Dictionary of Arguments


Philosophical and Scientific Issues in Dispute
 
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The author or concept searched is found in the following 4 entries.
Disputed term/author/ism Author
Entry
Reference
Hermeneutics Gadamer I 169
Hermeneutics/Gadamer: Hermeneutics should (...) be understood so comprehensively that it would include the whole sphere of art and its questions. Like any other text to be understood, any work of art must not only
I 170
understand the literary. Thus the hermeneutic consciousness acquires a comprehensive breadth that even surpasses that of the aesthetic consciousness. Aesthetics must merge into hermeneutics. Cf. >Aesthetic Consciousness. The task today could be to escape the dominating influence of Dilthey's question and the prejudices of the "history of ideas" founded by him. >Hermeneutics/Dilthey.
I 171
(...) art [is] never only past (...), but [it] knows how to overcome the distance between times through its own presence of meaning. In this respect, the example of art shows an excellent case of understanding on both sides. It is not merely an object of historical consciousness, but its understanding nevertheless already includes historical mediation. How then is the task of hermeneutics determined? See >Hermeneutics/Schleiermacher, >Hermeneutics/Hegel.
I 177
Hermeneutics/Gadamer: The art doctrine of understanding and interpretation was developed in two ways, the theological and the philological, from an analogous drive: theological hermeneutics, as Dilthey showed(1), from the self-defense of the Reformation's understanding of the Bible against the attack of the Tridentine theologians and their appeal to the indispensability of tradition to rediscover philological hermeneutics as an instrument for the humanist claim to the
I 178
classical literature. Biblical Hermeneutics: its precondition is the scriptural principle of the Reformation. >Interpretation/Luther.
I 280
Hermeneutics/Gadamer: The fundamental discrediting of all the prejudices that the experiential pathos of the new natural science connects with the Enlightenment becomes universal and radical in the historical Enlightenment. This is precisely the point at which the attempt at philosophical hermeneutics must be critically applied. The overcoming of all prejudices, this blanket demand of the Enlightenment, will prove itself to be a prejudice, the revision of which will first clear the way for an appropriate understanding of the finite nature that dominates not only our humanity but also our historical consciousness. Cf. >Tradition/Romanticism. Does tradition really mean in the first place: to be subject to prejudice and to be limited in one's freedom? Is not rather all human existence, even the freest, limited and conditioned in manifold ways? If this is true, then the idea of an absolute reason is no possibility of historical humanity at all. Reason is for us only as real historical reason, i.e. par excellence: It is not master of itself, but always remains dependent on the circumstances in which
I 281
it is active. This applies not only in the sense that Kant, under the influence of Hume's sceptical criticism, limited the claims of rationalism to the a priori moment in the knowledge of nature - it applies much more decisively to historical consciousness and the possibility of historical knowledge. Understanding/Gadamer: The human is alien to him- or herself and his or her historical fate in still quite a different way than nature is alien to him or her, which does not know about the human.
For historical understanding see also >The Classical/Gadamer.
I 295
Hermeneutics/Gadamer: Understanding itself is not so much to be thought of as an act of subjectivity, but rather as moving into a process of tradition (i.e. handing down) in which past and present are constantly mediated. This is what must be brought to bear in hermeneutic theory, which is far too much dominated by the idea of a procedure, a method.
I 300
[A tension] plays between the foreignness and familiarity that tradition has for us, between the historically meant, distant representationalism and belonging to a tradition. In this in-between is the true place of hermeneutics.
I 313
Application of the understood: The inner fusion of understanding and interpretation led (...) to the fact that the third moment in the hermeneutical problem, the application, was completely pushed out of the context of hermeneutics. For example, the edifying application of Sacred Scripture in Christian proclamation and preaching seemed quite different from the historical and theological understanding of it. Now our reflections have led us to the insight that in understanding there is always something like an application of the text to be understood to the present >situation of the interpreter. We are thus forced to take a step beyond romantic hermeneutics, as it were, by thinking not only of understanding and interpreting, but also of applying, as part of a unified process. >Legal Hermeneutics/Gadamer, >Theological Hermeneutics/Gadamer.
I 334
Hermeneutics/Gadamer: Insofar as the actual object of historical understanding is not events but their "meaning", such understanding is obviously not correctly described when one speaks of an object that is in itself and the approach of the subject to it. In truth, historical understanding has always been based on the fact that the tradition that comes to us speaks into the present and must be understood in this mediation - even more: as this mediation must be understood.
I 391
Hermeneutics/Gadamer: Just as the translator, as interpreter, makes communication in conversation possible only by participating in the matter under discussion, so too, in relation to the text, the indispensable condition for the interpreter is that he or she participates in its meaning. It is therefore quite justified to speak of a hermeneutic conversation. But then it follows from this that the hermeneutic conversation, like the real conversation, must work out a common language, and that this working-out of a common language is just as little as in conversation the preparation of a tool for the purposes of understanding, but coincides with the accomplishment of understanding and understanding itself. Between the partners in this "conversation", as between two people, communication takes place that is more than mere adaptation. The text brings up a matter, but that it does so is ultimately the achievement of the interpreter. Both are involved.
I 392
In this sense, understanding is certainly not a "historical understanding" that reconstructs the correspondence of the text. Rather, one means to understand the text itself.
I 446
Hermeneutics/Humboldt/Gadamer: [Humboldt's] significance for the problem of hermeneutics lies (...) [in]: proving the language view as world view. >Language/Humboldt, >Culture/Humboldt. He recognized the living execution of speech, the linguistic energeia as the essence of language and thus broke the dogmatism of the grammarists. From the concept of force, which guides all his thinking about language, he has in particular also put into perspective the question of the origin of language, which was particularly burdened by theological considerations.
Origin of language/Humboldt: [Humboldt] rightly emphasizes that language is human from its very beginning(2).
I 479
Hermeneutics/Gadamer: Universality of hermeneutics: (...) linguistically and thus understandably is the human world relationship par excellence and by its very basis. Hermeneutics is (...) in this respect a universal aspect of philosophy and not only the methodological basis of the so-called humanities.
I 480
Art/history: (...) the concepts of "art" and "history" (...) are forms of understanding that are only just separated from the universal mode of being of hermeneutic being as forms of hermeneutic experience.



