Wittgenstein's Programme of a New Logic

Philosophy

The young Wittgenstein called his conception of logic âNew Logicâ and opposed it to
          the âOld Logicâ, i.e. Fregeâs and Russellâs systems of logic. In this paper the basic
          objects of Wittgensteinâs conception of a New Logic are outlined in contrast to
          classical logic. The detailed elaboration of Wittgensteinâs conception depends on the
          realization of his ab-notation for first order logic.

Wittgenstein"s programme of a New Logic Timm Lampert, Pittsburgh, Pennsylvania, United States 1. Introduction In his earliest writings, Notes on Logic (NL), Moore Notes (MN) and Tractatus logico-philosophicus (TLP), Wittgenstein calls his conception of logic self-confident ―New Logic‖. He opposes his New Logic to the ―Old Logic‖, which he identifies with the logic of Frege and Russell. From 1912 to 1914 he confronted Russell with his work on New Logic. Soon Russell accepted Wittgenstein as his ―master‖ (Monk (1990), chapter 3). Russell and Whitehead wanted Wittgenstein to work over Principia Mathematica (PM) (cf. Pinsent (1990), p. 60). Finally, Russell expected that the elaboration of Wittgenstein's New Logic would displace PM as paradigm of modern logic. This expectation was not fulfilled. The explanation for this is at hand: Wittgenstein's conception of logic could only be realized in propositional logic but not in predicate logic. In fact, no suggestions according proofs of predicate logic can be found in TLP. This seems to confirm the common judgement that Wittgenstein's main contribution to logic consists in the development of truth-tables, while his conception of logic is not able to supply any substantial contribution beyond propositional logic (cf. Black (1964), p. 323, Anscombe (1996), p. 137, cf. also the footnote of the editors in Cambridge Letters (CL), p. 52). Yet, it is not taken into account that Wittgenstein did not think of truth-tables as the proof method of his New Logic but of the so called ―ab-notation‖, a logical notation he worked on intensively in 1913/14. It is this notation he identifies with the ―new notation‖ in opposition to the ―old notation‖ of Frege and Russell (NL, p. 93[1]). The method of truth-tables – ―WF-schemata‖ in Wittgenstein's terminology – was already worked out by Wittgenstein in 1912 (cf. Shosky (1997), p. 20). Contrary to the method of truthtables, Wittgenstein's intention by developing the abnotation was to realize his conception of logic in the realm of predicate logic (cf. CL, letter 28, p. 4, against Biggs (1996), p. 27). The question in how far Wittgenstein's New Logic can be realized depends first and foremost on the question in how far his ab-notation is applicable to predicate logic. Unfortunately, the notebooks from 1913/14 dealing with the ab-notation have not been received (cf. CL, letter 32, p. 58 and Biggs (1996), p. 11). Thus, one has to rely on the scanty remarks in NL, MN, CL from 1913/14. Furthermore, the understanding of the ab-notation even in the realm of propositional logic was hampered by the fact that all received diagrams of the ab-notation were reproduced mistakenly or not even printed in the first editions of NL, MN, CL. In addition to the misjudgement that the method of truth-tables displaced the ab-notation this accounts for the fact that Wittgenstein's ab-notation remained nearly disregarded up to now in the literature. Yet, Wittgenstein did not doubt the validity of the ab-notation for the whole realm of predicate logic. Merely the handling of identity within the ab-notation was an open question for him (cf. CL, letter 30, p. 53). Likewise, he does not confine his understanding of logical proofs to propositional logic in TLP and still speaks of the ―Old Logic‖ in opposition to his ―New Logic‖ (TLP 4.126, 6.125). It was not Wittgenstein's intention to work out in detail his conception of a New Logic in TLP, but he had no doubt on the feasibility of this project. As the editors of CL point out rightly this contradicts Church's theorem of the undecidability of predicate logic (cf. CL, p.52). However, one is unable to judge upon Wittgenstein's programme if one concludes from this that Wittgenstein's programme is doomed to failure. First of all, throughout his life Wittgenstein was critical about metamathematical proofs and their methods – these proofs are not independent of the conception of Old Logic. Furthermore, merits and anomalies of the Wittgensteinian paradigm can only be discussed in a logically and philosophically fruitful manner by elaborating it. This, in turn, presupposes an understanding of its main ideas. In what follows the objective of Wittgenstein's New Logic will be lined out in contrast to the Old Logic. The detailed elaboration of his programme of a New Logic is given in my book ―Wittgenstein's New Logic‖, which works out Wittgenstein's abnotation for first order logic. 2. Old vs. New Logic In MN, p. 109[5] Wittgenstein describes the ―procedure of the old Logic‖ as follows: This is the actual procedure of [the] old Logic: it gives so-called primitive propositions; so-called rules of deduction; and then says that what you get by applying the rules to the propositions is a logical proposition that you have proved. This is just the common understanding of logical proofs in the sense of derivations within an axiomatic system. Frege's and Russell's systems satisfy this proof conception as well as modern sequence calculi do: A formula is proven by deducing it from the axioms applying derivation rules. Wittgenstein does not deny that logical true formula, tautologies, can be identified by this procedure. Yet, he emphasizes that their logical truth cannot be proven this way. He goes on to say: The truth is, it tells you something about the kind of proposition you have got, viz that it can be derived from the first symbols by these rules of combination [...]. What is proven by the axiomatic proof procedure is simply the deducibility of the formulae from the axioms. This is not denied within the framework of classical logic either. It is an accepted truism that only by assuming the logical truth of the axioms and the correctness of the derivation rules the logical truth of theorems can be concluded from their deducibility. Not the content of Wittgenstein's remark that proofs within an axiomatic system are in need of a metalogical justification is illuminating but the fact that he opposes his conception of a New Logic to this common understanding of logical proofs. Through his life Wittgenstein opposed to the understanding of logical and mathematical proofs resting on axioms, because one has to rely on some metalogical, intuitive evidence if one does not only want to maintain the deducibility of theorems but their logical or mathematical truth. In PG, p. 297 (cf. TLP 6.1271) he says: Logic and mathematics are not based on axioms, [...]