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# The doctrine of external relations in Wittgenstein’s early philosophy

University of Bergen, March 8, 2013

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on 8 March 2013#### Transcript of The doctrine of external relations in Wittgenstein’s early philosophy

Neither external nor internal relations are can be constituents of facts. An external relation R is relating objects a and b into a state of affairs aRb.

If R were a simple constituent of a state of affairs, what would, then, relate R with its terms a and b?

It would have to be another relation S which would relate R, a, b into S(R, a, b) Bradley's regress external internal If an internal relation were a constituent of a state of affairs, there would have to be a name of this relation.

But this is by Moore's argument impossible. Internal and external relations A relation is internal if it A relation R is internal to its term a if and only if, from the fact that a’ is not related by R it follows that a’ is different from a (i.e. it is unthinkable that a’ = a). Tractarian ontology The world

facts states of affairs Language

(molecular) propositions elementary propositions names. Example: the whole-to-part relation

e.g. a stamp collection The doctrine of external relations Argument 1 (G. E. Moore, Principia Ethica, §22) Suppose an organic whole W which parts (P1, P2 ...) are internally related to the whole.

Parts of such a whole cannot be named in isolation.

Parts of W cannot be distinct objects of thought.

The whole situation is self-contradictory. All internal relations are unintelligible. consists of consists of which consist of which consist of which consist of objects. which consist of All relations are external.

(Russell, Moore) Internal relations are unreal.

(Bradley) Internal relations cannot be asserted in propositions.

(Wittgenstein) not wholly true Instead of, ‘The complex sign “aRb” says that a stands to b in the relation R’, we ought to put, ‘That “a” stands to “b” in a certain relation says that aRb.’ (TLP 3.1432) Tractarian objects are particulars. Relations are unreal. not part of the substance of the world If the part-to-whole relation were internal, it would be unintelligible. Wittgenstein External relations are unreal as well. are concatenations of are results of truth-operations on are results of successive applications of the operation N(ξ) to the definitions Argument 2 the identity theory of truth: (true) propositions to be identical with the facts they express the doctrine of external relations Logical entailment is an external relation. All relations between propositions directly standing for facts are external. All relations between elementary propositions are external. Wittgenstein, TLP 5.134: “One elementary proposition cannot be deduced form another.” All relations between states of affairs are external. the doctrine of external relations (2): How it is with internal relations between objects? Russell, Moore: All relations between objects are external. Wittgenstein: There are internal as well as external relations between objects. Certain combinations of names are nonsensical (TLP 4.1272).

Certain concatenations of objects in a state of affairs are impossible (TLP 2.012ff.).

Objects have their forms of dependence/independence (TPL 2.0123).

The form of an object makes up its identity (TLP 2.01231). The relation of dependence is an internal relation, for it is unthinkable that objects were not related by this relation. Argument 3 The doctrine of external relations does not prevent the whole-to-part relation being internal. (Wittgenstein) Logical analysis: elimination of the expression for the whole in favor of expressions for its parts. decomposition of a whole into its parts. Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely (TLP 2.0201). Logic is concerned with (forms of) molecular propositions. Russell in the Introduction to the Tractatus: “Thus the whole business of logical inference is concerned with propositions which are not atomic. Such propositions may be called molecular.” A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex (TLP 3.24). Logic is concerned with forms that fall under

the general propositional form. a form of how logical operations are applied to elementary propositions There are molecular propositions sharing the same form or the form of one proposition is a part of the form of another. p|q .|. p|q follows from p|p .|. q|q (LWL, p. 57) p q follows from p q < < Conclusion Logical entailment is based on the whole-to-part relation between forms of molecular propositions. Doctrine of external relations between molecular propositions: nonsense?

between elementary propositions: Russell, Moore, Wittgenstein

between objects: Russell, Moore Unreality of relations No relational statements can be wholly true (Bradley).

All signs for relations have to be eliminated in a logically adequate language (Wittgenstein).

No relational statements can be expressed by means of proposition (Wittgenstein). All relations that can be expressed in propositions are indeed external. Wittgenstein's doctrine of external relations The doctrine of external relations in Wittgenstein’s early philosophy "F. H. Bradley (1846–1924) was the most famous, original and philosophically influential of the British Idealists." (SEP) Jakub Mácha University of Bergen, March 8, 2013 falls within the nature of the related terms (Russell) makes difference to its terms so that if they were not related, they would be different (Moore, Joachim) pass into the being of its terms so that it affects their essences (Bradley) is unthinkable that its terms should not possess it (Wittgenstein, TPL 4.123) A relation is external if it is not internal. There are universals among Tractarian objects. Logic deals with forms

Full transcriptIf R were a simple constituent of a state of affairs, what would, then, relate R with its terms a and b?