1. Dilthey, Die Entstehung der Hermeneutik, Ges. Schriften vol. V, 317 338.
2. W. von Humboldt, „Über die Verschiedenheit des menschlichen Sprachbaus ..“
(first printed in 1836), § 9, p. 60

Gadamer I
Hans-Georg Gadamer
Wahrheit und Methode. Grundzüge einer philosophischen Hermeneutik 7. durchgesehene Auflage Tübingen 1960/2010

Gadamer II
H. G. Gadamer
The Relevance of the Beautiful, London 1986
German Edition:
Die Aktualität des Schönen: Kunst als Spiel, Symbol und Fest Stuttgart 1977

Interpretation Benacerraf Field I 22
Interpretation/Benacerraf: (1965)(1) Thesis: Identification of mathematical objects with others is arbitrary - E.g. numbers with quantities. - E.g. real numbers with Dedekind cuts, Cauchy sequences, etc. - There is no fact that decides which is the right one. - Field ditto.
I 22
Indeterminacy of reference/Field: is not a problem, but commonplace.
I 25
For Benacerraf it is about identity, not about reference - otherwise he might falsely be refuted with primitive reference: "Numbers" refers to numbers but not to quantities - But that is irrelevant.
I 25
BenacerraffVsPlatonism: locus classicus - VsBenacerraf: based on an outdated causal theory of knowledge.
Field I 25
BenacerrafVsPlatonism: (1973)(2): if without localization and interaction we cannot know whether they exist. VsBenacerraf: indispensability argument.

1. Benacerraf, P. What Numbers Could Not Be, The Philosophical Review 74, 1965, S. 47–73.
2. Benacerraf, P. Mathematical Truth, The Journal of Philosophy 70, 1973, S. 661–679.

Bena I
P. Benacerraf
Philosophy of Mathematics 2ed: Selected Readings Cambridge 1984


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
Modalities Field I 185
Modality/Field: many people believe there can be a simple exchange between modality and ontology: one simply avoids an enrichment of the ontology by modal statements. ---
I 255
Modalization/Mathematics/Physics/Field: "Possible Mathematics": 1. Does not allow to preserve platonic physics
2. Advantage: This avoids the indispensability argument
3. False: "It is possible that mathematics is true" - but correct: Conservativity of modality. ((s) Mathematics does not change the content of physical statements).
4. For Platonic physics one still needs to use unmodalized mathematics.
5. Field: but we can formulate physics based neither on mathematics nor on modality: comparative predicates instead of numeric functors. - (257 +)
---
I 272f
Modal translation/mathematics/Putnam/Field: the idea is that in the modal translation acceptable sentences become true modal statements and unacceptable sentences false modal statements. Field: then there are two ways of looking at the translations: 1. as true equivalences: then the modal translation shows the truth of the Platonic theorems. (Truth preservation).
---
I 273
Or 2nd we can regard the modal translation as true truths: then the Platonic propositions are literally false. ((S) symmetry/asymmetry). N.B.: it does not make any difference which view is accepted. They only differ verbally in the use of the word "true".
---
I 274
Truth/mathematical entities/mE/Field: if a modal translation is to be true, "true" must be considered non-disquotational in order to avoid mathematical entities. - True: can then only mean: it turns out to be disquotational true in the modal translation, otherwise the existence of mathematical entities would be implied. - ((s) "Non-disquotational": = "turns out as disquotational.") (No circle).

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

Tradition Gadamer I 285
Tradition/Gadamer: That is exactly what (...) we call tradition: to apply without justification. We do indeed owe this correction of the Enlightenment to Romanticism, that outside the grounds of reason, tradition also retains a right and determines our institutions and behaviour to a large extent. The superiority of ancient ethics over the moral philosophy of modern times is characterized by the fact that, in view of the indispensability of tradition, it justifies the transition of ethics into "politics", the art of right legislation.(1)
By comparison, the modern Enlightenment is abstract and revolutionary. However, the concept of tradition has become no less ambiguous than the concept of >authority, and for the same reason, namely that it is the abstract opposition to the principle of the Enlightenment that determines Romanticism's understanding of tradition. It conceives tradition as opposed to
I 286
reasonable freedom and sees in it a historical fact of the way of nature. Whether one fights it in a revolutionary way or wants to conserve it, it appears as the abstract opposite of free self-determination, since its validity does not require any reasonable reasons, but determines us without question. Gadamer: Of course, the case of the Romantic critique of the Enlightenment is not an example of the self-evident rule of tradition, in which the traditional is preserved unbroken by doubt and criticism. Rather, it is a critical reflection of its own, which here first turns again to the truth of tradition and seeks to renew it, and which can be called traditionalism.
I 393
Tradition/Gadamer: No matter how much linguistic tradition may be relegated to the background of monuments of the visual arts, for example, its vivid immediacy may be neglected. But their lack of immediacy is not a defect. What has come to us by way of linguistic tradition is not left over, but is handed over, i.e. it is told to us (...). >Writing/Gadamer.
I 394
Bearer: The bearer of the tradition is not this manuscript as a piece from back then, but the continuity of the memory. Through it the tradition becomes a part of the own world, and so what it communicates is able to come directly to speech.

