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Title: Wittgenstein on Internal and External Relations: Tracing all the Connections& U" g$ _" L) k1 ]& }
Author: Jakub Mácha
% ~) J5 A9 K N* w6 ^Series: Bloomsbury Research in Analytic Philosophy
" M+ q4 A* a9 Z" n/ \0 d# RPaperback: 277 pages1 L5 _1 p9 W% v5 V
Publisher: Bloomsbury Academic; First published 2015
$ x1 o1 ~1 v# @" ]% F! KLanguage: English
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In this book, the author mainly discussed the theme of external and internal relations, which had been briefly mentioned in Wittgenstein’s magnum opus <Tractatus LogicoPhilosophicus>(TLP for short). However , it is very important to distinguish between external relation and internal relation in TLP, which is crucial in understanding the whole point of what is interrogated by Wittgenstein in TLP.
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/ U1 k' o1 u% l" [8 P, E* z( Y8 \What is internal relation? According to Wittgenstein’s TLP, a relation is internal if it is unthinkable that its objects (or terms, or relata) should not possess it. However, there are more technical understandings of the notion of unthinkability. For instance, Wittgenstein’s own technical definitions of thinkability and unthinkability allow for tautologies being thinkable and contradictions being unthinkable.; . h, \; s' m7 v
4 n/ u, X' L, Q+ F; Z1 G! R G6 UThe first occurrence of internal/external distinction (in the sense of Wittgenstein) can be found in Wittgenstein’s notes that he dictated to G. E. Moore in Norway in April 1914. The following is Wittgenstein’s very first remark concerning this distinction: “Internal relations are relations between types, which can’t be expressed in propositions, but are all shown in the symbols themselves, and can be exhibited systematically in tautologies. Why we come to call them ‘relations’ is because logical propositions have an analogous relation to them, to that which properly relational propositions have to relations.” According to this remark, there is a close connection between internal relations and logical tautologies. In principle, the holding of an internal relation can be proven systematically just as logical tautologies can be deduced from axioms.
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# x8 S) S! X7 P/ J" nIf proposition P is related to proposition Q by an internal relation R, there must be a systematic way of transforming P into Q. In other words, there must be a formal operation Φ that transforms P into Q such that Φ(P) ↔Q is a tautology. For instance, in De Morgan’s law ¬( P ∧ Q ) ↔ ¬P ∨ ¬Q, the internal relation between ¬( P ∧ Q ) and ¬P ∨ ¬Q (where P and Q are propositions) is shown. The systematic operation of transforming one of these expressions into the other occurs here. This definition of internal relation can be thus rephrased by saying that a relation is internal if it is necessary for its relata to stand in this relation. A not holding of an internal relation is just as unthinkable as it is unthinkable that a tautology is not true. In short, a relation is internal if it is unthinkable that its terms should not possess it, and it is external otherwise.
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For Wittgenstein, ‘internal relation’ is synonymous with ‘structural relation’. Internal relations are those “relations” that are intrinsic to the nature of one or more of the relata. They are a kind of essential relation, rather than an essential property. For example, an arc of a circle is internally related to the center of that circle in the sense that it could not be that arc of that circle without having that relation to that center of the circle. Please NOTE that the class of all relations is not divided into external and internal relations. Strictly speaking, internal relations are NOT relations at all. The modifier ‘internal’ operates like ‘fake’ or ‘apparent.’ It is like the class of horses, which is not divided into real ones and wooden ones. We can distinguish between internal and external relations, but we have to keep in mind that only external relations are proper relations.What is the answer Wittgenstein gives us exactly? The answer is that the obtaining of an internal relation cannot be expressed by means of propositions. The obtaining of internal relations can only be shown in propositions that are concerned with the relevant relata. So Wittgenstein seems to side with Russell and Moore here that all relations are indeed external, but with the reservation that all relations that can be expressed by a proposition are external. He admits, however, contra Russell and Moore, that internal relations are nevertheless not nonsensical. They are part of the symbolism of a logically adequate language and they are thus shown in such a symbolism.
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In fact, the “relation” problem can be traced back to Bradley’s relation regress. In his work <Appearance and Reality>, Bradley analysed what is the crux to make a sentence unitive and complete as his starting point of discussing the “relation” problem, which was so called “Bradley’s Relation Regress Problem” on the nature of “Relations”. b0 j6 Q3 2 
, I' w; ?4 W. O) V3 S6 C3 iIf you are interested in the topics related with the external/internal distinction, the “Bradley’s Relation Regress Problem” , the method of analysis used by Wittgenstein in his philosophy, and so forth, you could consult this wonderful book<Wittgenstein on Internal and External Relations> by Jakub Mácha. By the way, the language of this book is so fantastic—Mácha does things with the appropriate words that make entire paragraphs very coherent— that every chapter seems to be a stunning essay. In short, this is a beautiful book, and I recommend this book to anyone with an interest in the philosophy of Wittgenstein and the Analytic Philosophy.
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