It would have to be another relation S which would relate R, a, b into S(R, a, b) Bradley's regress external internal If an internal relation were a constituent of a state of affairs, there would have to be a name of this relation.

But this is by Moore's argument impossible. Internal and external relations A relation is internal if it A relation R is internal to its term a if and only if, from the fact that a’ is not related by R it follows that a’ is different from a (i.e. it is unthinkable that a’ = a). Tractarian ontology The world

facts states of affairs Language

(molecular) propositions elementary propositions names. Example: the whole-to-part relation

e.g. a stamp collection The doctrine of external relations Argument 1 (G. E. Moore, Principia Ethica, §22) Suppose an organic whole W which parts (P1, P2 ...) are internally related to the whole.

Parts of such a whole cannot be named in isolation.

Parts of W cannot be distinct objects of thought.

The whole situation is self-contradictory. All internal relations are unintelligible. consists of consists of which consist of which consist of which consist of objects. which consist of All relations are external.

(Russell, Moore) Internal relations are unreal.

(Bradley) Internal relations cannot be asserted in propositions.

(Wittgenstein) not wholly true Instead of, ‘The complex sign “aRb” says that a stands to b in the relation R’, we ought to put, ‘That “a” stands to “b” in a certain relation says that aRb.’ (TLP 3.1432) Tractarian objects are particulars. Relations are unreal. not part of the substance of the world If the part-to-whole relation were internal, it would be unintelligible. Wittgenstein External relations are unreal as well. are concatenations of are results of truth-operations on are results of successive applications of the operation N(ξ) to the definitions Argument 2 the identity theory of truth: (true) propositions to be identical with the facts they express the doctrine of external relations Logical entailment is an external relation. All relations between propositions directly standing for facts are external. All relations between elementary propositions are external. Wittgenstein, TLP 5.134: “One elementary proposition cannot be deduced form another.” All relations between states of affairs are external. the doctrine of external relations (2): How it is with internal relations between objects? Russell, Moore: All relations between objects are external. Wittgenstein: There are internal as well as external relations between objects. Certain combinations of names are nonsensical (TLP 4.1272).

Certain concatenations of objects in a state of affairs are impossible (TLP 2.012ff.).

Objects have their forms of dependence/independence (TPL 2.0123).

The form of an object makes up its identity (TLP 2.01231). The relation of dependence is an internal relation, for it is unthinkable that objects were not related by this relation. Argument 3 The doctrine of external relations does not prevent the whole-to-part relation being internal. (Wittgenstein) Logical analysis: elimination of the expression for the whole in favor of expressions for its parts. decomposition of a whole into its parts. Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely (TLP 2.0201). Logic is concerned with (forms of) molecular propositions. Russell in the Introduction to the Tractatus: “Thus the whole business of logical inference is concerned with propositions which are not atomic. Such propositions may be called molecular.” A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex (TLP 3.24). Logic is concerned with forms that fall under

the general propositional form. a form of how logical operations are applied to elementary propositions There are molecular propositions sharing the same form or the form of one proposition is a part of the form of another. p|q .|. p|q follows from p|p .|. q|q (LWL, p. 57) p q follows from p q < < Conclusion Logical entailment is based on the whole-to-part relation between forms of molecular propositions. Doctrine of external relations between molecular propositions: nonsense?

between elementary propositions: Russell, Moore, Wittgenstein

between objects: Russell, Moore Unreality of relations No relational statements can be wholly true (Bradley).

All signs for relations have to be eliminated in a logically adequate language (Wittgenstein).

No relational statements can be expressed by means of proposition (Wittgenstein). All relations that can be expressed in propositions are indeed external. Wittgenstein's doctrine of external relations The doctrine of external relations in Wittgenstein’s early philosophy "F. H. Bradley (1846–1924) was the most famous, original and philosophically influential of the British Idealists." (SEP) Jakub Mácha University of Bergen, March 8, 2013 falls within the nature of the related terms (Russell) makes difference to its terms so that if they were not related, they would be different (Moore, Joachim) pass into the being of its terms so that it affects their essences (Bradley) is unthinkable that its terms should not possess it (Wittgenstein, TPL 4.123) A relation is external if it is not internal. There are universals among Tractarian objects. Logic deals with forms