Skip to main content Accessibility help
Hostname: page-component-7ccbd9845f-xwjfq Total loading time: 0.599 Render date: 2023-02-01T02:30:08.040Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Internal Relations and Analyticity: Wittgenstein and Quine

Published online by Cambridge University Press:  01 January 2020

Michael Hymers*
Calgary Institute for the Humanities, University of Calgary, Calgary, AB, T2N 1N4Canada


Since Russell and Moore forsook idealism, it has often been assumed that only analytic truths can express internal relations — relations which, in Russell's words, are ‘grounded in the natures of the related terms.’ An object, a, is internally related to another object, b, if and only if a is related to b in virtue of a's possessing some property, P. So if a has the property of being a branch, then it is internally related to some tree, b, as part to whole. In turn, ‘A branch is a part of some tree’ is (at least a plausible candidate for) an analytic truth. It is true in virtue of the meanings of its terms, or because the concept of the predicate contains the concept of the subject.

Quine's critique of analyticity has thus made the pragmatically minded wary of talk of internal relations.

Research Article
Copyright © The Authors 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


2 Russell, B.The Monistic Theory of Truth,’ reprinted in Philosophical Essays, rev. ed. (London: George Allen & Unwin 1966), 131–46, at 139Google Scholar

3 Rorty, R. Philosophy and the Mirror of Nature (Princeton: Princeton University Press 1979), 193Google Scholar

4 I draw on Baker, G.P. and Hacker, P.M.S. Wittgenstein: Rules, Grammar and Necessity (Oxford: Basil Blackwell 1985), 8591,338-47Google Scholar. See also Shiner, R.A.Wittgenstein and the Foundations of Knowledge,’ Proceedings of the Aristotelian Society 78 (1977/78) 103–24CrossRefGoogle Scholar, and Putnam, H.Rethinking Mathematical Necessity,’ in Words and Life (Cambridge, MA: Harvard University Press 1994) 245–63Google Scholar.

5 Most works by Wittgenstein and Quine will be cited thus:

Wittgenstein, L.: (TLP) Tractatus Logico-Philosophicus, Ogden, C.K. trans. (London: Routledge & Kegan Paul 1921)Google Scholar.

(PR) Philosophical Remarks, Rhees, R. ed., Hargreaves, R. and White, R. trans. (Chicago: University of Chicago Press 1975)Google Scholar.

(PG) Philosophical Grammar, Rhees, R. ed., Kenny, A. trans. (Oxford: Basil Blackwell 1974)Google Scholar.

(LFM) Wittgenstein's Lectures on the Foundations of Mathematics-Cambridge, 1939, Diamond, C. ed. (Chicago: University of Chicago Press 1976)Google Scholar.

(RFM) Remarks on the Foundations of Mathematics, rev. ed., Wright, G.H. von Rhees, R. Anscombe, G.E.M. eds., Anscombe, G.E.M. trans. (Cambridge, MA: The MIT Press 1978)Google Scholar.

(PI) Philosophical Investigations, 2nd ed. Anscombe, G.E.M. and Rhees, R. eds., Anscombe, G.E.M. trans. (Oxford: Basil Blackwell 1968)Google Scholar.

Quine, W.V.: (TO) ‘Two Dogmas of Empiricism,’ reprinted in From a Logical Point of View, 2nd ed. (Cambridge, MA: Harvard University Press 1980) 2046Google Scholar.

(WO) Word and Object (Cambridge, MA: The MIT Press 1960).

(OR) Ontological Relativity and Other Essays (New York: Columbia University Press 1969).

(RR) Roots of Reference (LaSalle: Open Court 1974).

(PT) Pursuit of Truth (Cambridge, MA: Harvard University Press 1990).

6 Ogden, C.K. and Richards, I.A. The Meaning of Meaning (New York: Harcourt Brace 1923), ch. 3Google Scholar

7 Russell, B. The Analysis of Mind (London: George Allen and Unwin 1921), 68Google Scholar. A related account of belief and verification appears at 269f.

8 Cf. the argument against process-reliabilism in Pollock, J. Contemporary Theories of Knowledge (Totowa: Rowman and Littlefield 1986), 118–20.Google Scholar

9 Wittgenstein later speaks of both concepts (PI, §569), on the one hand, and words (PI, §§11, 23, 360) and samples (PI, §§16, 53, 57), on the other, as being instruments or tools. Rules (PI, §54), descriptions (PI, §291), sentences (PI, §421), and language or languages (PI, §§492, 569) are also described this way. This variety should not bother us as long as we bear in mind that it is between or among the uses or roles of words or samples that internal relations obtain. See Section V below.

10 Russell, ‘The Monistic Theory of Truth,’ 144fGoogle Scholar; Moore, G.E.External and Internal Relations,’ reprinted in Selected Writings, Baldwin, T. ed. (London: Routledge 1993), 79105, at 85Google Scholar

11 Baker, G.P. and Hacker, P.M.S. Scepticism, Rules and Language (Oxford: Basil Blackwell 1984), 109Google Scholar

12 Wittgenstein, L. Zettel, 2nd ed., Anscombe, G.E.M. and Wright, G.H. von eds., Anscombe, G.E.M. trans. (Oxford: Basil Blackwell 1981), §488Google Scholar

