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The author or concept searched is found in the following 12 entries.
| Disputed term/author/ism | Author |
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| Axioms | Field | I 220 Axiom/Field: a required law can easily be proven by adding it as an axiom - Vs: but then you need for each pair of distinct predicates an axiom that says that the first one and the second does not, e.g. "The distance between x and y is r times that between z and w". Everything that substantivalism or heavy-duty Platonism may introduce as derived theorems, relationism must introduce as axioms ("no empty space"). >Substantivalism >Relationism That leads to no correct theory. Problem of quantities. The axioms used would precisely be connectable if also non-moderate characterizations are possible. The modal circumstances are adequate precisely then when they are not needed. I 249ff Axiom/Mathematics/Necessity/Field: axioms are not logically necessary, otherwise we would only need logic and no mathematics. I 275 Axioms/Field: we then only accept those that have disquotationally true modal translations. - Because of conservativism. >Conservativity. Conservatism: is a holistic property, not property of the individual axioms. Acceptability: of the axioms: depends on the context. Another theory (with the same Axiom) might not be conservative. Disquotational truth: can be better explained for individual axioms, though. >Disquotationalism. I 276 E.g. Set theory plus continuum hypothesis and set theory without continuum hypothesis can each be true for their representatives. - They can attribute different truth conditions. - This is only non-objective for Platonism. >Platonism. The two representatives can reinterpret the opposing view, so that it follows from their own view. >Kurt Gödel, relative consistency. II 142 Axiom/(s): not part of the object language. Scheme formula: can be part of the object language. Field: The scheme formula captures the notion of truth better. >Truth/Field. |
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 |
| Determinates/ Determinables | Bigelow | I 51 Definition Determinable/Bigelow/Pargetter: what the objects have in common, but what is differently strong in them. For example, mass. Definition Determinate/Bigelow/Pargetter: is the special property that distinguishes the objects (simultaneously). For example a mass of 2.0 kg. Both together show what is common and what is different. >Problem of quantities, >Methexis/Plato, >Distinctions. Quantities/Bigelow/Pargetter: Problem: the approach is still incomplete: I 52 Either the relation between determinates and determinables is objective or it is not objective. A) objective: if it is objective, we need an explanation in which it exists. B) non-objective: then it is arbitrary to assert that objects that have different Determinates fall under that same Determinable. W.E. Johnson: our approach is based on one of Johnson's: in it, both are Determinables and also Determinate properties of individuals. Bigelow/Pargetter: Variant: we can start with a special property for each individual (Determinate, e.g. color shading). Then we define the common: color, this commonality is a property of 2nd level Definition 2nd degree property/Bigelow/Pargetter: E.g. the commonality of all shades of a color. I 53 Hierarchy: can then be continued upwards. E.g. to have a color at all is one level higher. Level/degree: E.g. pain: is having a 2nd level property. >Pain. Functional role/Bigelow/Pargetter: is a commonality, so there is a property 2nd level to have a certain functional role. >Functional role. Hierarchy: then consists of three sets of properties. 1. Property 1st level of individuals. All other properties supervene on them. 2. Properties of properties 1st level: = properties of 2nd degree (commonality of properties) 3. Properties 2nd level of individuals: = the property to have that or that property of the 1st level which has that or that property of the 2nd degree. >Properties. Problem of Quantities/Solution/Bigelow/Pargetter: 1. Objects with different Determinates are different because each has a property of 1st level that another thing does not have. 2. they are the same because they have the same property of 2nd level. Determinables/Determinates/Johnson: are in close logical relations: to have a Determinate entails to have the corresponding Determinable. I 54 But not vice versa! Having a Determinable does not require possession of a particular Determinate! But it requires some Determinate from the range. BigelowVsJohnson: he could not explain the asymmetry. Solution/Bigelow/Pargetter: properties of 2nd level. Problem: our theory is still incomplete! Problem: to explain why quantities are gradual. This does not mean that objects are the same and different at the same time. New: the problem that we can also say exactly how much they differ. Or, for example, two masses are more similar than two others. Plato: Plato solves this with the participation. >Methexis. Bigelow/Pargetter: we try a different solution see >Relational theories. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| 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 |