1. Vgl. Aristoteles, Eth. Nic. K 10

Gadamer I
Hans-Georg Gadamer
Wahrheit und Methode. Grundzüge einer philosophischen Hermeneutik 7. durchgesehene Auflage Tübingen 1960/2010

Gadamer II
H. G. Gadamer
The Relevance of the Beautiful, London 1986
German Edition:
Die Aktualität des Schönen: Kunst als Spiel, Symbol und Fest Stuttgart 1977


The author or concept searched is found in the following 11 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Antirealism Field Vs Antirealism Field I 64
Indispensability: if it is true that mathematics does not only facilitate inferences, it would be theoretically indispensable. How can indispensability be represented in terms of conservatism? Quine-Putnam Argument/VsAnti-Realism: (see above): only through truth! We must assume the truth of mathematics for its usefulness in the non-mathematical realm.
FieldVs: that is certainly an exaggeration. Part of the benefit may also be explained by conservatism (but not only).
I 65
Ultimately, I try to show that mathematics is not indispensable after all.
Field I 66
Realism/Mathematics/Gödel: ("What is Cantor’s Continuum Problem?", 1947) (Per Quine-Putnam argument VsField, GödelVsAnti-Realism): even with a very narrow definition of the concept of "mathematical data" (only equations of the theory of numbers ) we can justify very abstract parts by explanation success: Gödel: even without assuming the need for a new axiom, and even if it has no intrinsic necessity, a decision about its truth is possible by studying its "explanation success" with induction. The fruitfulness of its consequences, in particular the "verifiable" ones, i.e. those that are demonstrable without the new axiom, but which are easier to prove with the new Axiom. Or if this allows us to combine several proofs into one.
E.g. axioms about the real numbers, which are rejected by the intuitionists.

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
Antirealism Quine Vs Antirealism Field I 64
Infinite/Anti-Realism/Field: the Anti-R can only assume an infinite number of entities if there is an infinite number of physical entities. (E.g. infinitely many parts of a light beam). But it would be inappropriate to want to test the adequacy of the number theory by assumptions about the physical world. Truth/Ontology/Field: sure, the truth of the number theory would require infinitely many objects for the quantifiers, but its conservatism would not! And conservatism is all we need! Physics: How about atypical applications such as differential equations, etc.? Here the existence of many entities such as real numbers, functions, differential operators, etc. seems to be called for. How should nominalistic inferences become easier here? Where ever are the nominalistic premises? We would only have them if we were able to somehow represent the theory of electromagnetism nominalistically, and that seems hardly possible. Indispensability: if it is true that mathematics does not only facilitate inferences, it would theoretically be indispensable. How can indispensability be represented in terms of conservatism? Quine Putnam Argument/VsAnti-Realism: (see above): only by truth! We must assume the truth of mathematics for its usefulness in the extra-mathematical realm. FieldVs: this is certainly an exaggeration. Parts of the usefulness may also be explained by conservatism (but not only).
Field I 65
In the end, I try to show that thesis: mathematics is not just indispensable.

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985

Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978

Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989

Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:
Unterwegs zur Wahrheit Paderborn 1995

Quine VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, Cambridge, MA 1953

Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982

Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967

Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005

Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Benacerraf, P. Field Vs Benacerraf, P. I 24
VsBenacerraf/Field: another argument could be brought forward: the problem of consistent arbitrariness of identifications is a phenomenon not only in mathematics, but also in other areas: E.g. PutnamVsMetaphysical Realism: E.g. some say it is arbitrary whether a point is a convergent number of ever smaller regions, all of which are non-zero. Anti-PlatonismVs: If no sets are assumed, the problem takes care of itself.
I 25
Arbitrariness/Field: Thesis: In the realm of physical objects, we do not have the same consistent arbitrariness as in mathematics. VsPlatonism/Mathematics/Field: 1) The most-discussed challenge to him is the epistemological position. Locus classicus: BenacerrafVsPlatonism: (1973): FieldVsBenacerraf: Problem: it relies on an outdated causal theory of knowledge. BenacerrafVsPlatonism: if there were language and mind-independent mathematical entities without spatiotemporal localization which cannot enter any physical interactions, then we cannot know if they exist nor know anything else about them. The Platonist had to postulate mysterious forces. VsBenacerraf: here we could respond with the indispensability argument: Mathematical entities (ME) are indispensable in our different theories about physical objects. FieldVsVs: but this assumes that they are indispensable, and I don’t believe they are. Benacerraf/Field: However, we can formulate his argument more sharply. Cannot be explained as a problem of our ability to justify belief in mathematical entities, but rather the reliability of our belief. In that, we assume that there are positive reasons to believe in such mathematical entities.
I 26
Benacerraf’s challenge is that we need to provide access to the mechanisms that explain how our beliefs about such remote entities reproduces facts about them so well. Important argument: if you cannot explain that in principle, the belief in the mathematical entities wanes. Benacerraf shows that the cost of an assumption of ME is high. Perhaps they are not indispensable after all? (At least this is how I ​​I understand Benacerraf).
I 27
VsBenacerraf/Field: 2) sometimes it is objected to his position (as I have explained) that a declaration of reliability is required if these facts are contingent, which would be dropped in the case of necessary facts. (FieldVs: see below, Essay 7).
I 29
Indispensability Argument/Field: could even be explained with evolutionary theory: that the evolutionary pressure led us to finally find the empirically indispensable mathematical assumptions plausible. FieldVsVsBenacerraf: Problem: the level of mathematics which applied in empirical science is relatively small! That means only this small part could be confirmed as reliable by this empiricism.