13 Wittgenstein, L. The Blue and the Brown Books (New York: Harper Torchbooks 1958), 17Google Scholar

14 This does not settle whether Wittgenstein thinks ‘criteria’ are decisive or defeasible. On the former see Cavell, S. The Claim of Reason (Oxford: Oxford University Press 1979)Google Scholar; Canfield, J.V. Wittgenstein: Language and World (Amherst, MA: University of Massachusetts Press 1981)Google Scholar; McDowell, J.Criteria, Defeasibility and Knowledge,Proceedings of the British Academy 68 (1982) 455–79Google Scholar. On the latter see, e.g., Hacker, P.M.S. Insight and Illusion (Oxford: Clarendon 1972), ch. 10Google Scholar. Hacker now holds that criteria can be either decisive or defeasible depending on the case. See Hacker, P.M.S. Wittgenstein: Meaning and Mind, Part I (Oxford: Blackwell 1993), ch. 13Google Scholar. Passages from RFM and LFM suggest that in at least some cases Wittgenstein held criteria to be decisive — for a proof is conclusive, constitutes a new criterion for the concepts of its theorem, and is definitive of those concepts. See RFM, 161, 187, 317, 319, and LFM, 54, 73, 127, 131, 164, 286.

15 Carnap, R. Meaning and Necessity, 2nd ed. (Chicago: University of Chicago Press 1956), §2Google Scholar

16 Given what Wittgenstein says about the standard metre (PI, §50), it might seem that the idea of extracting remarks about analyticity from his work is inappropriate. But I take the point of the example to be not that there is no truth-value that can be assigned to ‘The standard metre is a metre long,’ but that any truth-value that we do assign must apply for reasons very different from those for which we might say ‘This table is one metre long.’ See Baker, and Hacker, Rules, Grammar and Necessity, 343; Allen, B. Truth in Philosophy (Cambridge, MA: Harvard University Press 1993), 121–32Google Scholar.

17 This does not imply that I never grasp false mathematical propositions. See Coffa, J.A. The Semantic Tradition from Kant to Carnap, Wessels, L. ed. (Cambridge: Cambridge University Press 1991), 253f. and PR, §151.CrossRefGoogle Scholar

18 Grice, H.P. and Strawson, P.F.In Defense of a Dogma,Philosophical Review 65 (1956) 141–58, at 147fCrossRefGoogle Scholar.

19 Tarski, A.The Semantic Conception of Truth,’ in Sellars, W. and Feigl, H. eds., Readings in Philosophical Analysis (New York: Appleton-Century-Crofts 1949), 5284Google Scholar, and for related criticism, Lewis, O.K. Convention: A Philosophical Study (Cambridge, MA: Harvard University Press 1969), 206Google Scholar, and Putnam, H. Representation and Reality (Cambridge, MA: The MIT Press 1988), 61–8Google Scholar.

20 See Putnam, H. Reason, Truth and History (Cambridge: Cambridge University Press 1981), ch. 2-3CrossRefGoogle Scholar; Representation and Reality (Cambridge, MA: The MIT Press 1988), 115; ‘Replies,’ Philosophical Topics 20 (1992) 347-408, at 365f., 374, 393, 408 n. 82; ‘Sense, Nonsense, and the Senses: An Inquiry into the Powers of the Human Mind,’ Journal of Philosophy 91 (1994) 445-517, at 458.

21 Rorty, R. Objectivity, Relativism and Truth: Philosophical Papers, Vol.1 (Cambridge: Cambridge University Press 1991), 141 n. 30Google Scholar

22 See, e.g., Davidson, D.A Coherence Theory of Truth and Knowledge,’ in Truth and Interpretation: Perspectives on the Philosophy of Donald Davidson, LePore, E. ed. (Oxford: Basil Blackwell 1986), 306–19, at 319.Google Scholar

23 Quine, W.V.On the Very Idea of a Third Dogma,’ in Theories and Things (Cambridge, MA: Belknap 1981), 3842, at 38Google Scholar

24 See, e.g., Chomsky, N.Quine's Empirical Assumptions,’ in Davidson, D. and Hintikka, J. eds., Words and Objections: Essays on the Work of W. V. Quine (Dordrecht: D. Reidel 1969), 5368CrossRefGoogle Scholar; Rorty, R.Indeterminacy of Translation and of Truth,Synthese 23 (1972) 443–62CrossRefGoogle Scholar; Hackney, D.The Bifurcation of Scientific Theories and lndetenninacy of Translation,Philosophy of Science 42 (1975) 411–27CrossRefGoogle Scholar.

25 Putnam, H.There is at Least One A Priori Truth,’ in Realism and Reason: Philosophical Papers, Vol. 3 (Cambridge: Cambridge University Press 1983), 98114CrossRefGoogle Scholar

26 Quine sometimes speaks of physical objects as ‘cultural posits’ or ‘myths’ (TD, 44). This is at best a misleading metaphor. A cultural posit is as different from a posit as an unconscious intention is from an intention.

27 Wittgenstein, L. On Certainty, Anscombe, G.E.M. and Wright, G.H. von eds., Paul, D. and Anscombe, G.E.M. trans. (New York: Harper Torchbooks 1972), §§9799Google Scholar

28 Putnam, H.The Greatest Logical Positivist,Realism with a Human Face (Cambridge, MA: Harvard University Press 1990), 268–77Google Scholar

Cited by

Save article to Kindle

To save this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the or variations. ‘’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Internal Relations and Analyticity: Wittgenstein and Quine
Available formats

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Internal Relations and Analyticity: Wittgenstein and Quine
Available formats

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Internal Relations and Analyticity: Wittgenstein and Quine
Available formats

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *