Dieter Wandschneider Ultimate-Grounding Under the Condition of Finite Knowledge. A Hegelian Perspective1 Abstract Hegel's Science of Logic makes the just not low claim to be an absolute, ultimategrounded knowledge. This project, which could not be more ambitious, has no good press in our post-metaphysical age. However: That absolute knowledge absolutely cannot exist, cannot be claimed without self-contradiction. On the other hand, there can be no doubt about the fundamental finiteness of knowledge. But can absolute knowledge be finite knowledge? This leads to the problem of a self-explication of logic (in the sense of Hegel) and further, as will be shown, to a new definition of the dialectical procedure. The stringency of which results from the fact that always exactly that implicit content is explicated that was generated by the preceding explication step itself and is thus concretely comprehensible. At the same time, a new implicit content is generated by this act of explication, which requires a new explication step, and so forth. In the dialectical procedure reinterpreted in this way, dialectical arguments are not beheld, guessed at or even surreptitiously obtained, but are methodically accountable. Thereby dialectics is understood as a self-explication of logic by logical means and thus as a proof of the possibility of ultimate-grounding in the form of absolute and nevertheless finite – and thus also fallible – knowledge. 1. Can finite knowledge be absolute knowledge? 2. The problem of the recognition of fundamental-logic 3. The system perspective 4. The stringency of dialectical explication 5. Unassailability and fallibility of absolute knowledge 6. Conclusion 1. Can finite knowledge be absolute knowledge? Hegel's Science of Logic – the paradigm of modern metaphysics par excellence – makes the just not low claim to be knowledge of the Absolute, absolute knowledge. This project, which could not be thought of in a more ambitious way, has no good press nowadays. Our 'postmetaphysical' age is averse to metaphysical ventures that aim at super-empirical, unassailable knowledge (thus, following the traditional usage of language, metaphysical is understood in the following). So, in view of the clearly evident finiteness of knowledge, it is more obvious to consider it not as final and absolute, but as provisional and outdatable. In fact, it depends on a number of preconditions: on traditions of thought, on the state of scientific knowledge, on cultural and ideological perspectives, etc. Admittedly, this does not seem to apply to mathematical knowledge. It is true that this science is also advancing inexorably, but the fact that one plus one is two should undeniably be true. On closer inspection, however, this is based on preconditions, too, – the Peano axioms – which, as axioms, are not provable but hypotheses. In this sense even mathematical theorems are not of absolute but hypothetical charakter.2 The view that 1 Extended version of my contribution to the 2002 Congress of the International Hegel Society in Jena, Germany (28.08. – 01.09.2002). – Published: Dieter Wandschneider (2005) Letztbegründung unter der Bedingung endlichen Wissens. Eine Hegelsche Perspektive, in: Kellerwessel, Wulf/ Cramm, Wolf-Jürgen/ Krause, David/ Kupfer, Hans-Christoph (ed. 2005) Diskurs und Reflexion. Wolfgang Kuhlmann zum 65. Geburtstag. Würzburg: Königshausen & Neumann 2005, 353–372. 2 Plato therefore characterized mathematics as a 'hypothesis science' (Politeia 533b-c). One could argue: As hypothetical statements, i.e. if the axioms on which these are based are included in the mathematical statement, theorems have an absolute character: Thus, in the context of Euclidean geometry, i.e. assuming the corresponding axioms including the parallel axiom, the angular sum in the triangle is necessary 180° (if this axiom is dropped, one has, for example, a spherical geometry with a triangular angular sum greater than 180°) – but: mathematical 2 absolute knowledge cannot exist in principle is therefore obvious. The predominantly sceptical attitude of contemporary philosophy corresponds to this. Now, a view according to which absolute knowledge is impossible in principle, itself claims to be absolute knowledge, and thus gets entangled in a pragmatic contradiction, i.e. a contradiction between the content of the statement and the claim to validity inevitably connected with it. That absolute knowledge absolutely cannot exist cannot be claimed without selfcontradiction and is therefore a false statement. This is the type of a transcendental argument known from the current discussion on the ultimate-grounding,3 which is also essentially influenced by the works of Wolfgang Kuhlmann. In this context, it has been argued that not everything can be doubted and disputed per se; because doubting and disputing also presupposes meaningful concepts, the possibility of argumentation and thus logic. Insofar as these are preconditions of the possibility of