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Constructivism Verschiedene Vs Constructivism Barrow I 65/66
Constructivism: Founder Leopold Kronecker: "The whole numbers were made by God, everything else is human work." The meaning of a mathematical formula lies only in the chain of operations with which it is constructed. Constructivism introduces a third status: undecided! A statement that cannot be decided in a finite number of steps comes into the junk chamber of undecidedness.
I 67
VsConstructivism: before constructivism, mathematics had developed all possible methods of proof which are not feasible in a finite number of steps. Def Reductio ad absurdum/raa: evidence which assumes that something is wrong in order to prove its indispensability, in that a contradiction arises from the very assumption of falsity.
I 68
BrouwerVsHilbert: (Einstein: the "war of frogs and mice" also >"frog mouse war") Hilbert prevailed: The board of editors of the joint newspaper "Mathematische Annalen" was dissolved and refounded without Brouwer.
I 69
Constructivism: strange anthropocentrism: BarrowVsConstructivism: the idea of a universal human intuition of the natural numbers cannot be kept historically (see above). A constructivist cannot say whether the intuition of a human being is the same as that of another, nor whether such an intuition will develop further in the future.





B I
John D. Barrow
Warum die Welt mathematisch ist Frankfurt/M. 1996

B II
John D. Barrow
The World Within the World, Oxford/New York 1988
German Edition:
Die Natur der Natur: Wissen an den Grenzen von Raum und Zeit Heidelberg 1993

B III
John D. Barrow
Impossibility. The Limits of Science and the Science of Limits, Oxford/New York 1998
German Edition:
Die Entdeckung des Unmöglichen. Forschung an den Grenzen des Wissens Heidelberg 2001
Derrida, J. Putnam Vs Derrida, J. III 96 ff
However, the typical representatives of relativism paradoxically believe they had made something like a metaphysical discovery. Deconstructivism/Derrida/Putnam: he completes step from relativism to nihillism. This concept of truth is incoherent and belongs to a "metaphysics of presence" (Derrida). Derrida, allegedly: "the concept of truth is inconsistent, but absolutely essential!"
PutnamVsDerrida: What do you mean, every use of the word "true" contains a contradiction?
III 97
The failure of a number of mutually exclusive philosophical explanations of the concept of truth is something completely different from the failure of the concept of truth itself! LL Wittgenstein: the failure of a number of philosophical analyses of certainty is something other than the failure of the normal concept of certainty.
PutnamVsDerrida: but the collapse of a particular worldview is far from being a collapse of the concepts of representation and truth. Because if we equate this metaphysical tradition with our lives and our language, we would be giving metaphysics an entirely exaggerated importance.

DerridaVsSaussure: approves this, he criticized Saussure only in that he did not go further and abandoned the concept of the character altogether.
III 163
PutnamVsDerrida: Derrida overlooks here that Saussure's way of thinking was based on a utopian project. It had been hoped that a a stringent scientific explanation of the concept of meaning could be given. This hope has failed, but we are not forced to the absurd view that nobody could understand a language other than their own idiolect. Even Derrida himself does not go that far. He recognizes the indispensability of translations indeed.
III 164
Solution/Putnam: the alternative to Saussure's view is that retaining the concept of "meaning equality", while realizing that it must not be interpreted in the sense of self-identity of objects called "meaning" or "significate".
III 165
Can it be that Derrida makes the same mistake as Jerry Fodor? He does not even consider the possibility that the kind of "meaning equality" aimed at in translation could be an interest-relative (but still very real) relationship, which presupposes a normative judgment, i.e. a judgment about what is reasonable in the individual case.
III 168
Derrida/Putnam: his attitude is much harder to pin down. (DerridaVsLogocentrism.) Derrida himself emphasizes that the logocentric quandary was no "pathology" for which he had a cure to offer. We must fall into this quandary by fate. >Logocentrism.
By his leftist supporters Derrida has often been interpreted as if this justified even a consistent rejection of the idea of ​​the rational justification.
Forgery/Bernstein: "You cannot falsify just anything."
Richard BernsteinVsDerrida: what do the texts by Derrida have about them that permits, or even demands this double interpretation? It is ultimately true that "not just anything can be falsified".
III 171
PutnamVsDerrida: Derrida's quandary is one in which those fall who, albeit not wanting to be "irresponsible", also want to "problematize" the concepts of reason and truth by teaching that these concepts have failed. His steps amount to the fact that the concepts "rationale", "strong reason", "justification", etc. correspond to repressive practices more than anything. And this view is dangerous indeed, because it offers help and comfort to all sorts of left and right extremists.

