Dictionary of Arguments


Philosophical and Scientific Issues in Dispute
 
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Entry
Reference
Descriptions Kripke I 78 ff
You could say "The Jonah of the book never existed", as one might say "the Hitler of Nazi propaganda never existed." Existence independent of representation. ---
I 94
Reference by description: E.g. "Jack the Ripper"
E.g. "Neptune" was named as such before anyone had seen him. The reference was determined because of the description of its place. At this point they were not able to see the planet. Counter-example: "Volcano".
---
I 94f
It might also turn out that the description does not apply to the object although the reference of the name was specified with the description. E.g. the reference of "Venus" as the "morning star", which later turns out not to be a fixed star at all. In such cases, you know in no sense a priori that the description that has defined the reference applies to the object. ---
I 93ff
Description does not shorten the name. E.g. Even if the murdered Schmidt discovered the famous sentence, Goedel would still refer to Goedel. ---
I 112f
Description determines a reference, it does not provide synonymy. "Standard meter" is not synonymous with the length - description provides contingent identity: Inventor post minister. ---
I 115
Identity: Through the use of descriptions contingent identity statements can be made. ---
I 117
QuineVsMarcus ("mere tag") is not a necessary identity of proper names, but an empirical discovery - (Cicero = Tully) identity does not necessarily follow from description - identity of Gaurisankar is also an empirical discovery. ---
I 25/26
Description/names/Kripke: Serves only to determine the reference, not to identify the object (for counterfactual situations), nor to determine the meaning.
I 36
Description is fulfilled: Only one sole object fulfils the description (e.g. "The man drinking champagne is angry" (but he drinks water).) apparent description: e.g. Holy Roman Empire (neither holy nor Roman) hidden proper name.
---
III 353
Description/Substitutional Quantification: L must not occur in the substitution class: necessary and sufficient conditions to ensure that each sentence of the referential language retains its truth value is that whenever (Exi)f is true (when only xi is free), a substitution class f" of f will be be true (> condition (6)) - this does not work with certain L, even if (6) is fulfilled. ---
III 369
Theory of Descriptions/Russell: y(ixf(x)) where f(x) is atomic, analyzed as follows: (Ey)(x)(y = x ↔ f(x)) ∧ y(y)) (Wessel: exactly one": (Ex)(P(x) ∧ (y)(P(y) > x = y)) "There is not more than one thing": (x)(y)(x = y) - ambiguous, if more than one description: Order of elimination.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984

Number Theory Kripke III 383f
Substitutional Quantification/sQ/Number Theory/KripkeVsWallace: the object language should be written substitutionally: the substitution class then consists of the number names: 0,0",0""... - the meta language needs a referential variable about the expressions of the object language - could we replace it with Gödel numbers? No! - Because the question was whether an ontology of numbers was used in the meta language, in addition to the ontology of expressions. - We cannot even ask this question if we identify expressions with numbers, - The two have asked the wrong question twice: 1) By having treated the object language variables as referential about numbers rather than as a substitutional with number names as substitutes. - 2) By interpreting the referential variables of the meta language as Gödel numbers instead of as symbol chains of the object language. - Usually, identification of expressions with their Gödel numbers is harmless - but here we must distinguish numbers and expressions.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984

Proper Names Quine I 230
Ambiguity: The name Paul is not ambiguous, it is not a general term but a singular term with dissemination. - Ambiguity action/habit: delivery (action, object). >Ambiguity/Quine
I 316
Name: is a general term that applies only to one object - Ryle: x itself is not a property! - Middle Ages: Socrates, human, mortal: were on the same level - closes truth value gaps, claims no synonymy. >General Term/Quine, >Truth Value Gap/Quine
VII (a) 12ff
Name/Quine: is always eliminated - language does not need it.
VII (d) 75ff
Name/Quine: Frege: a name must be substitutable - this is even possible with abstract entities.
VII (i) 167
Proper Names/Quine: can be analyzed as descriptions. Then we can eliminate all singular terms as far as theory is concerned. >Descriptions/Quine
VIII 24ff
Name/Quine: names are constant substitutions of variables.
X 48
A name always refers to only one object - predicate: refers to many. We replace them in the standard grammar by predicates: first: a= instead of a, then predicate A. - The sentence Fa then becomes Ex(Ax.Fx). >Predicates/Quine
X 48
Name/Quine: it is not possible to quantify about them, so they are a different category than variables - names can be replaced by variables, but not always vice versa.
X 124
Name/logic/Substitutional Quantification/Quine: problem: there are never enough names for all objects of the world: e.g. if a set is not determined by any open sentence, it has no name either. - Otherwise E.g. Name a determination: x ε a - E.g. irrational numbers cannot be traced back to integers. ((s)>substitution class).
Lauener XI 39
Name/General Term/Quine/Lauener: names are eliminated by being reconstructed as a general term. As = a - then: Pegasus/truth value: then "Pegasus flies". (Ex)(X = c u Fx) is wrong, because Pegasus does not exist. (There is no pegasus, the conjunction is wrong). (>unicorn example). - The logical status of a proper name does not depend on the type of introduction, but only on the relation to other expressions.
XII 78
Name/Quine: is distinguished by the fact that they may be inserted for variables.