disputing, this itself has reached an unassailable limit here. In such an assertion of 'ultimate reasons', something Absolute is indeed sighted, something that is valid par excellence, whose validity is independent of changing, contingent conditions,4 and can be sweepingly characterized as the logical conditions of argumentation. To dispute these is pragmatically self-contradictory. The view that there can be no absolute, ultimate-grounded knowledge cannot therefore be consistently held. The ultimate-grounding argument rather implies a claim to absoluteness: Absolute knowledge must be possible in principle, and this very statement itself is already to be understood as an example of such absolute knowledge. Nevertheless, in view of our manifest cognitive limits, the suspicion of intellectual hubris – repeatedly articulated against the possibility of ultimate-grounding – remains: Is it not presumptuous to assume that this knowledge, characterized as absolute, is of quasi divine finality? The question arises how the pretended possibility of absolute knowledge can be compatible with the manifest finiteness of knowledge. Would it be conceivable, for instance, that the knowledge that is characterized as absolute can nevertheless be limited, for instance in the sense of partial knowledge? Let us look at a concrete example, familiar from the current discussion on ultimategrounding, in which a transcendental argument is asserted, similarly to the previous one: The statement 'truth is impossible' assumes that it itself is true. It contains a pragmatic contradiction and is therefore false. Also the possibility of truth proves to be something that cannot be meaningfully questioned and therefore has an absolute character. On the other hand, there is the problem of truth and a research literature devoted to it that fills shelves, so that the question arises how the possibility of truth can be shown to be absolute on the one hand and highly problematic on the other. The answer to this arises from the argument for the absoluteness of the possibility of truth itself: For this it is enough to know that a statement is always connected with the claim to be true – whatever 'truth' may mean beyond that. This minimal knowledge is sufficient, as explained, to prove that the statement 'truth is impossible' is self-contradictory. A theory of truth is not needed for this. The argument is valid without the need to solve the problem of truth first. It can and needs be clarified further, even if the possibility of truth in the given sense is to be re- statements of this kind still have an essential prerequisite, namely logic. 3 For example, Apel 1973, Kuhlmann 1985, Hösle 1990, Wandschneider 1994. 4 'Absolute knowledge' here is thus understood in the usual sense of logically unassailable, un-conditioned knowledge, in contrast to Hegel's linguistic usage at the end of the Phenomenology of the Spirit. 'Absolute knowledge', although according to its chapter title thematic, appears rather incidentally only in three places (Hegel 3.582 f, 591) and describes there the conclusion of the series of the forms of the spirit: "This last form of the spirit, the spirit, which gives its complete and true content the form of the self at the same time and thereby realizes its concept in the same way as it remains in its concept in this realization, is absolute knowledge; it is the spirit that knows itself in spirit form or comprehending knowledge (Hegel 3.582). The latter has understood that the object of knowledge is not absolutely alien to the spirit, but is nevertheless 'spirit-affine' in its otherness, and the spirit is thus "in its otherness in itself" (Hegel 3.583) and so only truly spirit: absolute knowledge as "the spirit that knows itself as spirit" (Hegel 3.591). 'Absolute' here, then, refers to the completion of the spirit as spirit, not to the logical unassailability of his knowledge, which is thematic in the present context. That there are connections here is of course not to be denied – what absolute knowledge logically aims at, according to Hegel, is "the absolute concept" (Hegel 3.591) and further its externalisation in nature and spirit (Hegel 3.590 f). 3 garded as an unassailable, absolute knowledge. In short: The example shows that absoluteness and finiteness of knowledge can very well go together. This lets it appear justified and meaningful to strive for absolute knowledge also under the – for humans irrevocable – condition of finite knowledge: a for Hegel's metaphysics characteristic perspective, as Karen Gloy notices.5 The addressed 'hubris suspicion' has been finished by this: With the pretension to possess absolute, ultimate-grounded knowledge the finiteness of the knowledge, properly understood, is not denied; God similarity is not laid claim to. 2. The problem of the recognition of fundamental-logic If the fundamental possibility of absolute, ultimate-grounded knowledge can be regarded as clarified so far, the further question arises