. The idea that they are involves the error of treating the intuitiveness, the self-evidence, of the fundamental propositions as a criterion for correctness in logic. Wittgenstein's programme of a New Logic - Timm Lampert 127 Axiomatic proofs do not deliver a purely syntactical criterion for logical properties of arbitrary formulae of a formal system. The axioms are taken for granted without a formal proof. They hold an exceptional position within the system, but this position is not justified syntactically – the axioms are formulae within the system and do not differ essentially from other formulae. This can be seen by the fact that there are several correct and complete axiom systems for the same formal system and by the fact that not all axioms have some syntactical feature in common that identifies them as axioms. The common understanding of logical proofs in the sense of derivations from axioms depends on proofs of the logical truth of the axioms and of the correctness and completeness of a calculus relative to some prior given semantics. Such proofs cannot be carried out within formal logic. Thus, the question arises to the metalogical justification of an axiomatic calculus. Such a foundation necessarily exceeds the limitations of admissible evidence in logic. One objective of Wittgenstein's New Logic is to replace axiomatic proof procedures by a proof procedure that is not in need of such a metalogical foundation. In TLP 6.1265f. he says: It is always possible to construe logic in such a way that every proposition is its own proof. All the propositions of logic are of equal status: it is not the case that some of them are essentially primitive propositions and others essentially derived propositions. Every tautology itself shows that it is a tautology. That logical propositions are ―their own proof‖ or tautologies ―show themselves‖ to be tautologies does not mean that there is no need for proofs in the sense of manipulations of formulae in order to identify tautologies as tautologies. It only means that this can be done by relying solely on the formulae themselves as starting points of the proof instead of relying on axioms. In this respect Wittgenstein was looking for something similar to tableaux procedures such as Beth's or Smullyan's procedure (cf. Beth (1962), Smullyan (1965)). Yet, contrary to these procedures New Logic does not only aim for a procedure in order to identify tautologies but for a procedure applicable to ―every proposition‖, i.e. any predicate formula, in order to identify its truth conditions. In Wittgenstein's conception proofs in the sense of derivations of theorems from axioms are replaced by proofs in the sense of converting formulae to symbols of an ideal notation that allow to identify unambiguously tautologies and, generally, the truth conditions of any formula by the syntactical features of the ideal symbols. Again and again Wittgenstein stresses that one has to identify tautologies ―from the symbol alone‖ (TLP 6.113) or that one can ―[recognize] in a suitable notation [...] the formal properties of propositions by mere inspection of the propositions themselves‖ (TLP 6.122). Axioms, i.e. formulae with an exceptional position within a logical system, are not needed in this conception, because presuming a sufficient notation, which identifies the truth conditions of all formulae likewise, every formula ―is its own proof‖ (TLP 6.1265, cf. 6.127f.): The proof does not consist in a derivation of formulae from formulae of the same system but in a conversion of the formula in the symbols of an ideal notation according to a general procedure wholly depending on the syntax of the initial formula. Put concisely, the proof conceptions can be opposed as follows. Proof conception of Old Logic: Axioms  formula The formula in question marks the end of the proof. It has to be a theorem in order to be provable. Proofs of the truth conditions of formulae not being theorems are not available in this conception. Proof conception of New Logic: Any Formula  ideal symbol The ideal symbol identifies the truth conditions of the initial formula. Wittgenstein exemplifies his proof conception in TLP 6.1203 for propositional formulae by introducing a notation using brackets that is similar to the ab-notation. One might also think of the truth-table method as a well known procedure that realizes this proof conception basically. In case of truth-tables the ideal symbol consists of the assignment of truth values, T and F respectively, below the main sentential connective to the truth values of the propositional variables in the left part of the truth-table. The objective of the ab-notation is to realize such a proof conception for predicate logic. By the endeavour of Wittgenstein's New Logic it shall be demonstrated by purely logical means that an understanding of logic in the sense of an axiomatic theory, which is not based on purely syntactical grounds, is superfluous. It is not maintained that axiomatic proof systems are mistaken. However, in logic their form is misleading in so far it suggests that logic rests on some truth beyond symbols and their rule-governed manipulation and in so far it evokes problems as the foundation of axioms or the correctness and completeness of the axiomatic system, which, according to Wittgenstein's point of view, should be solved by changing the logical point of view rather than going beyond it. Thus, with the conception of New Logic a certain philosophical point of view concerning the understanding and foundation of logic is at stake. The ambitious objective is to justify stringently a Wittgensteinian understanding of logic by construing a logic system of an alternative form without delivering different logical results, i.e. without identifying truth conditions of formulae that they do not have according to classical logic. Wittgenstein's proof conception brings forth that syntax and semantic do not fall apart as in classical logic. By the proof procedure the truth conditions of the formulae become obvious. In this respect it provides a semantic in the sense of a theory defining truth conditions of formulae. Thus, it is not in need to be justified by some prior, independent given semantics. This, of course, does not mean that it cannot be compared to classical semantics. Furthermore, it should be demonstrable that both concepts of semantics are compatible, because otherwise not both would concern the same logic. Yet, the truth conditions need not to be identified by some procedure or some considerations external to the syntactical manipulations of the proof procedure itself. Every step in the procedure is a step in clarifying the truth conditions and nothing more can and is to be done than defining the steps explicitly. In consequence, not the question of correspondence of syntax and semantic is in the focus of Wittgenstein's conception but the question how an ideal notation looks like that identifies truth conditions of the formulae unambiguously and how a procedure can be defined in order to convert formulae in the symbols of such an ideal notation. Wittgenstein's conception differs significantly from the traditional point of view by regarding the syntax of predicate logic as deficient because of the fact that the truth conditions of predicate formulae cannot be identified by relying on its syntactical features. Repeatedly he identifies as the reason of his rejection of the syntax of predicate logic – the ―old notation‖ – that syntactically different formulae might be equivalent. E.g. in NL, p. 102[3] he says (cf. NL, p. 93[1], TLP 5.43): Wittgenstein's programme of a New Logic - Timm Lampert 128 If p = not--not--p etc.; this shows that the traditional method of symbolism is wrong, since it allows a plurality of symbols with the same