories.

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Peculiarity Parameters

International Astronomical Union Colloquium ◽

10.1017/s0252921100080581 ◽

1976 ◽

Vol 32 ◽

pp. 233-254

Author(s):

H. M. Maitzen

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Theoretical Work ◽

Observational Evidence ◽

Rotator Model ◽

Peculiar Behaviour ◽

Field Spectrum ◽

Oblique Rotator ◽

Ap Stars ◽

The Way

Ap stars are peculiar in many aspects. During this century astronomers have been trying to collect data about these and have found a confusing variety of peculiar behaviour even from star to star that Struve stated in 1942 that at least we know that these phenomena are not supernatural. A real push to start deeper theoretical work on Ap stars was given by an additional observational evidence, namely the discovery of magnetic fields on these stars by Babcock (1947). This originated the concept that magnetic fields are the cause for spectroscopic and photometric peculiarities. Great leaps for the astronomical mankind were the Oblique Rotator model by Stibbs (1950) and Deutsch (1954), which by the way provided mathematical tools for the later handling pulsar geometries, anti the discovery of phase coincidence of the extrema of magnetic field, spectrum and photometric variations (e.g. Jarzebowski, 1960).

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The mensuration of interfaces

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010012148x ◽

1992 ◽

Vol 50 (1) ◽

pp. 216-217

Author(s):

W.M. Stobbs

Keyword(s):

Electron Microscopy ◽

50Th Anniversary ◽

Numerical Data ◽

Industrial Applications ◽

Dynamical Theory ◽

Large Strains ◽

Reasonable Approach ◽

Lattice Resolution ◽

Analogue To Digital ◽

The Way

I do not have access to the abstracts of the first meeting of EMSA but at this, the 50th Anniversary meeting of the Electron Microscopy Society of America, I have an excuse to consider the historical origins of the approaches we take to the use of electron microscopy for the characterisation of materials. I have myself been actively involved in the use of TEM for the characterisation of heterogeneities for little more than half of that period. My own view is that it was between the 3rd International Meeting at London, and the 1956 Stockholm meeting, the first of the European series , that the foundations of the approaches we now take to the characterisation of a material using the TEM were laid down. (This was 10 years before I took dynamical theory to be etched in stone.) It was at the 1956 meeting that Menter showed lattice resolution images of sodium faujasite and Hirsch, Home and Whelan showed images of dislocations in the XlVth session on “metallography and other industrial applications”. I have always incidentally been delighted by the way the latter authors misinterpreted astonishingly clear thickness fringes in a beaten (”) foil of Al as being contrast due to “large strains”, an error which they corrected with admirable rapidity as the theory developed. At the London meeting the research described covered a broad range of approaches, including many that are only now being rediscovered as worth further effort: however such is the power of “the image” to persuade that the above two papers set trends which influence, perhaps too strongly, the approaches we take now. Menter was clear that the way the planes in his image tended to be curved was associated with the imaging conditions rather than with lattice strains, and yet it now seems to be common practice to assume that the dots in an “atomic resolution image” can faithfully represent the variations in atomic spacing at a localised defect. Even when the more reasonable approach is taken of matching the image details with a computed simulation for an assumed model, the non-uniqueness of the interpreted fit seems to be rather rarely appreciated. Hirsch et al., on the other hand, made a point of using their images to get numerical data on characteristics of the specimen they examined, such as its dislocation density, which would not be expected to be influenced by uncertainties in the contrast. Nonetheless the trends were set with microscope manufacturers producing higher and higher resolution microscopes, while the blind faith of the users in the image produced as being a near directly interpretable representation of reality seems to have increased rather than been generally questioned. But if we want to test structural models we need numbers and it is the analogue to digital conversion of the information in the image which is required.

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Representing the Way to Language Learning and Expression

Perspectives on Augmentative and Alternative Communication ◽

10.1044/aac6.4.3 ◽

1997 ◽

Vol 6 (4) ◽

pp. 3-4

Author(s):

Beth Mineo Mollica

Keyword(s):

Language Learning ◽

The Way

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Process \'prǎ|,ses\n: The Action of Moving Forward Progressively from One Point to Another on the Way to Completion

Journal of Speech and Hearing Disorders ◽

10.1044/jshd.4401.03 ◽

1979 ◽

Vol 44 (1) ◽

pp. 3-30 ◽

Cited By ~ 20

Author(s):

Carol A. Pruning

Keyword(s):

Process Model ◽

Communicative Behaviors ◽

Adult Level ◽

Remedial Programs ◽

Stage Process ◽

The Way

A rationale for the application of a stage process model for the language-disordered child is presented. The major behaviors of the communicative system (pragmatic-semantic-syntactic-phonological) are summarized and organized in stages from pre-linguistic to the adult level. The article provides clinicians with guidelines, based on complexity, for the content and sequencing of communicative behaviors to be used in planning remedial programs.

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