as to what is meant by this in more detail. As the developed considerations have made clear, transcendental arguments are essential for ultimategrounded knowledge, i.e. arguments concerning the logical conditions of argumentation itself. Thus it has been shown that the assertion of the impossibility of truth itself claims to be true and is therefore self-contradictory. Generally speaking, the self-contradiction results from the fact that logical conditions of argumentation (here the possibility of truth) are disputed, but for this disputing itself must already be claimed and in this sense – namely as a condition of the possibility of argumentation – have transcendental character. In this sense it can be said: The argumentation is based on a transcendental logic, which as such is in principle unassailable regarding the logic of argumentation. And vice versa: Only structures that are themselves fundamental transcendental-logical conditions of possible argumentation can be argumentation-logically unassailable. In the following I would like to call the whole of such fundamental transcendental-logical structures (as in earlier works, e.g. 1994, 2013) in short as fundamental-logic. To the question of what absolute, ultimate-grounded knowledge is possible of, the answer in the sense of these considerations is: of that – and only of that – basis of possible argumentation called 'fundamental-logic'. Not to be misunderstood: This logic, characterized as 'fundamental', is not one of the many 'logics', if the different systems of formal logic are understood by that. These are rather system constructs, which as such always contain conventional elements. Fundamental-logic, on the other hand, has a transcendental character, i.e. it is to be understood as precondition of the possibility of argumentation at all and thus is ultimately also the basis of those diverse 'logics'. To return to the question under negotiation here: As has been shown, absolute, ultimategrounded knowledge is possible only from the fundamenta-logic (and, what I would like to only sweepingly point out, from 'fundamental-logically grounded objects', howsoever these were to be determined6 – this topic is not dealt with here). Admittedly, concerning the fundamentallogic, it must be stated that it is not remotely known and argumentatively available in its entirety, at least at the moment. The case of an absolute and nevertheless incomplete knowledge at any rate is given here. The fundamental-logical knowledge that has been already proven to be absolute at first only has punctual character. In this situation, the existence of a comprehensive system of fundamental-logic is at first a hypothesis. At the same time, it is this anticipation of the whole that motivates philosophical recognition in general to continue on the path of recognition of the absolute, this initially in the general sense of logical conditions of argumentation. Yet this reveals a highly worrying problem: For the further exploration of the fundamental-logic it needs to be argued. But the 'means of argumentation' are elements of this fundamental-logic itself, which itself has still to be recognized. These means of argumentation needed for this knowledge are not available, but are first to be made available by argumentation. But is it 5 "It is Hegel's specific achievement to have provided with his theory a model which permits the absolute and the finite [...] to think in one" (Gloy 1981: 135). As the author here parallelizes the Absolute and the Finite with reason, as "the possession of the system reason", and understanding, as "the ability of systematic explanation", she sees in Hegel's philosophy the possibility of "assuming the coincidence of system reason and explicit system" (ibid.) – a thought, which is confirmed in the following (ch. 3 and 4). 6 Here, for example, the possibility of an a priori natural ontology could be considered; cf. e.g. Hösle 1987, Wandschneider 1985. 4 possible to argue, without already having the necessary logic of argumentation? What is still to be recognized needs already to be presupposed for its recognition here – a typically occurring problem, which Hegel points out e.g. in the introduction to the Phenomenology of Spirit (Hegel 3.69), as soon as recognition starts to recognize transcendental conditions of its recognition itself (see also Plato, Theaitetos, 196 d-e). This re-referencing of recognition to itself is characteristic of the ultimate-grounding project. Can philosophy cope with this problem? In the introduction to phenomenology, Hegel argues that although recognition cannot step out of itself for grounding itself from outside, as it were, it does not need to do so, because it has "its measure in itself" (Hegel 3.76). These statements are very general. To give a concrete example, let us again consider the verdict of truth just discussed, 'truth is impossible'. This statement, as has been shown, is self-contradictory in the sense that it must claim what it