sense; and thence it follows that, in analyzing such propositions, we must not be guided by Russell's method of symbolizing. Commonly, the language of predicate logic is regarded as an ideal language in contrast to natural language, because it is set up recursively and it is unambiguous in so far every formula expresses a certain truth function of atomic propositions. However, according to Wittgenstein's point of view this is not sufficient, because identical truth functions can still be expressed differently. In this sense, the syntax of predicate logic shares a deficiency with natural language. The problem is not primarily that signs of different types are equivalent, but that no general syntactical criterion exists to identify equivalent symbols as equivalent (cf. NL, p. 94[3], p. 99[2], p. 101[7]). This gets manifest by considering equivalent formulae differing in several respects, such as the following formulae: (1) x1x2((Q x((yzIxyz  ¬Q)  (x3x4Hx3x4  ¬Q)))  ((¬Fx2  Gx1)  Hx2x1)) (2) ¬yx¬((¬Fx  Gy  P)  (¬Fx  Gy  ¬P)  Hxy) (3) yxHxy  y(x(¬Fx  Hxy)  Gy) According to classical logic it is possible to prove their equivalence by deducing one from the other. However, it is not possible to identify a syntactical feature that (1) to (3) have in common in virtue of that they are equivalent. The fact that the truth conditions cannot be identified by means of the syntax of predicate formulae also becomes evident if one considers non-equivalent formulae: The differences of their truth conditions cannot be identified by syntactic criteria. Moreover, mostly it cannot even been proven syntactically that the formulae are not equivalent. In the framework of Wittgenstein's New Logic not laying down axiomatic calculi with certain metalogical properties is the first task of logic but solving the equivalence problem. Equivalence problem: The equivalence problem is the problem to define a mechanical procedure such that the same symbol is assigned to every predicate formula of a class of equivalent formulae and different symbols are assigned to non-equivalent predicate formula in a finite number of steps. To solve this problem, syntactical differences of equivalent formulae must me minimized systematically. The symbols assigned to the formulae – in case of the ab-notation the ―ab-symbols‖ – shall identify the truth conditions of predicate formulae. This means that the absymbols can be paraphrased by a mechanical procedure such that they denote common features of the models and counter-models of the initial formula. This, in turn, implies the possibility of construing the totality of models and counter-models from the ab-symbol of a formula without reckoning single interpretations. The understanding of logical proofs in the framework of New Logic can be characterized as follows: Logical Proof: A proof according to the conception of New Logic consists in the application of a mechanical procedure assigning an ab-symbol to a predicate formula identifying its conditions of truth and falsehood unambiguously. In how far this proof-conception will be realized is, in turn, to be measured against the extent of the solution of the equivalence problem and against the possibility of construing the totality of models and counter-models of a formula given merely its ab-symbol. The complete realization of this proof-conception is the core problem of logic according to the Wittgensteinian view. In fact, no satisfying answer to the question of the truth conditions of predicate formulae can be put forward in the framework of classical logical. Paraphrases of the formulae identify their truth conditions just as little as the formulae themselves. Derivations are only capable of identifying internal relations between formulae. And in the framework of classical semantics no general descriptions of the models and counter-models of a predicate formula can be delivered but only single models and counter-models (cf. Lampert (2006)). Even for subclasses of predicate logic that exceed propositional logic and monadic predicate logic no answer is given to the question of the truth conditions of a predicate formula in terms of a mechanical produced, finite expression explicating the truth conditions of the formula in a satisfying manner. This is not only deficient from the point of view of New Logic but from the perspective of everyone handling with predicate formulae and seeking to understand them. This deficiency should be resolved for as many subclasses of predicate logic as possible. Thus, the project to realize Wittgenstein's programme of a New Logic is motivated by philosophical as well as by logical grounds. And its feasibility should be measured by the question to what extent the elaboration of Wittgenstein's ab-notation for first order logic is able to solve the equivalence problem. Literature Anscombe, E. 1996: An Introduction into Wittgenstein's Tractatus. Bristol: Thoemmes. Biggs, M. 1996: Editing Wittgenstein's  Notes on Logic', Vol. 2. Bergen: Wittgensteinarkivet. Beth, E. 1962: Formal Methods. Dortrecht: Reidel. Black, M. 1964: A Companion to Wittgenstein's Tractatus. Cambridge: Cambridge University Press. Lampert, T. 2006: ―Explaining formulae of first order logic‖, Ruch Filozoficzny LXIII.2, p. 459-480. Monk, R. 1990: Ludwig Wittgenstein. London: Jonothan Cape. Pinsent, D. 1990: A Portrait of Wittgenstein as a Young Man. Oxford: Blackwell. Shosky, J. 1997: ―Russell's Use of Truth Tables‖, Russell: the Journal of the Betrand Russell Archives 17, p. 11-26. Smullyan, R. 1995: First-order logic.New York: Dover. Email: email@example.com


The One Is Not : On the Fate of Unity in Post-Metaphysical Philosophy

Philosophy

JUSSI BACKMAN University of Jyväskylä THE ONE IS NOT ON THE FATE OF UNITY IN POST-METAPHYSICAL PHILOSOPHY A Turkish translation of a version of this essay has been published as "Bir, bir şey değildir: post-metafizik düşüncede birlik ve çokluğun akıbeti," trans. Mustafa Yalçınkaya, Sabah Ülkesi: Üç aylık kültür-sanat ve felsefe dergisi, no. 51, Nisan 2017, 16–19. Available online at http://www.sabahulkesi.com/sayi.php?no=51, retrieved 27 April 2017. The themes of this essay are discussed in more detail, with a special focus on Heidegger, in Jussi Backman, Complicated Presence: Heidegger and the Postmetaphysical Unity of Being (Albany, NY: State University of New York Press, 2015). Metaphysics as a Quest for Unity n an important sense, the entire Western philosophical tradition-the tradition of Islamic Aristotelianism included-has been about unity. Unity, Hegel maintains, is the "content" and the "result" that connects modern philosophy to its ancient beginnings.1 At the origins of Greek philosophy, in the famous turn from mythos to logos, we discover a new attempt to consider all beings, all of reality, as one, in terms of a common denominator or a unifying point of reference. Thales of Miletus, who since ancient times was regarded as the first philosopher, was supposedly the first to seek a single principle for all things (for him, water). Anaximander, said to have been his pupil, saw an indeterminate (apeiron) unity as the origin of differentiated and determinate beings. For Parmenides of Elea, the discursively articulated binary oppositions and differences of the everyday world of the "mortals" are reducible to being as such in the sense of the pure and indivisible intelligibility of all things. For Heraclitus of Ephesus, it is discursive and linguistic articulation, logos itself, that in differentiating opposites (night and day, war and peace, freedom and slavery) also makes them conceptually dependent on each other and thus ties them together as one. In the Platonic and Aristotelian hierarchical or "ontotheological" metaphysical models, the question concerning the unity of being becomes a matter of determining the supreme and perfect instance of being to which all inferior instances refer. In Plato's Republic, this is the Idea of the Good as the Idea of Ideality as such, presupposed by all other Ideas. In Aristotle's Metaphysics, it is the metaphysical divinity (theos) as pure actuality, as an absolute and indivisible selfawareness, that provides the ontological ideal or "final cause" for all other entities. 