| Operators | Field | I 157f Operators/sets/Field: sets can be gained from the operator exactly the same things that are __, the things that are __ plus predicate functor {x I ...}. I 220 Problem of actuality/Field: cannot be solved by an actuality operator. >Actuality. I 222 Problem of Quantities/possible worlds/Field: with possible worlds and cross world identity we could avoid the possibility operator. >Cross word identity, >Possible worlds. FieldVs: we wanted to avoid the ontology of pace-time-regions. Possible worlds/Field: only heuristically harmless. I 249ff Ontology/theory/mathematics/Anti-Realism/Field: e.g. metalogical terms such as consistency: instead of the predicate "the theory has the property of consistency": Operator: "It is consistent that the conjunction of the axioms is true". ((s) ontologically economical: operator instead of a predicate.) >Predicates. |
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 |
| Possibility | Field | I 86 Logically possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth. FieldVsKripke: yes it is, this is only due to Kripke's model-theoretical definition. - It should not be read "mathematically" or "metaphysically possible". >Logical truth, >Metaphysical possibility. --- I 87 E.g. Carnap: "He is bachelor and married": is logically wrong. >Meaning postulates. FieldVsCarnap: Meaning relations between predicates should not count to logic. - Then the sentence is logically consistent. Consistency operator/Field: MEx (x is red & x is round) should not only be true, but logically true. - ((s) Also without meaning postulates.) ((s) Meaning postulate/(s): here it is about the extent of the logic.) --- I 203 Geometric Possibility/Field: instead of logical possibility: there are different geometries. >Geometry. Precondition: there are empirical axioms which differentiate the possibility from impossibility. However, the existential quantifier must be within the range of the modal operator. >Existential quantification, >Modal operator, >Scope. --- I 218 Problem of Quantities/mathematical entities/me/Field: For example, it is possible that the distance between x and y is twice as long as the one between x and w, even if the actual distance is more than twice as long. Problem: extensional adequacy does not guarantee that the defined expression is true in every non-actual situation - that is, that we must either presuppose the substantivalism or the heavy duty Platonism. That is what we do in practice. I 192 Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. >Substantivalism. |
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 |
| Possible Worlds | Field | I 41 Possible World/difference/differentiation/Field: E.g. we cannot postulate a possibel world which is isomorphic to ours and in which only Nixon is like Humphrey (here) and Humphrey like Nixon (here) - (throughout the whole story). >Cross world identity, cf. >Centered worlds. I 75 Possible Worlds/Lewis: (Counterfactuals, Section 4.1): possible Worlds are 4-dimensional slices of a broader reality, like other possible world. All together form the actual universe. FieldVsLewis. NominalismVsPossible Worlds: these are abstract entities. I 222 Problem of quantities/Possible World/Field: with possible world and cross-world-congruence we could avoid the possibility operator. FieldVs: we exactly wanted to avoid the ontology of the space-time regions. Possible World/Field: are only heuristically harmless. I 223 Possible World/StalnakerVsLewis: (Stalanker 1976)(1): Alternative to Lewis: Speech of possible worlds should be understood as a speech about a property Q, so it is necessary that if the universe has Q, then there is x*, y*, z*, w* and u*, so that F (x*, y*, z*, w*, u*). Problem: How should we understand the cross-world congruence? The last incidents of x* are not bound by quantifiers during the comparison. FieldVsStalnaker: Problem: interpretation of the expression "spatial relation". --- II 89 Possible world/Quantities of/Field: what is relevant for sets of possible worlds as objects of states of the mind is that they form a Boolean algebra. N.B.: then the elements themselves need not be a possible world - any other kind of elements are then just as good for a psychological explanation. They could simply be everything - e.g. numbers. Numbers: do not pretend to represent the world as it is. II 90 Intentionality/Possible world/FieldVsStalnaker/Field: The wit of the possible world assumption is the Boolean Algebra, the boolean relation that prevails between possible worlds. Problem: then the empty set of possible worlds which contains the trisection of the angle, which is a subset of the set of the possible world, in which Caesar crossed the Rubicon. Problem: what fact does that make? - Without it the approach is meaningless. >Nonfactualism. 1. Robert C. Stalnaker, 1976. Possible Worlds. ous 10, 65-75. |