denies for this very denial; a contradiction that proves such a position untenable7 – according to the principle of the to be avoided contradiction. Now, the principle of contradiction itself has not been explicitly established here as a principle of argumentation, and thus is not explicitly available for argumentation. It has therefore not been explicitly claimed, too, and yet the validity of the exclusion of contradiction is evident – why? The contradiction cannot be admitted for the reason because it would level the difference between position and negation and thus eliminate the possibility of delimitation and definiteness (see Aristotle, Metaphysics Γ3-6): If both statements: 'truth is possible' and 'truth is impossible' were equally admitted, then the predicates 'possible' and 'impossible' would no longer be distinguished; likewise in all other cases: 'red'/'non-red', 'heavy'/'non-heavy' etc., i.e. there would be no negation. Yet without negation there would be no definiteness, because all determining, according to Spinoza, is a delimitation.8 Thus, there could not be terms with a certain meaning, i.e. the possibility of meaning would be eliminated at all. Rather there can only be certainty and meaning if there is a negation, and this can only exist if the contradiction is excluded, in other words: Those who use senseful, meaningful terms have thus implicitly always already excluded the contradiction, without being to be explicitly formulated that as a principle of argumentation. The principle of contradiction implicitly comes into effect in all argumentation; it is, so to speak, effective 'under the surface'. Question: Is it possible to generalize this fact established for the contradiction principle; is the fundamental-logic altogether effective under the surface? This question seems to be unanswerable, inasmuch as it concerns fundamental-logic in its entire, still unknown extent. Nevertheless: If it were not always already entirely effective in argumentation, it would not be possible to argue, because thatfore not only the principle of contradiction is needed, but – in principle – the entire fundamental-logic. Yet is it possible in principle to doubt the possibility to 7 This, of course, only applies if a 'third' is excluded, i.e. the tertium non datur also applies. But this does not seem to be self-evident in the same way as the validity of the principle of contradiction. Think, for example, of the fundamental discussion in mathematics, according to which the principle of contradiction is irrevocable, but not the principle of the excluded third (cf. Thiel 1972: 110 f). Moreover, this principle seems obsolete in view of the existence of multi-value logics in which 'the third' is no longer excluded. One example is the reflection-logic with six truth values conceived by Ulrich Blau, which was developed primarily to deal with logical indeterminacy and paradoxes (cf. Blau 1985). – In general it can be said that such multi-value logics are constructs in which certain possibilities of validity are fixed by convention. It is essential that such constructs also require fundamentallogical means on the meta-level – namely for their introduction and rules of operation. However, the logic operating at this level, at least the logic operating at the highest meta-level, at any rate is two-valued. For (I take over this argument from U. Blau, oral communication) there is only the alternative of 'true' and 'false', for example regarding the question whether a proposition within the framework of a trivalent logic has that third truth value or not: there cannot be a third again. But the 'highest' meta-level – in the perspective of the theory of justification relevant here – is the transcendental-logical one. The fact that it this absolutely unassailable means, in the sense of these considerations, that its logic is two-valued and that on this level the principle of the excluded third applies. From a transcendental-logical point of view, this principle is thus just as unassailable as the principle of contradiction and (more on this in a moment) the principle of the non-equivalence of position and negation. The recourse to the principle of the excluded third in the previous considerations is thus also transcendentally legitimized. See also footnote 13. 8 "Determinatio negatio est" (Hösle 1987: 195). 