1 G. W. F. Hegel, Vorlesungen: Ausgewählte Nachschriften und Manuskripte, vol. 7: Vorlesungen über die Geschichte der Philosophie, vol. 2: Griechische Philosophie, 1: Thales bis Kyniker [1825–26], ed. Pierre Garniron und Walter Jaeschke (Hamburg: Meiner, 1989), 52–54; Lectures on the History of Philosophy 1825–6, vol. 2: Greek Philosophy, ed. and trans. Robert F. Brown (Oxford: Oxford University Press, 2006), 57–58. JCRT 17.3 (2018) Backman: On the Fate of Unity in Post-Metaphysical Philosophy 481 This model, identified by Martin Heidegger as the cornerstone of Western metaphysics as a whole, decisively informed the entire later tradition. Through the mediation of Neoplatonic metaphysics, which conceived the different levels of being as a series of emanations from an original, absolute, and ineffable unity, the Aristotelian God of metaphysics became assimilated, in medieval Islamic and Christian philosophy, with the God of monotheism as the creator of all things. For modern metaphysics since Descartes, the unifying Archimedean point of reality was gradually shifted from divine transcendence into the immanence and immediacy of self-conscious subjectivity-the Cartesian cogito ergo sum. This metaphysics of the unifying subject is manifested by the Leibnizian monadology, the Kantian unity of transcendental apperception, and, finally, by Hegelian absolute idealism in its attempt to think the "substance" of reality as subjectivity. The Late Modern Disintegration of Metaphysical Unities However, while the German idealists still took for granted the conception of philosophy as a quest for ultimate unity, in philosophical late modernity since Nietzsche-separated from Hegel by what Reiner Schürmann calls "the most difficult decades to understand in our entire history"2-the status of unity becomes profoundly unsettled and transformed. In one of his late fragments, Nietzsche exclaims that "the overall character of existence may not be interpreted by means of the concept of 'aim,' the concept of 'unity,' or the concept of 'truth.' . . . [A]ny comprehensive unity in the plurality of occurrences is lacking."3 The category of unity is one that we "used to insert some value into the world," but with the advent of modern nihilism and its "devaluation of the supreme values," this category is once again extracted. Like all other values, unity was no more than a temporary instrumental projection. "We need 'unities' in order to be able to reckon [rechnen]: that does not mean we must suppose that there are such unities."4 For Nietzsche, reality is a chaotic plurality without inherent unity, aim, or structure, ceaselessly rearticulated by the will to power as the essence of subjectivity. This unending and aimless process of ceaseless reconfiguration is the only permanent identity, the cyclic "eternal recurrence of the same." For Heidegger, Nietzsche's metaphysics of the will to power represents the final stage, completion, and closure of the modern metaphysics of subjectivity-and, in this sense, the "end" of the Western metaphysical tradition as a whole. In Nietzsche, the principal hierarchies of Platonic metaphysics are inverted: being is subordinated to becoming, ideality to sensuousness, truth to art-and unity to multiplicity. For post-Nietzschean thought, an ultimate unity of being, situated in a supreme substance or a fundamental, constitutive subjectivity, became a chimera. The philosophical hermeneutics, poststructuralism, empiricism, and naturalism of the twentieth century all came to a harmonious agreement in their rejection of any foundational metaphysics of unity and identity. 2 Reiner Schürmann, Des hégémonies brisées (Mauvezin: Trans-EuropRepress, 1996), 641; Broken Hegemonies, trans. Reginald Lilly (Bloomington, IN: Indiana University Press, 2003), 513. 3 Friedrich Nietzsche, "Aus dem Nachlass der Achtzigerjahre" [1884–88], in Werke in drei Bänden, vol. 3, ed. Karl Schlechta (München: Hanser, 1956), 678 (Der Wille zur Macht n. 12); The Will to Power, trans. Walter Kaufmann and R. J. Hollingdale (New York: Vintage Books, 1968), 13. (Tr. mod.) 4 Nietzsche, "Aus dem Nachlass der Achtzigerjahre," 777 (Der Wille zur Macht n. 635); The Will to Power, 338. (Tr. mod.) JCRT 17.3 (2018) Backman: On the Fate of Unity in Post-Metaphysical Philosophy 482 In a 1963 paper, W. V. O. Quine notes-very much in tune with Nietzsche-that systematic virtues such as simplicity and coherence are to be perceived as values intrinsic to theoretical "beauty and convenience"; no metaphysical principle of "unity of nature" follows from the quest for unity in the field of science and theory.5 In the French crazy year 1968, we hear Jacques Derrida's diagnosis of différance-of the endless referentiality of meaning and the endless deferral of the referent-as "what is most irreducible about our 'epoch',"6 as well as Gilles Deleuze's more Nietzschean declaration that (late) modern thought is born out of the loss of the traditional metaphysical identities of the substance and of the subject, which are now being referred back to a "more profound game of difference and repetition."7 It is in Heidegger that we find the prototypical postmetaphysical rearticulation of the metaphysical quest for ultimate unity. In the fragmentary main work of his middle period, Contributions to Philosophy (1936–38), Heidegger notes that because the Presocratic thinkers focused on being (Sein) as the pure intelligibility and accessibility of things, they inevitably came to regard being as that which unifies everything that is intelligible and accessible. However, in the forthcoming postmetaphysical "other beginning" of Western thinking foreshadowed by Heidegger, this unity of meaningful presence is to be referred back to an underlying temporal structure.8 In several of his deconstructive readings of Heidegger, Derrida draws attention to the presence of a certain discourse of unity and "gathering" (Versammlung) in the Heideggerian opus itself.9 To be sure, we find in Heidegger's Being and Time, for example, a concern with working out the unity and coherence of the structure of human existence, Dasein. This unity, however, is not that of a selfidentical substance, but rather the "ecstatic"-dynamic, contextual, and heterogeneous-unity of existence in a singular meaningful situation in which the different dimensions of existential temporality intertwine. A similar structure can be found in the later Heidegger's enigmatic figure of the fourfold (Geviert), in which the meaningful presence of a simple thing, such as a jug, is seen as the focal point of convergence or as a "onefold" of four background dimensions of meaningfulness (which Heidegger evocatively names divinities, mortals, sky, and earth). For Heideggerian post-metaphysics, the unity of being is no longer a universal and comprehensive point of reference but rather a local, singular, and situated unity of an event (Ereignis) of meaning, embedded in a multidimensional meaning-context. As Heideggerian 5 W. V. O. Quine, "On Simple Theories of a Complex World," Synthese 15:1 (1963): 103. 