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 |
| Quantities | Quantities, philosophy: quantity is an expression for the set of countable objects, which is referred to in a statement, or correspondingly the expression for the mass of an uncountable material substance about which a statement is. Today, quantity is no longer regarded fundamentally as a category, as it was the case in the traditional philosophy since Aristotle. See also qualities, categories, mass terms, problem of quantities. |
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| Quantities | Bigelow | I 49 Quantities/Quantity/Bigelow/Pargetter: with quantities we are going to refer to the core area of metaphysics. >Metaphysics. Universals/Bigelow/Pargetter: universals emerge from the confrontation that certain things can be something and something else at the same time. That is only a superficial contradiction. >Universals. Quantity/Bigelow/Pargetter: Example: a) two things are equal by both having a mass. b) they differ at the same time because they have different masses. Quantities/Plato/Bigelow/Pargetter: Problem: if properties are something that a thing can either have or not have, there is a problem of quantities. >Properties, >Problem of quantities. Solution/Plato: Participation in forms. This allows a gradual treatment. >Methexis. Bigelow: We are a moving a little away from Plato. Quantity/Plato/Bigelow/Pargetter: Solutions of this kind have in common that they postulate an entity and vary the relation between this entity and the individuals who own it. I 50 The entity explains what individuals have in common. The relation explains the different degrees. >Relations. Nominalism/Berkeley/Bigelow/Pargetter: this is Berkeley's nominalism: a platonic, abstract form is replaced by a special individual, a "paradigm". (Terminology). >Nominalism. Commonality: individuals have commonality when they resemble the same paradigm. Similarity: is, of course, also gradual, like gradual participation in forms in Plato. >Similarity. Berkeley/Plato/Bigelow/Pargetter: the theories are quite similar: they explain how properties can be gradual. >Plato, >G. Berkeley. Quantities/Bigelow/Pargetter: this does not solve the general problem of quantities (that they are gradual). Problem: Degrees of a relation. >Degrees/graduals. Solution: Similarity and participation are an attempt. Forms/Plato/Bigelow/Pargetter: we do not claim that his theory of forms is wrong. BigelowVsPlato: it does not solve the problem of quantities. (The nature of quantity). >Forms. I 264 Quantities/Possible Worlds/Bigelow/Pargetter: Question: What should we allow as basic equipment? Forces, for sure. Thesis: there are essential connections between fundamental forces and the fundamental causal relation. Causality/Bigelow/Pargetter: must therefore also be part of the basic equipment of our world. >Forces, >Causality, >Ontology. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Quantities | Field | I 195 Problem of quantities/Field: e.g. definition of distance with congruence and "between" but without numbers - not "distance three times as large as ...". - E.g. acceleration: not - "twice as much as". I 198 Problem of quantities/relationism: e.g. takes a whole bunch of infinite families of comparative acceleration predicates. - That is the reformulated version -> Motion. |
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 |
| Relation-Theory | Relation-Theory A. Relation-Theory: takes belief to be a relation to internal objects (entities). Virtually all authors are against the assumption of thoughts as internal objects. See also intensional objects, intensions, propositional attitudes, mentalism. B. Relational Theory/Bigelow/Pargetter: (Science and Necessity Cambridge University Press 1990 p55): assumes universals (e.g. sets, numbers, properties) and relations between them in order to explain the problem of quantities. See also change, motion, quantities, universals, Platonism, nominalism. |
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| Relation-Theory | Bigelow | I 55 Quantity/relational theory/Bigelow/Pargetter: Quantities are general relations between objects. They seem to be consequences of the intrinsic properties of objects. But one would not have to postulate an intrinsic relation "greater than", but only e.g. the size. >Quantity, >Sizes/Physics, >Relations, >Objects, >Intrinsic, >Properties. Greater than/relational property/problem/Bigelow/Pargetter: one might wonder if there really is an intrinsic property to be that and that big. Cf. >Haecceitism. Relational property/Bigelow/Pargetter: one might be tempted to assume that everything is based on relational properties, rather than vice versa. But we are not going to go into that here. Intrinsic property/Bigelow/Pargetter: we think that in the end they can be defended against relational properties as a basis. Nevertheless, we certainly need relational properties, e.g. for the order of events. These do not just stand in time. So we definitely need relations. Relations/Bigelow/Pargetter: we definitely need relations. Because events never stand for themselves. >Events. I 56 Also for expressions such as "twice the size" etc. Quantity/Bigelow/Pargetter: Quantities cannot be based on properties alone, but need relations. For example, having this or that mass is then the property of being in relation to other massive objects. Participation/BigelowVsPlato: Plato has all things in a more or less strong relation to a single thing, the form. We, on the other hand, want relations between things among themselves. >Methexis, >Plato. BigelowVsPlato: we can then explain different kinds of differences between objects, namely that they have different relational properties that other things do not have. E.g. two pairs of things can differ in different ways. I 57 Relational Theory/Bigelow/Pargetter: can handle differences of differences well. Question: can it cope well with similarities? For example, explain what mass is at all? Problem: we need a relation between a common property and many relations to it. There are many implications (entailments) which are not yet explained. Property/Bigelow/Pargetter: 1. in order to construct an (intrinsic) property at all, we must therefore specify the many possible relations it can have to particalur. Solution: one possibility: the sentence via the property of the 2nd level. 2. Problem: how can two things have more in common than two other things? Ad 1. Example Mass Common/Commonality/Bigelow/Pargetter: must then be a property of relations (of the many different relations that the individual objects have to "mass"). I 58 Solution: property of the 2nd level that is shared by all massive things. For example, "stand in mass relations". >Comparisons, >Comparability, >Similarity, >Identity. Entailment/N.b.: this common (2nd level property) explains the many relations of the entailment between massive objects and the common property of solidity. Problem/Bigelow/Pargetter: our relational theory is still incomplete. Problem: to explain to what extent some mass-relations are closer (more similar) than others. Relations/common/Bigelow/Pargetter: also the relations have a common: a property of the 2nd level. Property 2. Level/difference/differentiation/problem/Bigelow/Pargetter: does not explain how two things differ more than two other things. >Levels/order, >Description levels. It also does not explain how, for example, differences in masses relate to differences in volume. For example, compare the pairs "a, b" "c, d" "e, f" between which there are differences in thicknesses with regard to e.g. length. Then two of the couples will be more similar in important respects than two other pairs. I 59 Solution/Bigelow/Pargetter: the relation of proportion. This is similar to Frege's approach to real numbers. Real numbers/Frege: as proportions between sizes (Bigelow/Pargetter corresponds to our quantities). >Real numbers, >Quantity/Bigelow. Bigelow/Pargetter: three fundamental components (1) Individuals (2) Relations between individuals (3) Relations of proportions between relations between individuals. Proportions/Bigelow/Pargetter: divide the relations between individuals into equivalence classes. >Proportions/Bigelow. Mass/Volume/Proportions/Bigelow/Pargetter: N.b. all masses are proportional to each other and all volumes are proportional to each other, but masses and volumes are not proportional to each other. Equivalence classes/Bigelow/Pargetter: arrange objects with the same D-ates into classes. So they explain how two things ((s) can be more similar in one respect, D-able) than in another. >Determinates/Determinables, >Equivalence classes. Level 1: Objects Level 2: Properties of things Level 3: Proportions between such properties. Proportions/Bigelow/Pargetter: are universals that can introduce finer differences between equivalence classes of properties of the 2nd level. Different pairs of mass relations can be placed in the same proportion on level 3. E.g. (s) 2Kg/4kg is twice as heavy as 3Kg/6Kg. N.b.: with this we have groupings that are transverse to the equivalence classes of the mass relations, volumetric relations, velocity relations, etc. Equal/different/Bigelow/Pargetter: N.B:: that explains why two relations can be equal and different at the same time. E.g. Assuming that one of the two relations is a mass relation (and stands in relation to other mass relations) the other is not a mass relation (and is not in relation to mass relations) and yet... I 60 ...both have something in common: they are "double" once in terms of mass, once in terms of volume. This is explained on level 3. Figures/Bigelow/Pargetter: this shows the usefulness of numbers in the