5 argue ? As already mentioned in the introduction, there could then not be any doubt, too; because even those who doubt must argue, use meaningful terms etc. In the sense of such a transcendental argument, it is generally to be assumed that the possibility of argumentation cannot be doubted and thus – in principle – the entire fundamental-logic is already involved and implicitly 'effective'.9 However, if the logic in this sense implicitly comes to be effective, then can be stringently argued without the whole instrument of fundamental-logic having to be explicitly available for this – just as it is also possible to prove by mere counting that one and one is two without having to explicitly resort to the Peano axioms (which are of course implicitly used in counting). This is a significant circumstance; for it means that cognition, although it does not explicitly have the entire fundamental-logic at its disposal, can nevertheless progress to new cognition. Recognition is not limited to a factual state of knowledge – for example, in the form of innate or empirical knowledge – but can, so to speak, draw from an underground potential that not only lends validity to its argumentation, but above all enables it to progress. The just formulated question concerning the knowledge of fundamental-logic itself, and that means the acquisition of absolute, ultimate-grounded knowledge, can therefore be answered in this way: That which is only to be recognized here, must and can already be implicitly actuated for this recognition. Thus, it becomes possible to expand our limited knowledge of the fundamental-logic. According to what has been said, this extension of knowledge is to be understood as that is further explicated of what is implicitly effective in such arguments. The recognition of fundamental-logical structures is to be understood as their explication with implicit fundamental-logical means and thus, so to speak, as a self-explication of the fundamental-logic (cf. Wandschneider 2000 and 2013). Recognition has, as it were, only a 'releasing' – explicating – function in this respect: to catch up with and explicate, whereby it is implicitly always already guided and determined – a genuine Hegelian perspective.10 3. The system perspective Now, what has been called 'fundamental-logic' here is certainly not a chaotic mélange, but, as logic, essentially system. Its structure as well as its contents, to affirm this once more, are not explicitly known and available to us due to the finite nature of our knowledge. Nevertheless, in the sense of the developed conception of the implicit effectiveness of the fundamental-logic, the hope is not unfounded that also the system of the fundamental-logic is principally accessible to recognition and that the system knowledge thus gained is progressively expandable. The project in question is no less than an undertaking of the type of Hegelian 'logic'. In this context, the first question that arises is how access can be found at all to the presumed system of fundamental-logic, or in Hegel's well-known formulation: "What must be the beginning of science made with"? (Hegel 5.65). The characteristic of the beginning is usually defined as to be free of prerequisites. According to what has been said, however, this is misunderstandable: Because for all argumentation the entire fundamental-logic is implicitly always already presupposed as transcendental condition of the possibility of argumentation. The question of the beginning is therefore rather to be understood as the question of the beginning of the explication of fundamental-logic: What would to be supposed as the first step of the explication? Here the question arises: What at all is 'explicating'? Of course, it is an making explicit of what is implicitly the case – with which already a first issue has been explicated, namely that explicating is always about expressing that something is the case, or in short: that something is 9 Hegel characterizes the inconsistency of a principled doubt as follows: "If the concern to fall into error places a mistrust in science, which goes to work and really recognizes without such concerns, then it is not foreseeable why, conversely, a mistrust should not be placed in this mistrust and why it should not be worried that this fear to err is already error itself. In fact, it presupposes something, and indeed many things, to be true, and bases its concerns and consequences on it" (Hegel 3.69). 10 It is to be reminded here of the reference given by K. Gloy that regarding Hegel's metaphysics the possibility of the 'coincidence of system reason and explicit system is to be assumed' (see footnote 5). 6 being. The category of being must be considered elementary in this predicative sense. Without the category of being ('is') nothing can be explicated. This explication, that 'being' – in the sense of 'being the case' – is the condition of the possibility of explication at all, thus forms the beginning of the explication process. In Hegel's 'Logic', too, the category of being is the first category. The argument given by Hegel is that of the indeterminacy of the meaning of 'being', i.e. 