I (a) 22
PutnamVsDerrida: its criticism of "logocentrism" is not only wrong, but dangerous.
I (k) 266
Deconstruction/PutnamVsDerrida: is right in that a certain philosophical tradition (for example, binary logic) is simply bankrupt. But identifying this tradition with our lives and our language is to give metaphysics a completely exaggerated importance. Meaning Equality/PutnamVsDerrida: is actually an interest-relative one! It contains a judgment about what is reasonable in each case.
I (k) 273
PutnamVsDerrida: deconstruction without reconstruction is irresponsibility. >Deconstructionism.

Putnam I
Hilary Putnam
Von einem Realistischen Standpunkt
In
Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993

Putnam I (a)
Hilary Putnam
Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973)
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (b)
Hilary Putnam
Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (c)
Hilary Putnam
What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194.
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (d)
Hilary Putnam
Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482.
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (e)
Hilary Putnam
Reference and Truth
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (f)
Hilary Putnam
How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (g)
Hilary Putnam
Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982)
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (h)
Hilary Putnam
Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (i)
Hilary Putnam
Realism with a Human Face, Cambridge/MA 1990
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (k)
Hilary Putnam
"Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam II
Hilary Putnam
Representation and Reality, Cambridge/MA 1988
German Edition:
Repräsentation und Realität Frankfurt 1999

Putnam III
Hilary Putnam
Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992
German Edition:
Für eine Erneuerung der Philosophie Stuttgart 1997

Putnam IV
Hilary Putnam
"Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164
In
Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994

Putnam V
Hilary Putnam
Reason, Truth and History, Cambridge/MA 1981
German Edition:
Vernunft, Wahrheit und Geschichte Frankfurt 1990

Putnam VI
Hilary Putnam
"Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98
In
Truth and Meaning, Paul Horwich Aldershot 1994

Putnam VII
Hilary Putnam
"A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43
In
Theories of Truth, Paul Horwich Aldershot 1994

SocPut I
Robert D. Putnam
Bowling Alone: The Collapse and Revival of American Community New York 2000
Fictionalism Putnam Vs Fictionalism Fraassen I 34
Indispensability-argument/Putnam/Fraassen: (Putnam Philosophy of Logic): Thesis: terms of mathematical entities are essential for non-elementary mathematics, theoretical terms (TT) are indispensable for physics. Cf. >As if, >Fictions, >Theoretical Terms, >Theoretical Entities.
Fraassen I 35
Fictionalism/Vaihinger/Duhem/Putnam: (puts it opposite it): the theoretical terms are probably indispensible, but thus, no tendency is connected to show that certain entities do exist, they are merely useful fictions. Fraassen: i.e. also that it is not required that the relevant theories are true.
PutnamVsFictionalism: (first, bad arguments): 1. verificationism: (PutnamVsVerificationism) the logical positivists sticked to a verificationist meaning theory, that is, the complete cognitive content of an assertion is a function of the empirical results that would verify it or disprove it. Therefore, there can be no real differences between two hypotheses with the same empirical content.

Putnam I
Hilary Putnam
Von einem Realistischen Standpunkt
In
Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993

Fr I
B. van Fraassen
The Scientific Image Oxford 1980
Field, H. Quine Vs Field, H. Field I 128
Quine-Putnam-Argument/VsField: we must assume the truth of mathematical statements in order to be able to do academic work. >indispensability argument). FieldVs: the only way around this: show that the nominalistic resources for good science are adequate. This is not a consequence of conservatism.

Field II 202
Partial Signification/Field: is not so unusual: we often apply it implicitly in the case of vague expressions. Ex what is the extension of the term e.g. "big man" in German? There is no fact which decides whether 185 or 180 cm. Solution: "big man" partially signifies a set and partially other sets. Namely, the sets of shape
{xI x is a person taller than h}.
FieldVsQuine: that is quite unlike in Quine.
QuineVsField: it is not necessary to abandon the normal semantic concepts of denotation and signification. Instead, we can make them relative.
(1) for a foreign language: here we do not have to refrain from talking about the signification of a foreign word. But we must say that relative to the obvious translation manual ...
FieldVsQuine: but apparently that makes no sense. (1) seems to suggest that we could explain relative signification as:
(2) saying that a term T used in one language signifies the amount of rabbits, relative to a ÜH M, actually means that M translates T as "rabbit".
FieldVs: that is not sufficient.