treatment of quantities. (BigelowVsField). >Hartry Field, >Numbers, >Mathematical Entities, >Ontology. Real numbers/Frege: Lit: Quine (1941(1), 1966(2)) in "Whitehead and the Rise of Modern Logic") Measure/Unit/Measuerment Unit/To Measure/Bigelow/Pargetter:"same mass as" would be a property of the 2nd level that a thing has to an arbitrary unit. >Measurement, >Equality. Form/Plato/Bigelow/Pargetter: his theory of forms was not wrong, but incomplete. Objects have relations to paradigms (here: units of measurement). This is the same relation as that of participation in Plato. I 61 Level 3: the relations between some D-ates can be more complex than those between others. For mass, for example, we need real numbers, other terms are less clear. Quantities/Bigelow/Pargetter: are divided into different types, which leads to interval scales or ratio scales of measurement, for example. >Scales. Pain/Bigelow/Pargetter: we cannot compare the pain of different living beings. Level 3: not only explains a rich network of properties of the 2nd level and relations between objects,... I 62 ...but also explain patterns of entailments between them. NominalismVsBigelow: will try to avoid our apparatus of relations of relations. >Nominalism. BigelowVsNominalism: we need relations and relations of relations in science. Realism/Bigelow/Pargetter: we do not claim to have proven it here. But it is the only way to solve the problem of the same and the different (problem of the quantities with the 3 levels). >Realism/Bigelow, >Problem of quantities. Simplicity/BigelowVsNominalism: will never be as uniform as our realistic explanation. Nominalism would have to accept complex relational predicates as primitive. >Simplicity. Worse still, it will have to accept complex relations between them as primitive. 1. Quine, W.V.O. (1941). Whitehead and the rise of modern logic. In: The philosophy of Alfred North Whitehead (ed. P.A. Schilpp). pp.125-63. La Salle, Ill. Open Court. 2. Quine, W.V.O. (1966). Selected logic papers. New York: Random House. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Relationism | Field | I 171 Def Relationism: Thesis: no empty space exists. Def Substantivalism/Field: Thesis: empty space exists. Part-relation: exists in both. >Space, >Absoluteness, >Motion, >Spacetime points. I 181 Relationism/Field: makes field theory impossible - because it excludes empty space. I 182 Putnam: Relationism can take the field as an enormous (because of the infinity of the physical forces) object. - Then for each region one part of it. - FieldVs: this trivializes the relativism. I 183 Field theory/FT/Substantivalism/Field: for the substantivalism the field is not a gigantic object, but no entity at all. Field theory: is for the substantivalism only the attribution of causal predicates to regions. I 216 Problem of Quantities/FieldVsRelationism: the only way to show that there is a (narrow) spatial relation, is to assume that the double distance itself is a spatial relation. But relationism cannot do this because it wants to define it first, and cannot presuppose it as defined. |
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 |
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| Counterfactual Conditional | Field Vs Counterfactual Conditional | I 220 Problem of Quantities/PoQ/Modality/Field: but this does not exclude a possible modal solution to the PoQ: perhaps other operators can help? Anyway, I do not know how that could be excluded, even if I do not know what these operators should look like. I 221 Counterfactual Conditional/Co.Co./PoQ/Field: one suggestion is to use Counterfactual Conditional to solve the PoQ: FieldVsCounterfactual Conditional: 1) they are known to be extremely vague. Therefore, you should not rely on them when formulating a physical theory. Neither should we use Counterfactual Conditional for the development of geometrical concepts. 2) DummettVsCounterfactual conditionals: They cannot be "barely true": if a Counterfactual Conditional is supposed to be true, then there must be some facts (known or unknown facts) that can be determined without Counterfactual Conditional, and by virtue of which the Counterfactual Conditional are true. (Dummett, 1976, p.89). Then the relationism cannot use the Counterfactual Conditional for the PoQ, because in that case the principle requires: if distance relations are counterfactually defined, then situations that differ in their distance relations (like situations A and B) must also differ in non-counterfactual respects!. Substantivalism: can guarantee that. Relationism: cannot, and if it could, it would need no Counterfactual Conditional. 