'being', according to Hegel, does not contain any determinateness at all and is therefore to be regarded as the beginning of determining. (Hegel 5.82) The argument given here basically boils down to the same thing: for the 'is' also does not yet contain any determinateness, but is only the possibility of determining in the sense of the statement that something is the case. In the statement 'the rose is red' the property red is assigned to the rose by means of the 'is', which itself carries no definiteness and therefore applies to everything and anything, provided that it has the sense of 'being the case'. The category 'being' is thus to be understood as the beginning of the explication of fundamentallogic. Explicating is determining. With the explication of the category of indetermined being now, through this very act of explication, something explicit, and that is to say somthing determined, is generated, namely the category 'being': The category of 'indetermined being' is – as this category – determined, i.e. 'being' is the category with the meaning of indetermined being, but as such a well-determined category. For a determined category, however, there is always – qua determinateness – also the opposite-determined category, and that is 'non-being', in other words: The explicit introduction of the category 'being' immediately also requires the explicit introduction of the opposite category 'non-being'.11 Although 'being' here means something indetermined, with this definition of meaning the category itself is something definite, which as definite at the same time is opposed to its definite opposite 'non-being', which it thus principiates. With the now gained duality of the categories 'being' and 'non-being' a new constellation of explicit categories has arisen, which further implies the question of the relationship between the two. First of all, it must be noted that each is the negation of the other: The category 'being' is not the category 'non-being'. So, in the twinkling of an eye, the category 'being' proves itself to be a case of 'non-being'. Although it means 'being', it is infected with 'non-being' precisely because it is not 'non-being'. Thus it has, as it were, the property of non-being upon itself, and in this respect it is 'non-being-like'. Admittedly, in that it is non-being-like, it again has the property of being in this respect, so that it is again 'being-like'. This, in turn, is not non-being-like, so that thereby the property non-being-like is given again, and so forth. The category of being thus alternately shows the property of being and non-being. The property of 'being-like' turns into 'non-being-like', and 'non-being-like' turns into 'being-like'. In the relationship of the category 'being' to its opposite category 'non-being' a strange ambivalence becomes visible with regard to its properties: They oscillate, as it were, between 'being' and 'non-being'. This is the characteristic of an antinomic relationship.12 This is not the place for an indepth analysis of antinomic structures. As I have shown elsewhere (Wandschneider 2013; 1993), this oscillation of the category 'being' on the property level of the category also has consequences for the meaning 'being' of the category: It follows that this itself has antinomic character, too, and that means that the category 'being' is not only opposite to the category 'nonbeing', but also equivalent to it – equivalent in the sense that the meaning 'being' always implies the meaning 'non-being' and vice versa. So 'being' proves to be inseparably connected with 'nonbeing'. 11 Here the argument differs from that of Hegel, who identifies the meaning 'indetermined being' with the meaning 'nothing'. In his note 3 to the dialectic of being/nothing, however, Hegel expresses himself also in the sense of what is said here: "It is precisely this indeterminacy (sc. of 'indetermined being'), however, that constitutes the determinacy of the same (sc. of the category 'indetermined being')" (Hvh. D.W.) (Hegel 5.103 f). 12 Special emphasis was given to the importance of antinomic structures for dialectics by Thomas Kesselring (1984). Hegel himself has also pointed out the antinomic character of the "being-nothing-dialektic" (Hegel 5.94). A detailed analysis of the antinomic structure and its consequences for dialectic I have undertaken in Wandschneider 2013, see also 1993. 7 This is certainly an odd result, which at first suggests the suspicion of a contradiction. However, it can be shown (see Wandschneider 2013: 46 f, 58 f) that the two opposing provisions, although inseparably linked, concern different aspects: Semantically, the inseparable belonging-together of 'being' and 'non-being' leads to a new category, namely 'determined-being', in the sense that the being of something determined is at the same time non-being, namely of something else determined. The being of a chair is at the same time a non-being of a table, and vice versa. Determined-being is a being that is, in another respect, at the same time a non-being, and that means a synthetic structure!13 Plato already has pointed out something like this in the dialogue Sophistes (e.g. 256 d ff): So Parmenides' central thought that being can never be non-being has become obsolete for Plato (on this, also Düsing 1997); in this sense, he speaks of a 'patricide' of Parmenides (241 d). In short: Starting from the categories of 'being' and 'non-being', a new category of 