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Philosophical and Scientific Issues in Dispute
 
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The author or concept searched is found in the following 3 entries.
Disputed term/author/ism Author
Entry
Reference
Communication Models Economic Theories Kranton I 423
Communication Models/Bloch/Demange/Kranton/Economic Theories: (…) the model [by Bloch, Demange and Kranton] combines two classic elements of information games: “cheap talk” (Crawford and Sobel, 1982)(1) in the decision of the initial receiver of the signal as to whether or not to create a truthful message, and “persuasion” (Milgrom, 1981(2); Milgrom and Roberts, 1986(3)) in the decision of agents who subsequently choose whether to transmit the message, which they cannot transform. In our model, there are multiple equilibria, along the lines of cheap talk games. However, as in persuasion games, at the transmission stage agents have an incentive to pass on credible information to other agents. In our model (Bloch/Demange/Kranton), there is a single unknown source of information and agents are Bayesian, but due to differences in their preferences and the possibility of falsification and blocking, they may end up with different beliefs and choose different actions. >Misinformation/Economic Theories, >Communication Models/Kranton.

1. CRAWFORD, V. P., AND J. SOBEL, “Strategic Information Transmission,” Econometrica 50 (6) (1982), 1431–51.
2. MILGROM, P. R., “Good News and Bad News: Representation Theorems and Applications,” Bell Journal of Economics 12 (2), (1981), 380–91.
3. MILGROM, P., AND J. ROBERTS, “Relying on the Information of Interested Parties,” Rand Journal of Economics 17 (1986), 18–32.

Francis Bloch, Gabrielle Demange & Rachel Kranton, 2018. "Rumors And Social Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(2), pages 421-448.


Kranton I
Rachel E. Kranton
Francis Bloch
Gabrielle Demange,
Rumors And Social Networks 2018

Kranton II
Rachel E. Kranton
George A. Akerlof
Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being Princeton 2011
Loewenheim Field I 131
Löwenheim-Skolem/downward/Field: says that there must be no uncountable models for 1st order consistent theories. Compactness theorem/Löwenheim-Skolem/upward: says that each 1st order space-time theory, according to which there are infinitely many space-time points, will have models, in which the set of the space-time points is mightier than the set of real numbers.
Problem: then the representation theorem does not apply.
>Representation theorem.

Field I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Field II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Field III
H. Field
Science without numbers Princeton New Jersey 1980

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994

Motion Field I 193
Def Problem of Quantities/S/R/Field: the representational theorems used for the generation of many numerical functors in physics (e.g. distance, relative velocity, acceleration). - They are not available for relativism because they depend on structural regularities of the space time which are lost when one discards those parts of the space time that are not completely occupied by matter as the space is. - Definition of distance without numbers by congruence and "between". >Spacetime, >Representation theorem.
III 84f
Law of movement/Nominalisation/Field: therefore we need the concepts trajectory and differentiation of the vector field. Cf. >Nominalism.
Derivation: of scalars can be equated with differences of scalars - so also derivations of vectors with differences of vectors.
Problem: differences of vectors are themselves vectors; spacetime can be assumed to be infinite, but not temperature.
III 88
Law of movement/Nominalisation/Field: with the concept of the tangent on a trajectory. - The trajectory can be differentiated if the tangent is not purely spatial. - The accelerations of points (on one or more trajectories) are compared with the gradients of the gravitational potential at the points. Def Law of movement/Newtonian gravitational theory/Field: (if only gravitational forces are effective): for every such T, T',z,z',S,S', y and y': there is a positive real number k so that
a) the second directional derivative of the spatial separation of S from T to z in relation to zy> is taken twice is k-times the gradient of the gravitational potential on z.
b) the second directional derivative of the spatial trajectory from S' from T' to z' corresponding to the other coated symbols.
Nominalistic: one only has to use the second directional derivative in (12').

Field I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Field II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Field III
H. Field
Science without numbers Princeton New Jersey 1980

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994


The author or concept searched is found in the following controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Mundy, B. Field Vs Mundy, B. I 199
Representation Theorem/VsRelationism: Relationism cannot take over the representation theorems from substantivalism either, because these depend on structural regularities (regularity of spacetime structure). And this regularity of spacetime is lost in relationalism. ((s) because there should be no empty sp.t., the sp.t. itself is bound to (empirically irregularly) occurring matter). Wrong Solution/Mundy: (1983): has proven a "representation theorem" which is not based on structural regularities. But that does not help heavy duty Platonism, because it generates numerical functors only from other numerical functors. That means he does not take predicates which put matter particles (point particles) in relation to each other, but a functor k: that refers particles to real numbers. E.g. For every three-point particle a real number that represents the inner product of two vectors which have one of these points as a common starting point, and the other two as endpoints. From this he extracts (several) coordinate systems, so that we have a representation theorem of species. FieldVsMundy: this does not serve the purposes for which representation theorems were originally developed, because it does not depart from a non-numeric base. Mundy: also sees that the R should not use any functions of point particles to real numbers as the basis for its formulation of physics. Therefore, he reformulates the equation: old: k(p,q,r) = a (where a is a real number) new: ka(p,q,r) so that we have an uncountable, infinite set of 3-digit space relations, one for every real number. (Mundy, 1983, p 212, 223.) FieldVsMundy: this does not solve any problem, because it’s only a notational trick. ((s) notation, orthography, paraphrasing, renaming >Rorty: "redescription" not a mere renaming, because description (language) necessitates stronger revision than replacing individual predicates with others. Potentially different number of digits). FieldVsMundy: if you really wanted to interpreted the ka’s as 3-digit spatial relations, the a’s would have to be considered as unquantifiable indices. Then we would have uncountably many primitive predicates, and thus no theory would be possible. Index/Quantification/(s): it is impossible to quantify on indices. Indices are not quantifiable. Mundy: of course, does not treat the indices as unquantifiable, but he re-writes them: k(p,q,r) = a if he wants to quantify on a. FieldVsMundy: but a quantifiable index is simply a variable that appears in a different place. And with the re-naming we do not change the fact that we have a 4-digit relation of which one term is a real number. Conclusion: With that you cannot take advantage of the difference between moderate Platonism and heavy duty Platonism.

Field I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Field II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Field III
H. Field
Science without numbers Princeton New Jersey 1980

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994