3) VsCounterfactual conditionals: does not work for very similar reasons for which the version with impredicative properties (P3) did not work: no theory about counterfactually defined relations works if these relations cannot also be counterfactually defined, (This is the formal reason for the metaphysical argument of Dummett, for why Counterfactual Conditional cannot be "barely true"). E.g. In order to prove the incompatibility of "double distance" and "triple distance" (given that z and w do not occupy the same point, i.e. given that zw is not congruent with zz - (logical form: local equality) - then you would need the incompatibility of the following: a) if there were a point u in the middle between x and y, then uy would be congruent with zw. b) if there were a point s between x and y, and a point t between s and y, so that xs, st and ty were all congruent, then ty would be congruent with zw. If these Counterfactual Conditional were somehow derivable from non-counterfactual statements, E.g. statements about spacetime points (ST points), then you could probably, and by way of derivation. I 222 Together with the demonstrable relations between the non-counterfactual statements win an argument for the incompatibility of (a) and (b). But if we have no non-counterfactual support, we would have to consider them as bare facts. That would not be so bad if you only needed a small amount of them, but we would need a very large number of them. |
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 |
| Horwich, P. | Field Vs Horwich, P. | I 175 Relationism/Field: Advantage: good technical conditions for the formulation of field theories and to avoid long-distance effect. Also: "Problem of Quantities": >acceleration. (see below) Def Monadicism/Horwich/Field: (Horwich, 1978): Thesis: denies just like Relationism that there is spacetime (sp.t.). ((s) empty, self-relying sp.t.). Sp.t. only logical construction! VsRelationalism: no aggregates of matter or relations between them. Instead: primitive monadic properties of sp.t. places. ((s) as the fundamental concept). SubstantivalismVsMonadicism/Field: according to substantivalism such monadic local properties are not primitive: they are gained from the two-digit relation "occupied", with an argument being instantiated with a sp.t. point. MonadicismVs: denies sp.t. in general. Instead, a piece of matter can either have or not have these primitive properties. FieldVsMonadicism/FieldVsHorwich: this is mainly based on a confusion of the "predicate interpretation" and the "interpretation of a higher level": Reduction/Field: when we say that we want to reduce the ontology by a stock of primitive properties, I 176 we mostly think in reality that we expand our stock of primitive predicates. This can often be very important in order to gain simplicity. Monadicism/M/Horwich: Substantivalism and M acknowledge a lot of properties that can be expressed by predicates of the form "appears at time t". Only difference: Substantivalism/S: double-digit predicates such as "Brother of John" or place occupied by a name or description of a moment. Monadicism: purely monadic predicates. FieldVsMonadicism/FieldVsHorwich: the "predicate monadicism" does not look attractive: it is unclear what analogues it has to the sp.t. points of S. Talk about regions or points cannot simply be replaced by talk about properties, because: M does not quantify at all on local properties, but it uses predicates. ((s) no existence assumptions). Then we have to assume a supply of uncountably many semantically primitive predicates. II 71 Def Fallacy of the Constitution/Horwich/Field: the (false) assumption that what constitutes relational facts would itself be relational. Representation/Horwich: instead we would have to find a monadic physical property that constitutes "believing that snow is white", etc. for each and every belief. E.g. that Pius X was the brother of Malcolm X!. These individual properties would not need to have anything in common. Important argument: above all, they do not need to involve a physical relation. Deflationism: Horwich pro, he needs his thesis for that. Field pro Deflationism. FieldVsHorwich: his resources are not fit for deflationism: because the "Fallacy of the Constitution" is not indeed a fallacy. His demands to a physicalist approach are too weak. E.g. a physical relation like "has the same temperature as". Surely you will not say that "having the same temperature as b" constituted another monadic property in the case of object b2, etc. through a monadic property in the case of b1, with these properties having nothing in common. II 72 If other requirements are to apply to the physical relation between people and propositions than for other physical relations, then you have to say why. FieldVsHorwich: it would not help him to say that other reduction standards apply if one of the sides is abstract. Because we also have this in the case of assigning numbers to objects, which preserves the relational character. But that may not be just transferred to intentional relations, as we have seen. ((s) FieldVsDavidson?). But as long as we cannot specify a reason for weaker standards, it is not shown that we do not need a genuinely relational approach, only that it is