'determinate-being' has thus been explicated, which is characterized as the synthesis of both. Now, 'determinate-being' references to something determined, that, as such, is not something other determined – note: the being of a chair is not the being of a table, and vice versa. In other words, 'determinate-being' more concretely unfolds as the pair of opposite categories 'so-determinatebeing' and 'other-determined-being' So a new pair of opposite categories has been explicated. With the appearance of a new pair of opposites, however, the question of the relationship of both categories arises again, with the consequence – what is no longer explained here (developed in detail in Wandschneider 2013; see also 2010) – an antinomic structure arises again, and from it, as before, the necessity of a synthetic connection of the opposites, and so forth.14 Thus a procedure of successive explication of fundamental-logical categories is outlined. This has a dialectical character in the sense that it leads again and again to oposites, which make antinomic structures visible, that demand a new, synthetic category, which in turn 'dissociates' again into new opposites, and so forth. The procedure thus basically ties in with the form of dialectical argumentation as presented in Hegel's Science of Logic. An essential difference, which is central to the procedure outlined here, compared to Hegel's, is to be seen in the systematic demonstration of antinomic structures, from which, as I have explained elsewhere (Wandschneider 2013: Ch. 2 and 3), only an explicit justification of the synthesis formation results. These considerations will not be continued here. What is decisive is that a methodical procedure has thus been found which allows to explicate the initially implicit system of fundamental-logic. I think this is an important result for the question of the possibility of absolute, ultimately-grounded knowledge, because, as explained, only fundamental-logical relations can claim absolute validity; on the other hand, the system of fundamental-logic is not already explicitly available. The procedure of dialectic now, as has been shown, opens up the possibility of tackling the systematic explication of fundamental-logic, and is thus to be understood as a method for obtaining absolute, ultimate-grounded knowledge. 4. The stringency of dialectical explication Of course, this also raises the question of the extent to which this conception can claim stringency. Indeed, it is difficult to name a philosophical concept that has been judged more controversially than dialectics. A reassurance regarding the stringency of dialectical argumentation is therefore inevitable. In the following I would like to say something more about this. 13 This transition to the synthetic category 'determined-being' again marks a difference regarding Hegel's argument, which, starting from the opposition of 'being' and 'nothing' (instead of, as done here, from 'being' and 'non-being'), introduces the category 'becoming' as synthesis. To justify my rejection of Hegel's version, see Wandschneider 2013, ch. 3.3. 14 It has been said that the principle of the excluded third no longer applies strictly regarding dialectics. Admittedly that is to be understood in the sense of the level structure that is essential here: Thus, with the synthesis of the opposite categories a new semantic level is reached that leaves behind the preceding opposition and insofar indeed represents a third in relation to the mutually exclusive opposites – but not on the same level as this one; see also footnote 7. 8 Wolfgang Wieland (1978) and Vittorio Hösle (1987) have pointed out that dialectical progression is essentially based on a discrepancy between the meaning of a term and its conceptual properties. Wieland, for example, argues that "the category of being is something other than what it designates [...] The evidence of such a discrepancy is enough [...] to force the progress" (Wieland 1978: 201), namely "through the insight developed in a different way at each level [...] that the respective category does not yet give the adequate representation of the Absolute" (Wieland 1978: 203). As Hösle, following on from this, argues, the development of categories thus ultimately aims at a category "which that explicitly asserts what it implicitly presupposes" (Hösle 1987: 201). Only then would the conclusion of the dialectical movement be reached, in Hegel's Logic thus with the 'absolute idea'. Each step in the process thus leads to the fact that "that which in itself or for us [implicitly, D.W.] was always already there, [...] becomes, at least partially, explicit in the new category". "If one explicates everything that is implied in the concept of being, one comes to the 'absolute idea'" (Hösle 1987: 203). According to this, the procedural progress is "motivated by the systematic ultimate goal of logic" (Wieland 1978,: 202). Does this mean that one must know this goal in advance in order to get