6 Jacques Derrida, Marges de la philosophie (Paris: Minuit, 1972), 7; Margins of Philosophy, trans. Alan Bass (Brighton: Harvester Press, 1982), 7. (Tr. mod.) 7 Gilles Deleuze, Différence et répétition [1968], 11th ed. (Paris: Presses Universitaires de France, 2005), 1; Difference and Repetition, trans. Paul Patton (New York: Columbia University Press, 1994), xix. 8 Martin Heidegger, Gesamtausgabe, vol. 65: Beiträge zur Philosophie (Vom Ereignis), ed. Friedrich-Wilhelm von Herrmann (Frankfurt am Main: Klostermann, 1989), 459–60; Contributions to Philosophy (Of the Event), trans. Richard Rojcewicz and Daniela Vallega-Neu (Bloomington, IN: Indiana University Press, 2012), 361–62. 9 See, e.g., Jacques Derrida, Psyché: inventions de l'autre (Paris: Galilée, 1987), 439; "Geschlecht II: Heidegger's Hand," trans. John P. Leavey, Jr., in Deconstruction and Philosophy: The Texts of Jacques Derrida, ed. John Sallis (Chicago: University of Chicago Press, 1987), 182. JCRT 17.3 (2018) Backman: On the Fate of Unity in Post-Metaphysical Philosophy 483 thinkers such as Schürmann, Gianni Vattimo, and Jean-Luc Nancy have emphasized, Heidegger's heritage consists in a "constitutive" disintegration of foundational unities and hegemonic metaphysical principles in favor of an "anarchic" embracement of difference and singularity. Local, heterogeneous unities, understood as dynamic effects rather than as monolithic and static foundations; temporary and renegotiable identities rather than permanent ideal essences; situated micronarratives rather than all-encompassing metanarratives; context-sensitivity rather than absolute self-sufficiency; referentiality rather than fundamentality; singularity rather than universality- these are the signs of our philosophical times, the hallmarks of what, since Jean-François Lyotard's 1979 book, has prematurely been labeled "postmodern" thought. As is well known, however, increasing distrust in the Western Enlightenment's "master narratives" of historical progress has gone hand in hand with a cynicism regarding its universalistic emancipatory projects, the credibility of which depends on the acceptance of certain unifying aims. The loss of universal teleology would leave us with nothing but undecidable differends between incommensurable language games. Badiou – Platonism of the Multiple During the past few decades, Alain Badiou's highly original approach to this predicament has emerged as the perhaps most engaging contemporary philosophy of unity and multiplicity. Badiou's diagnosis of the late modern intellectual and ideological situation is twofold. On the one hand, Badiou welcomes the late modern demise of ultimate unities and the entry of contemporary thought "into a new phase of the doctrine of truth, that of the multiple-without-One."10 He agrees that the core of Western ontology since Parmenides has always been the dialectic of the one and the many, and in this sense, ontology is mathematics, a formal study of the structures of unity and multiplicity. This has only become evident with the advent of modern set theory, particularly in its axiomatic version which prohibits the existence of a universal set, a set of all sets. For Badiou, this amounts to nothing less than the radical ontological hypothesis that there is no ultimate unity, either in the sense of a comprehensive totality or in the sense of fundamental indivisible "atoms" (since the elements of any set can in themselves be conceived as multiplicities). That "the One is not" is the fundamental "decision" of Badiou's own, "subtractive" ontology, worked out in his magisterial Being and Event (1988): being as such is pure inconsistent multiplicity, which is only conceivable in negative terms, as reality minus all unifying structure.11 As philosophy has always known, all thinking requires structure, an operation of "count-as-one" in which the fundamental void multiplicity of being becomes articulated into a "situation" or "world" of coherent intelligibility. Western philosophy's focus on intelligibility and discursive meaning, together with its failure to grasp the ontological power of formal mathematics, has prevented it from accepting the ultimate lack of unity that, for Badiou, is the true sense of all progressive materialist thought. This incapacity is visible even in the concentration on experience and language in 10 Alain Badiou, Manifeste pour la philosophie (Paris: Seuil, 1989), 39; Manifesto for Philosophy, trans. Norman Madarasz (Albany, NY: State University of New York Press, 1999), 58. 11 Alain Badiou, L'être et l'événement (Paris: Seuil, 1988), 31–39; Being and Event, trans. Oliver Feltham (London: Continuum, 2005), 23–30. JCRT 17.3 (2018) Backman: On the Fate of Unity in Post-Metaphysical Philosophy 484 contemporary phenomenological, hermeneutic, and poststructuralist approaches. On the other hand, Badiou, whose philosophical project is deeply motivated by his commitment to progressive emancipatory politics, is dissatisfied with the ideological outcome of late modernity- "democratic materialism," a cynical and relativistic ideology for which there are no universal truths, only languages and bodies. To rehabilitate, against the postmetaphysical "Great Sophistry" of "antiphilosophers" such as Nietzsche, Heidegger, and Wittgenstein, a Platonic commitment to universal truths that are potentially timedefying and accessible to everyone, but without thereby taking recourse to the transcendent unity of the Platonic Ideas, is the basic aim of what Badiou characterizes as his "Platonism of the multiple."12 However, truths, for Badiou, are not veridical statements, nor are they disclosures of meaningful presence-they are infinite sets that are gradually constructed by progressive political, scientific, artistic, or amorous "truth-procedures." These truth-constructing processes have a beginning in time-they start from the recognition of a subversive historical event, such as a political or artistic revolution, a scientific breakthrough, or falling in love, and begin to articulate existing historical reality anew in terms of that event. For example, modern emancipatory revolutionary politics starts from the event of the French Revolution of 1789 and amounts to a transformative process of carving out an entirely new category, a revolutionary truth guided by the idea of the equality of all humans- an idea that makes no sense at all in the pre-revolutionary political and social reality. Along with the concept of unifying universal truths, Badiou's ontology rehabilitates the concept of a unified subject, but not in the sense of the Cartesian individual ego: the "subject" of revolutionary politics is the collective body unified by the commitment of its members to the