more difficult here. 2) On the other hand: some of the mental relations for which Horwich tries to avoid a relational approach exist between physical entities: E.g. "x has a belief about the person p". II 243 Nonfactualism/Value/Assessment/Ethics/Evaluative/Horwich/Field: (Horwich 1990): the deflationism that is attached to the ENT (Horwich pro) can still make sense of emotivism. Emotivism/Horwich: ...can say that the meaning of "x is good" sometimes is given by the rule that a person is in the position to express it if he is aware that he assesses X as good... (p. 88). FieldVsHorwich: this is the same problem as with Horwichs handling of vagueness: it boils down to him denying vagueness! Vagueness/Horwich/Field: he says that we cannot know if Jones is bald, because we can only know his physical description and baldness is not determinable from it. Assessment/Horwich/Field: here his remarks are compatible with the fact that "good" denotes a completely factual (evidence-based) property, but one with the special characteristic that our own assessment gives us the evidence that a thing instantiates this property - ((s) circularly) - and/or that our belief that something has this property, somehow to brings us to evaluate it ((s) just as circularl Unlike >Euthyphro). FieldVsHorwich: it is completely unclear now what nonfactualism actually is. |
Hartry Field I Field Realism, Mathematics and Modality Oxford 1989 II Field Truth and the absence of facts Wahrheit ohne Tatsachen Oxford, New York 2001 III Field Science without numbers Princeton University Press 1980 |
| Nominalism | Bigelow Vs Nominalism | I 62 NominalismVsBigelow: will try to avoid our apparatus of relations of relations. BigelowVsNominalism: we need relations and relations of relations in science. Realism/Bigelow/Pargetter: we do not claim to have proved him here. But he is the only way to solve the problem of the similar and the different (problem of quantities) (namely with the 3 levels). Simplicity/BigelowVsNominalism: will never be able to be as uniform as our realistic explanation. Nominalism would have to assume complex relational predicates as primitive. I 97 Quantities/BigelowVsNominalism/Bigelow/Pargetter: if he eliminated quantities, they would come back in through the back door because of the rules of composition. I 98 E.g. instead of refering to the quantity of rabbits, he might say it applies to all and only rabbits. BigelowVsNominalism: one could say this is just an abbreviation for "the quantity of all and only the rabbits". Be true/BigelowVsNominalism/Bigelow/Pargetter. "Is true" must be discussed further before this paraphrase could proof something ontological. ((s) BigelowVsQuine, > semantic ascent). Quantities/Bigelow/Pargetter: whether one believes in it, is not sure. The semantics does certainly not decide that. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
| Plato | Bigelow Vs Plato | I 49 Quantities/Plato/Bigelow/Pargetter: Problem: if properties are something that a thing can either have or not have, there is a problem of quantities. Solution/Plato: participation in forms: Allows gradual treatment. We differ slightly from Plato: Quantity/Plato/Bigelow/Pargetter: solutions of this kind have in common that they postulate an entity and the relation between that entity and the individuals who own it varies. I 50 Properties/Gradual/Degree/Berkeley/Plato/Bigelow/Pargetter: the theories are quite similar: they explain how properties can be gradual. Quantities/Bigelow/Pargetter: this does not solve the general problem of quantities (that they are gradual). Problem: degrees of relation. Solution: similarity and participation are an attempt. Forms/Plato/Bigelow/Pargetter: we do not claim that his theory of forms is incorrect. BigelowVsPlato: but does not solve the problem of quantities. (The nature of the quantity). I 51 VsPlato: Assuming many differnet properties instead of a variable relation, each for one quantity: E.g. to have the property having a mass of 2.0 kg, etc. This approach makes much of what is hard for Plato to explain easier: he shows what distinguishes objects (while Plato rather shows what they have in common). Def Determinable/Bigelow/Pargetter: what the objects have in common, but what is differently pronounced them. E.g. mass. Def Determinate/Bigelow/Pargetter: is the special property that distinguishes the objects (at the same time). E.g. a mass of 2.0 kg. I 51 Participation/BigelowVsPlato: with Plato, all things have a more or less strong relation to a single thing, the form. We, on the contrary, want relations of things to each other. BigelowVsPlato: that allows us to explain different types of differences between objects, namely, that they have different relational properties which other things do not have. E.g. two pairs of things may be different in different ways. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |
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