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Field, H. Wright Vs Field, H. Field I 43
Anti-Platonism/AP/WrightVsField: (Hale, 1987): claims that modal considerations undermine my version of the anti-platonism. Because I take mathematics and the existence of mathematical entities (mE) as consistent, and consistency as the modal basic concept (possibility), I would be bound to think that it is wrong that there are mathematical entities - that the existence of mathematical entities is "contingent wrong". ((s) "There could just as well have been mathematical entities, i.e. empirical question").
Contingent/Wright/HaleVsField: is not logical, and thus something other than "neither logically true nor logically contradictory". And that makes Field's position absurd.
WrightVsField: where should Fields "contingency" be contingent on? For example, according to Field, the actual world contains no numbers, but it could have contained some. But there is neither an explanation for why not, nor would there be an explanation if there were numbers.
FieldVsVs: if the argument were good, it would be equally valid against (nonlogical) platonism, for which mathematics goes back behind logic. Then the denial of all mathematics would be logically consistent and therefore "contingent". But this is a confusion of the different meanings of "possible". Analog:
For example, if the existence of God is logically consistent, and there is none, then it is contingent wrong that there would be one.
Problem: the atheist has no access to what the contingent is supposed to be on. There would be neither an explanation for the existence nor for the non-existence. There are no favorable conditions for God's existence and no unfavorable ones. (>Anselm, 2. Ontological argument).
But WrightVsField: has even more interesting arguments: 1. without the assumption that mathematics consists of necessary truths, the view that mathematics is conservative (preserving) is unjustified.
I 44
Analog: without the assumption that mathematics is true, the assumption that it is consistent is unjustified. Justification/FieldVsWright: You can justify any belief by a stronger belief from which it follows. (>Strength of Theories).
Wright and Hale would have to show that Platonism has better reasons for the necessary truth of mathematics than Anti-Platonism has for assuming that mathematics is conservative (or consistent). And it is not certain that this is true.
WrightVsField: 2. Anyone who represents both:
a) that the existence of mathematical entities is "contingent false" and
b) that mathematics is conservative,
can give no reason not to believe in mathematical entities!
Def Conservativity/Mathematics/Field: means that any internally consistent combination of nominalistic statements is also consistent with mathematics.
Then no combination of nominalistic statements can provide an argument against belief in mathematics (ontology).
WrightVsField: how then can there be any reason at all not to believe in mathematics? He has no proof of his own nominalism. It follows that Field cannot be a nominalist, but that he must be an agnostic.
FieldVsWright: this one misjudges the relevance that I attribute to the question of renunciability and indispensability.
Conservativity: does not automatically show that there can be no reason to believe in mathematics.
To succeed with VsPlatonism, we must also show that mathematics is dispensable in science and meta logic. Then we have reason not to literally have to believe in mathematics.
I 45
If that succeeds, we can get behind the agnosticism.

WrightCr I
Crispin Wright
Truth and Objectivity, Cambridge 1992
German Edition:
Wahrheit und Objektivität Frankfurt 2001

WrightCr II
Crispin Wright
"Language-Mastery and Sorites Paradox"
In
Truth and Meaning, G. Evans/J. McDowell Oxford 1976

WrightGH I
Georg Henrik von Wright
Explanation and Understanding, New York 1971
German Edition:
Erklären und Verstehen Hamburg 2008

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Field, H. Verschiedene Vs Field, H. Field I 51
Infinity/Physics/Essay 4: even without "part of" relation we do not really need the finity operator for physics. VsField: many have accused me of needing every extension of 1st level logic. But this is not the case.
I 52
I rather assume that the nominalization program has not yet been advanced far enough to be able to say what the best logical basis is. Ultimately, we are going to choose only a few natural means that go beyond the 1st level logic, preferably those that the Platonist would also need. But we can only experience this by trial and error.
I 73
Indispensability Argument/Logic/VsField: if mE may be dispensable in science, they are not in logic! And we need logic in science. Logical Sequence Relation/Consequence/Field: is normally defined in terms of model theory: (Models are mE, semantic: a model is true or not true.)
Even if one formulates them in a proven theoretical way ("there is a derivation", syntactically, or provable in a system) one needs mE or abstract objects: arbitrary sign sequences of symbol tokens and their arbitrary sequences.
I 77
VsField: some have objected that only if we accept a Tarski Theory of truth do we need mE in mathematics. FieldVsVs: this led to the misunderstanding that without Tarskian truth mathematics would have no epistemic problems.
Mathematics/Field: indeed implies mE itself, (only, we do not always need mathematics) without the help of the concept of truth, e.g. that there are prime numbers > 1000.
I 138
Logic of Part-of-Relation/Field: has no complete evidence procedure. VsField: how can subsequent relations be useful then?
Field: sure, the means by which we can know that something follows from something else are codifiable in an evidentiary procedure, and that seems to imply that no appeal to anything stronger than a proof can be of practical use.
FieldVsVs: but you do not need to take any epistemic approach to more than a countable part of it.
I 182
Field Theory/FT/Relationalism/Substantivalism/Some AuthorsVsField: justify the relevance of field theories for the dispute between S/R just the other way round: for them, FT make it easy to justify a relationalist view: (Putnam, 1981, Malament 1982): they postulate as a field with a single huge (because of the infinity of physical forces) and a corresponding part of it for each region. Variant: the field does not exist in all places! But all points in the field are not zero.
FieldVsPutnam: I do not think you can do without regions.
Field II 351
Indeterminacy/Undecidability/Set Theory/Number Theory/Field: Thesis: not only in the set theory but also in the number theory many undecidable sets do not have a certain truth value. Many VsField: 1. truth and reference are basically disquotational.
Disquotational View/Field: is sometimes seen as eliminating indeterminacy for our present language.
FieldVsVs: that is not the case :>Chapter 10 showed that.
VsField: Even if there is indeterminacy in our current language also for disquotationalism, the arguments for it are less convincing from this perspective.
For example, the question of the power of the continuum ((s)) is undecidable for us, but the answer could (from an objectivist point of view (FieldVs)) have a certain truth value.
Uncertainty/Set Theory/Number Theory/Field: Recently some well-known philosophers have produced arguments for the impossibility of any kind of uncertainty in set theory and number theory that have nothing to do with disquotationalism: two variants:
1. Assuming that set theory and number theory are in full logic of the 2nd level (i.e. 2nd level logic, which is understood model theoretically, with the requirement that any legitimate interpretation)
Def "full" in the sense that the 2nd level quantifiers go over all subsets of the 1st level quantifier range.
2. Let us assume that number theory and the set theory are formulated in a variant of the full logic of the 2nd level, which we could call "full schematic logic of level 1".
II 354
Full schematic logic 1st Level/LavineVsField: denies that it is a partial theory of (non-schematic!) logic of the 2nd level. Field: we now better forget the 2nd level logic in favour of full schematic theories. We stay in the number theory to avoid complications. We assume that the certainty of the number theory is not in question, except for the use of full schemata.





Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Indispensability Field Vs Indispensability I 14
Indispensability Argument/Field: here it’s all about purposes - such an argument must be based on the best explanation (BE).
I 17
FieldVsIndispensability Argument: we can show that there are good theories that do without mathematical entities - Justification/Field: is gradual. FieldVsIndispensability Argument: two points which together make it seem untenable: 1) if we can show that there are equally good theories that do not involve ME. I believe that we can show that in the case of ME, but not in the case of electrons! (Lit.Field: "Science without Numbers"). At the moment, we do not yet know exactly how to eliminate ME, and our method of ((s) complete) induction gives us some confidence in mathematical entities 2) Justification is not a question of all or nothing! (justification gradual)
I 29
Indispensability Argument/Field: Might even be explained by way of evolutionary theory: that evolutionary pressure finally led us to find the empirically indispensable mathematical assumptions plausible. FieldVsVsBenacerraf:. Problem: the scope of mathematics which is used in empirical science is relatively small! That means that only this small portion could be confirmed as reliable by empiricism. And inferences on the rest of mathematics are not sustainable, there are simply too many possible answers to questions about large cardinals or the continuum hypothesis or even about the axiom of choice. These work well enough to provide us with the simpler "application mathematics". ((s) That means that we cannot infer a specific answer to the questions of the higher levels from application mathematics.)
II 328
Utility/Truth/Mathematics/Putnam/Field: (Putnam 1971 locus classicus, unlike 1980): Thesis: we must consider mathematics as true in order to be able to explain its utility (benefit) in other fields. E.g. in science and metalogic. (i.e. the theory of logical consequence). Modality/Modal/Mathematics/Field: this is in contrast to his former view that we can use modality instead of mathematical objects to explain mathematical truth.
II 329
Modal Explanation: will not work for other disciplines such as physics, however. (FieldVsPutnam, Field 1989/91: 252-69). Putnam/Field: the general form of his argument is this: (i) we must speak in terms of mathematical entities in order to study science, metalogic, etc. (ii) If need them for such important purposes, we have reason to believe that this kind of entities exists. VsPutnam/Field: there are two possible strategies against this: 1) Vs: "foolhardy" strategy: requires us to substantially change premise (i): we want to show that we basically do not need to make any assumptions which require mathematical entities. I.e. we could study physics and metalogic "nominalistically". Problem: in a practical sense, we still need the mathematical entities for physics and metalogic. We need to explain this practical indispensability. "foolhardy" strategyVs: in order to explain them, we just have to show that mathematical entities are only intended to facilitate inferences between nominalistic premises. And if this facilitation of inference is the only role of mathematical entities, then (ii) fails. Solution: In that case, something much weaker than truth (E.g. "conservatism") suffices as an explanation for this limited kind of utility. FieldVs: Unfortunately, the project of nominalization is not trivial. (Field 1980 for physics, 1991 for metalogic). At that time I found only few followers, but I am too stubborn to admit defeat. 2) Vs ("less foolhardy strategy"): questions (ii) more profoundly: it denies that we can move from the theoretical indispensability of existence assumptions to a rational belief in their truth. That is what Putnam calls "indispensability argument". Putnam pro. FieldVsPutnam: that requires some restrictions and ManyVsPutnam: these restrictions ultimately prevent an application in mathematics. And ultimately, because mathematical entities are simply not causally involved in physical effects.
II 330
FieldVsPutnam: that’s plausible. PutnamVsVs: If mathematical entities are theoretically indispensable in causal explanations (such as (i) claims), however, there seems to be a sense in which they are very well causally involved. Conversely, it would have to be explained why they should not be causally involved. FieldVs: a closer look should reveal that the role of mathematical entities is not causal. And that it supports no indispensability argument. E.g. the role of quantities in physics was simply to allow us to assert the local compactness of physical space. Other E.g. role of quantities in physics. Allow us to accept (Cp) instead of (Cs). (Field, 1989) 1, 136-7). ... + ...