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


Q XI
H. Lauener
Willard Van Orman Quine München 1982
Referential Quantification Referential Quantification: is an expression for the form of quantification normally used in predicate logic ("There is at least one object x with the property ..." or "For all objects x applies...."). Here, something is said about objects, with their existence being presupposed. On the other hand, substitutional quantification is about linguistic expressions ("There is a true sentence that ..."). The decisive difference between the two types of quantification is that, in the case of the possible replacement of a linguistic expression by another expression, a so-called substitution class must be assumed which cannot exist in the case of objects since the everyday subject domain is not classified into classes is. E.g. you can replace a table by some box, but not the word table by an available word. See also substitutional quantification, quantification, substitution, inference, implication, stronger/weaker.

Referential Quantification Kripke III 378
Referential quantification: if sentences are substitutes, it is again about referential quantification: (s) sentences treated as objects? - Kripke: in any case there is a dispute: are the variables going over sentences, propositions or truth values?
III 377
Referential Quantification/Interpretation/KripkeVsSubstitutionalism: the point is that an uninterpreted formal system is exactly what it is: uninterpreted! Then it is simply impossible to ask for the "right interpretation"!
III 378
1. Kripke: Surely there are certain formal systems that allow referential interpretation but not substitutional interpretation. Example Quine: If (Ex)φ(x) is provable but ~φ(t) (negation!) is provable for any expression t that can be used for x, resulting in a meaningful sentence φ(t), it is obviously impossible to give the system a substitutional interpretation, but if the formation rules are standard, and it is formally consistent, a referential interpretation is possible.
((s) Although the referential interpretation makes "ontologically stronger assumptions"!).
If ~φ(t) is provable for each expression in a class C, while ((s) simultaneously) (Ex)φ(x) is provable, it is impossible to let all theorems be true and interpret the quantifier as replaceable with substitution class C.
These conditions are sufficient, but demonstrably not necessary, so that a first-stage theory does not receive a substitutional interpretation that makes all theorems true.
2. What about the common problem? (Referential interpretation excluded but substitutional interpretation allowed):
The autonymous interpretation (see section 3 above, where each term denotes itself) could suggest a negative answer. And this will be one reason why many mathematical logicians did not want to treat substitutional quantification as an independent model-theoretical topic.
KripkeVs: however, there may be cases where substitutional quantification is more appropriate than referential quantification.
For example, if the substitution class insists on sentences of L0, a referential interpretation with sentences as substitutes leads to philosophical dispute: do the variables go over propositions, over sentences or over truth values? Are the entities in the area denoted by the sentences?
Links/Kripke: do not play a threefold role now: as
a) sentence links, b) function symbols, c) predicates: in Frege's system they play such a triple role!

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984

Substitutional Quantification Kripke III 325ff
Substitutional Quantification/SQ/Kripke: ontologically neutral, perhaps purely linguistic - truth and satisfaction are defined here - contrast: referential quantification/RQ - refers to objects (world) - referential quantification: no satisfaction, only truth - Wallace/Tharp: thesis no difference between substitution quantification and referential quantification - KripkeVsWallace/VsTharp.
III 330
Substitutional quantification: formulas: that are no sentences do not receive any semantic interpretation here, they have only an auxiliary function - referential quantification: here such formulas define relations and are "satisfied" by sequences.
III 367
Form/Kripke: must include sentence - well-formed/WFF/Kripke: Problem: T(a) ↔ x is not well-formed when x is replaced by strings of symbols that are no sentences and therefore no form. Substitutional quantification/(s): needs substitution class: set of true sentences from the extended language from the set of true sentences in the source language (it must be unambiguous, i.e. the only such set) - referential quantification: does not need that.
III 332
Substitution Class/SC/Kripke: must not contain any specific descriptions.
III 349
Substitutional Quantification/Kripke: does not interpret formulas at all - but there is satisfaction if there is a denotation relation - but only for transparency.
III 352
Substitutional quantification/Kripke: E.g. Cicero/Tullius: dramatic difference: (Sx1)((Sx2)(x1 = x2 u f(x1) u ~f(x2)) true (not interpreted), but the same with (Ex1) (Ex2) ... false (standard q) - if opacity is to be eliminated from the metalanguage, then its referential variables have to work through denotations of expressions ((s) objects), not only through expressions - then (substitutional) quantification in opaque contexts possible.
III 352
Substitutional Quantification/Quantification in opaque contexts/Kripke: E.g. R(a): may then be explicitly defined when there are suitable predicates in the metalanguage: R(a) applies only if either a) a is a formula of the form P(t) (pseudo predicate "was so-called because of its size") and d(t) is named through the term t because of the size of d(t), or b) A is a formula of the form Q(t) and d(t) is bold - so that R(a) is eliminated as a primitive notation and the metalanguage only includes referential quantification without opacity - meta-language: it had to be expanded: so that the referential variables do not only work through expressions alone, but also through the denotations of these expressions.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg) Oxford/NY 1984