revolutionary egalitarian idea and to the construction of a new, revolutionary truth. While being as such remains a void material multiplicity, the highest ethical calling of the human being, the source of meaningfulness in human existence, is to unite with others into collective subjectivities for the purpose of creating unities, for producing new sets of coherence in which new discourses will be meaningful and veridical. While Badiou's project remains extremely complex, not least because of its intricate formal apparatus, and also inherently problematic because of its seeming historical naïvetés (the four supposedly timeless truth-procedures named by Badiou-politics, science, art, and love-are all more or less modern and Western concepts), it captures and addresses, with unique intellectual ambition, a fundamental dilemma of postmetaphysical philosophy. While we tend to be increasingly suspicious of the unifying hegemonic principles of traditional metaphysics, such as ideal truth and unified subjectivity, we are even less inclined to accept the loss of unifying, universal, and potentially infinite aims and projects. Borrowing Nietzsche's words, we seem to need art, the production of meaning and coherence, in order not to perish from the truth-that is, from the void of pure multiplicity that has become the late modern "truth of being."13 Jussi Backman is a senior researcher in philosophy at the University of Jyväskylä, Finland. He is the author of Complicated Presence: Heidegger 12 Badiou, Manifeste pour la philosophie, 85; Manifesto for Philosophy, 103. 13 Nietzsche, "Aus dem Nachlass der Achtzigerjahre," 831 (Der Wille zur Macht n. 822); The Will to Power, 435. JCRT 17.3 (2018) Backman: On the Fate of Unity in Post-Metaphysical Philosophy 485 and the Postmetaphysical Unity of Being (State University of New York Press, 2015) as well as numerous articles on contemporary continental philosophy and ancient philosophy.


Renewing Medicineâs basic concepts: on ambiguity

Philosophy

RESEARCH Open Access Renewing Medicine's basic concepts: on ambiguity Joel Michael Reynolds Abstract Background: Edmund Pellegrino lamented that the cultural climate of the industrialized West had called the fundamental means and ends of medicine into question, leading him to propose a renewed reflection on medicine's basic concepts, including health, disease, and illness. My aim in this paper is take up Pellegrino's call. I argue that in order to usher in this renewal, the concept of ambiguity should take on a guiding role in medical practice, both scientific and clinical. After laying out Pellegrino's vision, I focus on the concept of normality, arguing that it undergirds modern medicine's other basic concepts. I draw on critiques by scholars in disability studies that show the concept of normality to be instructively ambiguous. Discussing the cases of Deafness and body integrity identity disorder (BIID), I argue that if medicine is to uphold its epistemic authority and fulfill its melioristic goals, ambiguity should become a central medical concept. Methods: In this theoretical paper, I consider how central concepts in the philosophy of medicine are challenged by research on experiences of disability. In particular, the idea that medical knowledge produces universal truths is challenged and the importance of historical, cultural, and otherwise situated knowledge is highlighed. Results: I demonstrate how experiences of disability complicate dominant theories in the philosophy of medicine and why medical practice and the philosophy of medicine should make ambiguity a central concept. Conclusions: If medical practitioners and philosophers of medicine wish to improve their understanding of the meaning and practice of medicine, they should take seriously the importance and centrality of ambiguity. Keywords: Ambiguity, Deafness, BIID, Normality, Patient-provider communication, Edmund Pellegrino, Philosophy of medicine, Philosophy of disability, Disability studies Background "Medicine qua medicine comes into existence when it appropriates knowledge and skills, no matter what their origin, in order to further its healing purposes." -Pellegrino. "The philosopher is the man who has to cure himself of many sicknesses of the understanding before he can arrive at the notions of the sound human understanding." -Wittgenstein. "May I never see in the patient anything but another creature in pain." -Maimonides. Just 9 years before his death, Pellegrino lamented that our cultural climate had called the fundamental means and ends of medicine into question, leading him to propose a renewed reflection on medicine's basic concepts, including health, disease, and illness [1]. This call dovetailed with a central theme of his oeuvre, the push for and articulation of a philosophical basis for modern medicine oriented by the realities of clinical practice and human existence [2]. My aim in this paper is take up Pellegrino's call. I argue that in order to renew the project of medicine today, the concept of ambiguity should take on a central role in "the science and praxis of medicine" [3]. While the philosophy of science has since Kuhn openly wrestled with the historical variability of scientific knowledge and rationality, including the role of sociological factors occasioning its revolutions, biomedical science and practice has on the whole been resistant to admitting the limitations of its paradigms [4, 5]. Given a political atmosphere in which all scientific Correspondence: email@example.com Rice Family Fellow in Bioethics and the Humanities, The Hastings Center, 21 Malcolm Gordon Road, Garrison, NY 10524-4125, USA © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Reynolds Philosophy, Ethics, and Humanities in Medicine (2018) 13:8 https://doi.org/10.1186/s13010-018-0061-4 claims, not just those pertaining to biomedicine, are being called into question, this resistance is especially understandable today. However, I hope to show that this resistance is ultimately misguided. If, as I argue below, resistance to changes in the understanding of medical phenomena negatively impacts care in multiple respects, then it undermines what Pellegrino holds to be medicine's fundamental goal: the search for truth in the service of the health and the healing of human beings [3]. After laying out Pellegrino's vision of medicine as well as the philosophy of medicine, I discuss the concept of normality and the role ambiguity plays-and ought to play-in transforming how we understand the ends of medicine and philosophical inquiry into it. Discussing the cases of Deafness and body integrity identity disorder (BIID), I conclude by arguing that ambiguity should itself become a central concept for medical science and praxis. Pellegrino, the philosophy of medicine, and the role of history Pellegrino defined the philosophy of medicine as consisting in "a critical reflection on the matter of medicine – on the content, method, concepts and presuppositions peculiar to medicine as medicine" [3]. Whether one looks to the titanic promises made by proponents of the Human Genome Project [6] or more recent pledges offered under the auspices of the Precision Medicine Initiative/All of Us Research Program, the gears which churn the medical enterprise forward in the global North too often leverage dogmatic faith in a