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Putnam, H. Field Vs Putnam, H. III 113
Pure Mathematics/Putnam: should be interpreted in a way that it asserts the possible existence of physical structures that satisfy the mathematical axioms. FieldVsPutnam: pure mathematics should not be interpreted at all.
I 211
Properties/Relations/Putnam: (1970): are predicative, according to them we have a few basic physical prop and rel from which all others are derived: 1st order: Allows no reference to a totality of physical objects when a new property is constructed.
2nd order: Allows reference to the totality of the properties of the 1st order.
3rd order: Allows reference to the totality of the properties of the 1st and 2nd order. - Every physical property appears on any level of the hierarchy -> functionalism.
Functional properties are 2nd or higher order properties - the prop that the role has may differ from person to person.
I 214
FieldVsPutnam: instead of properties provide instantiations of properties with steps.
I 268
Mathematics/Ontology/Putnam: ("Mathematics without foundations", 1976b, 1975 "What is mathematical truth?"): Field: Putnam Thesis: the mathematical realist does not have to accept the "mathematical object picture". He can formulate his views in purely modal terms. And that not as an alternative, but only as another formulation of the same view.
I 269
Indispensability Argument/Putnam: appear in the subsequent text. Field: If "Mathematics as a modal" logic was really an equivalent description of mathematics in terms of mathematical objects (MO), then it should also be possible to reformulate the Indispensability Argument so that there is a prima facie argument for one or the other kind of modalized mathematics and mathematical objects.
FieldVsPutnam: but Section 6 and 7 show that we cannot formulate the indispensability argument like that: it requires MO and modalized mathematics does not bring them forth.
VSVs: but beware: I have not studied all the possibilities.
I 269
FieldVsPutnam: his mathematical realism seems puzzling: Mathematics/Ontology/Putnam: Thesis: there is a modal translation of pure mathematics: he presents a translation procedure that turns mathematical statements into modal statements, one that transforms acceptable mathematical statements (E.g. axioms of set theory) into true modal assertions that include no quantification, unless it is modalized away. (I.e. ​​no mathematical entities (ME) in the modal statements).
I 270
FieldVsPutnam: two general questions: 1) what kind modality is involved here?
2) what benefit is the translation to have?
ad 1): Putnam thinks that the "object-image" (the starting position) and its modal translation are equivalent at a deeper level.
FieldVs: that’s really not interesting: "mathematically possible" should coincide with "logically possible" in any reasonable view (this is stated by conservatism). ((s) contrary to the above).
Important argument: if A is not mathematically possible, then "~A" is a consequence of mathematics - i.e. if A (and then also its negation) are purely non-mathematically, then "~A" is logically true.
If Putnam now says that his modal translation involves a "strong and clear mathematical sense of possibility", then a mathematical possibility operator must be applied to sentences that contain ME.
However, such a sentence A could also be a mixed sentence (see above, with purely mathematical and purely physical components).
I 271
FieldVsPutnam: for purely mathematical sentences mathematical possibility and truth coincide! But then the "modal translations" are just as ontologically committed as the mathematical assertions.
FieldVs"Mathematical Possibility"/FieldVsPutnam: we had better ignore it. Maybe it was about 2nd order logical possibility as opposed to 1st order for Putnam?
I 271
FieldVsPutnam: what benefits does his modal translation have? Does it provide a truth transfer (as opposed to the transmission of mere acceptability)? And what value has it to say that the mathematical statements are both true and acceptable? Etc. Mathematics/Realism/Putnam/Field: Putnam describes himself as
"mathematical realist": Difference to Field’s definition of realism: he does not consider ME as mind-independent and language-independent, but (1975):
Putnam: you can be a realist without being obliged to mathematical objects.
I 272
The question is the one that Kreisel formulated long ago: the question of the objectivity of mathematics and not the question the existence of mathematical objects. FieldVsPutnam: this is puzzling.
I 277
Model Theory/Intended Model/Putnam/Field: this morality can be strengthened: there is no reason to consider "∈" as fixed! Putnam says that in "Models and Reality": the only thing that could fix the "intended interpretation" would be the acceptance of sentences that contain "∈" through the person or the community. Putnam then extends this to non-mathematical predicates. ((s)> Löwenheim-Skolem).
FieldVsPutnam: this is misleading: it is based on the confusion of the view that the reference is determined, E.g. by causal reasoning with the view that it is defined by a description theory (description theory, (labeling theory?), in which descriptions (labels?) that contain the word "cause" should play a prominent role. (> Glymour, 1982, Devitt, 1983, Lewis 1984).

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 theses of the more related field of specialization.
Disputed term/author/ism Author
Entry
Reference
Platonism Field, Hartry I 44
To succeed in VsPlatonism, we must also show, thesis: that mathematics is dispensable in science and metalogic. Then we have reason not to literally have to believe in mathematics. (>Indispensability argument).
I 45
If that succeeds, we can get behind the agnosticism.
I 186
Def moderate platonism/mP/Field: the thesis that there are abstract objects like numbers. Then one probably also believes that there are relations of physical size between objects and numbers. (But only derived): Example "mass in kilogram" is then relation between a given physical object and the real number 15,2.
Example "distance in meters" is a relation between two objects ((s) on one side) and the real number 7,4.
The difference to high-performance platonism (HPP) lies in the attitude to these relations:
Moderate Platonism: Thesis: These are conventional relations derived from more fundamental relations existing between physical objects alone.
Def High Performance Platonism/Field: denies that and takes the relations between objects and numbers as a bare fact that cannot be explained in other terms.
Inflated one could explain this as "platonistic participation".
II 332
Standard Platonism: Thesis: Mathematical theories such as set theory or the theory of real numbers are about different mathematical domains, or at least about certain structures, because there is no need to assume that isomorphic domains (i.e. domains with the same structure) would be mathematically indistinguishable. Thus, "regions" should not be assumed as sets.
II 333
Def "Platonism of perfection": (plenitude): postulates a set of mathematical objects. Thesis: Whenever we have a consistent purely mathematical theory, there are mathematical objects that fulfill the theory under a standard-fulfillment relation. Platonism of perfection: but also suggests that we can consider all quantifiers about mathematical entities in this way,
I 334
that they are implicitly limited by a predicate to which all other predicates of mathematical entities are subordinated: The "overarching" predicate: is then different between the different mathematical theories. These theories then no longer conflict.
II 335
Universe/Standard Platonism/Field: (Thesis: "Only one universe exists"). Problem/PutnamVsPlatonism: how do we even manage to pick out the "full" (comprehensive) universe and confront it with a sub-universe, and accordingly the standard element relationship as opposed to a non-standard element relationship? (Putnam 1980). (Here placed from the perspective of "Universe").
Putnam: Thesis: We simply cannot do that.