Substitutional Quantification Quine V 140
Substitutional quantification/Quine: is open for other grammatical categories than just singular term but has other truth function. - Referential quantification/Referential Quantification: here, the objects do not even need to be specifiable by name. ---
V 141
Language learning: first substitution quantification: from relative pronouns. - Later: referential quantification: because of categorical sentences. - Substitution quantification: would be absurd: that every inserted name that verifies Fx also verifies Gx - absurd: that each apple or rabbit would have to have a name or a singular description. - Most objects do not have names. ---
V 140
Substitutional Quantification/Referential Quantification/Truth Function/Quine: referential universal quantification: can be falsified by one single object, even though this is not specifiable by a name. - The same substitutional universal quantification: in contrast, remains true. - Existential quantification: referential: may be true due to a non-assignable value. - The same in substitutional sense: does not apply for lack of an assignable example. ---
V 146f
Substitutional Quantification/Quine: Problem: Blind spot: substitutional universal quantification: E.g. none of the substitution cases should be rejected, but some require abstention. - Existential quantification: E.g. none of the cases is to be approved, but some abstention is in order.- then neither agree nor abstain. (Equivalent to the alternation). ---
Ad V 170
Substitutional Quantification/(s): related to the quantification over apparent classes in Quine’s meta language? ---
V 175
Numbers/Classes/Quantification/Ontology/Substitutional quantification/Quine: first substitutional quantification through numbers and classes. - Problem: Numbers and classes can then not be eliminated. - Can also be used as an object quantification (referential quantification) if one allows every number to have a successor. - ((s) with substitution quantification each would have to have a name. Class quantifier becomes object quantifier if one allows the exchange of the quantifiers (AQU/AQU/ - EQu/EQu) - so the law of the partial classes of one was introduced.
---
X 124
Substitutional quantification/Quine: requires name for the values ​​of the variables. Referential quantification/(s) speaks of objects at most. - Definition truth/Substitutional Quantification/Barcan/Quine: applying-Quantification - is true iff at least one of its cases, which is obtained by omitting the quantifier and inserting a name for the variable, is true. - Problem: almost never enough names for the objects in a not overly limited world. - E.g. No Goedel numbers for irrational numbers. - Then substitutional quantification can be wrong, because there is no name for the object, but the referential quantification can be true at the same time - i.e. both are not extensionally equal.
---
X 124
Names/logic/substitutional quantification/Quine: Problem: never enough names for all objects in the world: e.g. if a set is not determined by an open sentence, it also has no name. - Otherwise E.g. Name a, Determination: x ε a - E.g. irrational numbers cannot be attributed to integers. - (s) > substitution class. ---
XII 79f
Substitutional Quantification/Quine: Here the variables are placeholders for words of any syntactic category (except names) - Important argument: then there is no way to distinguish names from the rest of the vocabulary and real referential variables. ((s) Does that mean that one cannot distinguish fragments like object and greater than, and that structures like "there is a greater than" would be possible?). ---
XII 80
Substitutional Quantification/Quine: Problem: Assuming an infinite range of named objects. - Then it is possible to show for each substitution result of a name the truth of a formula and simultaneously to refute the universal quantification of the formula. - (everyone/all). - Then we have shown that the range has at least one unnamed object. - ((s) (> not enough names). - Therefore QuineVsSubstitutional Quantification. E.g. assuming the range contained the real name - Then not all could be named, but the unnamed cannot be separated. - The theory can always be strengthened to name a certain number, but not all - referential quantification: attributes nameless objects to itself. - Trick: (see above) every substitution result with a name is true, but makes universal quantification false. ((s) Thus an infinite number of objects secured). - A theory of real names must be based on referential quantification.

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