progressive, promissory vision of medical knowledge and in the infallibility of its guiding concepts [7, 8]. Such a vision stands in stark contrast to the humanistic, patient-centered reflections on the nature and aims of medicine characteristic of doctor-scholars such as Pellegrino and, more recently, Rita Charon, Atul Gawande, and Jay Baruch. Speaking of his work with David Thomasma, Pellegrino writes, "our philosophy of medicine, and hence the ethics we derive from it, is teleologically structured. It is derived a posteriori from the universal realities of the clinical encounter, i.e., healing, helping, caring, health" [9]. If there is any issue the turbulence of the late twentieth century has brought most forcefully to the realities of the clinical encounter, it is that of normality. Whether with respect to questions of gender, sex, and sexuality, short stature, pregnancy, deafness, racialized medical interventions and categorization, cosmetic surgery, menopause, erectile dysfunction, obesity, ADHD, or any number of mental health issues, the idea that there is a typical or normal human body exhibiting normal behaviors and desires which can serve as a guide for medical praxis has been thrown into question. Scholars across feminist philosophy, gender, sexuality, and trans studies, critical disability studies, and critical philosophy of race have criticized assumptions about "normality" and how such assumptions feed into common psychological processes, such as implicit bias and confirmation bias, that hamper clinical care and hinder health outcomes [10–16]. By homing in on everything from the selection of clinical research subjects to the treatment of minority groups to the philosophical and historical origins of the concept of "normality" itself, such scholarship has demonstrated that the concept of normality is fundamentally unstable and ambiguous. It is not surprising that so many debates have turned on the concept of normality, for it is the glue that renders any given modern concept of health, illness, or disease coherent. Just as one must assume or construct a moral exemplar in order to articulate a theory of virtue [17], one must assume or construct a psycho-physiological exemplar in order to articulate a theory of health, illness, and disease. On the whole, these critiques have had a noticeable impact. Despite the influence and standing of scholars like Boorse [18], much contemporary scholarship in the philosophy of medicine follows Tristram Engelhardt and others in holding the concept of health to substantively rely on social, cultural, and historical factors [19]. Notably, even the most trenchant critiques of the concept of normality have not shown it to be entirely useless or incoherent, but problematic and irremediably ambiguous [20, 21]. As philosophers from Wittgenstein to de Beauvoir averred, facing and coming to terms with the ambiguity of life, its forms, and its expressions is one of the more important steps we can take in the project of forging a life worth living [22, 23]. If "the philosophy and ethics of medicine should be grounded in the realities of clinical practice," as Pellegrino professed, then should not ambiguity itself be a foundation of medicine and its contributions to the good life [9]? Having laid out the relationship between Pellegrino's vision of medicine and the philosophy of medicine with critiques of the concept of normality, I will turn to two examples that demonstrate the role and import of ambiguity for a medical praxis grounded in the clinical encounter and steadfastly oriented towards health and healing. The ambiguity of normality: deafness A number of decades ago, the prevailing conceptualization of deafness was in terms of audiological loss [24]. Signing and sign language, though existing in human cultures in various forms since time immemorial, was seen as an unchosen strategy to overcome the inability to hear and one which paled before the advantages of hearing. Fast forward to the present day and thanks to a confluence of sociological, political, and historical factors, one appears Reynolds Philosophy, Ethics, and Humanities in Medicine (2018) 13:8 Page 2 of 5 uninformed if one fails to contrast this audiological loss view with that of the Deaf (capital D) community. The Deaf community understands 'deafness' to refer to a set of rich cultural, historical, and linguistic practices pertaining to groups of people who communicate through signing [25]. While debates both outside and within Deaf communities continue to rage on about things like cochlear implants, the idea that deafness is solely and without argument defined by audiological loss is today seen as a hangover from a past age, much like understandings of homosexuality as a disease or of certain races or sexes as biologically inferior [26]. Deafness does not demonstrate that the concept of normality-in this case the presence of certain audiological capacities relative to species-level, phenotypic expression-is wrong as much as it shows that the meaning of normality within a given domain and sociopolitical context is often ambiguous and in principle defeasible. Under the sway of normality, we easily lose sight of the fact that much we find clear-cut is not, and much more is up for debate than we realize. In ways that are sadly characteristic of the ivory tower, it took years of testimony, cultural dissemination, and dogged activism for those in the humanities and social sciences to take seriously the fact that Deaf people command and create bodies of knowledge that should indeed count as "evidence." That is to say, it was in part due to the recognition of these bodies of knowledge as knowledge that the reigning biomedical conception of deafness as audiological loss was called into question. Why did this take so long and so much labor? The answer I propose here, unsurprising to those who have read Foucault and Kuhn alike, is that the "normal science" of medicine in a given epoch is oriented towards stability and clarity based upon extant assumptions concerning its central concepts, principles, and goals. Among other factors, had medical professionals, social scientists, bioethicists, and philosophers been more open to question their assumptions and more attuned to the ambiguity of lived experience, including the experiences of health itself, then it might have taken less of a gargantuan effort for the Deaf community to be recognized on its own terms. It is important to note that the idea that deafness should be "corrected" does not arise out of evidence that people who are deaf are in pain or suffering. It arises due to the intuition that deafness is abnormal and due to the conviction that medicine's goals include normalization. Such an intuition, as the twentieth century taught well, is profoundly dangerous when not subject to critical reflection and beholden to the testimony and lived experience of the people to whom the interventions of medicine are aimed and applied [27]. I here argue for the role of ambiguity in medical science and practice because it could work against such dangers, dangers which Anita Silvers argues have been and still can be fatal [20]. Placing the concept of ambiguity at the center of medical praxis would have the additional benefit of giving a greater role to the virtue of humility or, as Eva Kittay puts it, the virtue of epistemic modesty: "know what you don't know" [28]. The range of human experience is profoundly wide, and there are many sorts of experiences the contours of which we simply can't imagine thanks to the particularity of the embodied, embedded, and social worlds in which humans live [29]. To understand the practice of medicine as admitting of ambiguity is to admit that that there are many cases where we don't know, we can't help, and even with the best laid plans, intentions, and science, we might simply be wrong. As a central concept for medical praxis, ambiguity invokes the need for medical scientists and practitioners to substantively look to other, non-medical ways of knowing for insight-whether it be sociology, history, anthropology, etc.-and look especially to those ways of knowing that are reflexive and critical of reigning paradigms. The ambiguity of normality: body integrity identity disorder BIID is in many respects a more complicated case than d/ Deafness. It refers to a very rare condition describing those who feel an intense need to become comparatively impaired, typically through amputation or severance of their spinal cord [30]. It was only after cognitive neuroscientists conducted studies suggesting that it may result from a body-mapping issue related to dysfunction of the right parietal lobe that the dominant medical conceptualization of this condition moved from the psychological (referred to as apotemnophilia) to the physiological [31, 32]. This shift from "abnormal desire" to "abnormal physiology" well exemplifies the role of ambiguity in determining the scope and aims of not just medical intervention, but medical perception of a given phenomenon. As is unsurprising, the idea of therapeutic amputation of a healthy limb or therapeutic severing of a healthy spinal cord strikes the majority of practitioners as a contradiction in terms [33]. Indeed, even disability studies scholars have labored to conceptualize the many theoretical and practical issues that BIID raises [34, 35]. Therein lies the rub: it is the confidence over what counts as normal (in this case: being able-bodied and not disabled, having all of one's limbs, being able to ambulate, etc.) and what constitutes maleficence and beneficence that is the core issue in these debates [36]. Despite neurological evidence suggesting an underlying physiological etiology insufficiently addressed by behavioral therapy and also despite the sociological evidence Reynolds Philosophy, Ethics, and Humanities in Medicine (2018) 13:8 Page 3 of 5 that people with BIID experience significant and persistent suffering, many practitioners will not carry out these surgeries [37]. This is a case where certainty about the normality of a given condition and the parameters of normal therapy seem to undercut the aims of therapy. This has led some to sadly take matters into their own hands [38]. BIID is a very complex case, and it is quite understandable that the idea of therapeutic amputation would cause some practitioners concern, if not moral distress. Still, perhaps with more sensitivity and comfortability concerning the ambiguity of medical knowledge and of human corporeal variation, the larger aims of the health and healing of human beings would here be better and more capaciously addressed. Whatever position one ultimately takes, both Deafness and BIID demonstrate how the concept of normality is rendered ambiguous when brought under the light of historical and sociological factors central to the production and development of scientific knowledge and the multifactorial conditions by which it progresses. In defense of ambiguity Models of flourishing upon which canonical normative theories are based assume a general minimization of pain and suffering. We may not agree on the summum bonum, the greatest good, but we do agree on the summum malum, the greatest bad: suffering. A central problem for medicine is the fact that what is taken to be painful or suffered is sometimes not. And that which is taken to be the cause of pain or suffering can turn out instead to be an effect. Whether one looks to debates over Cochlear implants or the revolutions epigenetic research has yielded in molecular biology, the role of psychosocial, historical, and environmental factors continues to force revisions of medicine's central concepts, both broad ("health") and narrow ("genetic expression") in scope. In The Ethics of Ambiguity, Simone de Beauvoir writes of the human: At every moment, he can grasp the non-temporal truth of his existence. But between the past which no longer is and the future which is not yet, this moment when he exists is nothing. This privilege, which he alone possesses, of being a sovereign and unique subject amidst a universe of objects, is what he shares with all his fellow [humans]...As long as there have been men and they have lived, they have all felt this tragic ambiguity of their condition...And the ethics which they have proposed to their disciples has always pursued the same goal. It has been a matter of eliminating the ambiguity...Since we do not succeed in fleeing it, let us therefore try to look the truth in the face. Let us try to assume our fundamental ambiguity. It is in the knowledge of the genuine conditions of our life that we must draw our strength to live and our reason for acting [22]. Medical phenomena are multifactorial, scientific knowledge is defeasible, and human wellbeing is equifinal. Each of these truths demonstrate the centrality and import of ambiguity as a description of where we find ourselves and as a condition of how purposive action is ever oriented. Conclusions Pellegrino held that "medicine...is both a science and in many senses one of the humanities" [3]. The concept of ambiguity attunes medical science and praxis, both of which are ultimately in the service of human ends, to better approach the objects and goals of its inquiry and practice. In concert with a Pellegrinian view of medicine as arising out of the realities of the clinical encounter and oriented towards the health and healing of humans, I have argued that medicine ought to reorient itself to become more comfortable with and forthright about the ambiguities that define its objects, bound its goals, and shape its practice both in the lab and the clinic. If the human condition frames medicine and not the other way around, then our age calls not for a more exact, but a humbler medicine. Abbreviation BIID: Body Integrity Identity Disorder Acknowledgements I thank my colleagues at The Hastings Center, especially Erik Parens, for many rich conversations and for their ongoing support. Availability of data and materials The data in the manuscript is contained in the reference list. There are no separate data sets. Author's contributions I am the only author. The author read and approved the final manuscript. Authors' information JMR is the Rice Family Fellow in Bioethics and the Humanities at The Hastings Center and Assistant Professor of Philosophy at the University of Massachusetts Lowell. Ethics approval and consent to participate Not applicable. Consent for publication Not applicable. Competing interests The author declares that he/she has no competing interests. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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