there? Wieland denies this: That goal is "nowhere explicitly presupposed in the progress of logic; it does not enter into any of the conceptual operations as an element" (ibid.). Nevertheless, "the progress [...] is forced [...] by the insight, developed in a different way on each level, that the respective category does not yet give the adequate representation of the Absolute" (Wieland 1978: 203) – which is then again relativized by Wieland: "In these cases one has to consider that this is only an aid to understanding" (Wieland 1978: 205). Hösle, however, maintains "that according to Hegel philosophy is the science of the Absolute" and "that a definition of the essence of the Absolute that proves itself to be incomplete [...] is self-contradictory. Indeed, it is of utmost importance to assume a claim of completeness for the individual categories; only then the contradiction becomes apparent with many of them" (Hösle 1987: 201) – 'contradiction' in the sense of a discrepancy between explicitly expressed and the implicit claim to express the Absolute. Must the dialectician after all constantly consider the Absolute, which he admittedly does not yet know at all? From this point of view, let us once again mind the considerations developed here. First a problem arose with regard to the beginning: The explication procedure can only use what is already explicitly available. Yet as explained before, the argumentation necessarily always makes use of other, initially still implicit elements of fundamental-logic, but in order to be justifiable, the procedure must adhere to what is explicitly available. Now, the beginning is characterized by the fact that nothing is explicated yet. How can the procedure then begin at all? The answer given here is based on the explication of the sense of explication itself: What is to be explicated must in any case 'be the case', or in short: it must, howsoever, 'be'. The category of being claimed here is thus to be understood as the first explicit element of fundamental-logic. With this first step of explication, however, the second step is already initiated: As this determined category that categorizes 'being', it is not the category 'non-being', whereby the category of nonbeing is also directly involved: The explication of 'being' inevitably entails that of 'non-being'. Thus a new constellation of explicit elements has arisen: Now that two explicit categories exist, the question of their relationship arises. As explained above, this leads to a complex structure which, when viewed more closely, has an antinomic character. Thus, the next step is marked out: The antinomic structure of the relationship of 'being' and 'non-being' means that both belong inseparably together and thus necessitate the introduction of a synthetic relationship, which connects the meaning of 'being' with that of 'non-being' – a new meaning of 'being', so to speak, which is linguistically conceptualized as 'determined-being', i.e. as a being that, as being of a particularly determined being, is at the same time non-being of another determined being. 'Being' in the sense of 'determined-being' thus further forces the introduction of a new pair of opposites, 'so-being' and 'other-being ', which, as can be shown (Wandschneider 2013: Ch. 3.5), in turn makes antinomic structures visible, thereby again forces them to a new synthesis and so on. The procedure of dialectical category explication thus provides a sequence of categories in 9 the sense of a progressive explication of semantic basic categories.15 The fact that this procedure is not arbitrary – otherwise it would have no explanatory value – results from the fact that it is strictly oriented, in a reflexive turn back to itself, to what was explained in the respective preceding procedural step, in order to add a further explicit element to what had already been explicated before. So, by the act of explication itself, at the same time a new situation is created: A new element has, so to speak, appeared on the stage of explication and has thereby brought about a new constellation of explicit elements – whereby at the same time implicitly a new fact is given – an antinomic structure – which as such now sets the next explication task and thus motivates a new explication step, and so on. In other words, each explication step creates a new discrepancy between what has just been explicated and what thus has been newly implicitly created, which in turn requires a new explication step. This incongruity, which guides the explication procedure, between what has just been explicated and the implicit fact that has been newly produced in the act of explication itself, is what I would like to call the explication discrepancy. In this way, the explication procedure is determined by itself and thus – in principle – all arbitrariness is eliminated: Each explication step is determined by the preceding one. Thus, not just any implicit content is explicated, but rather exactly that implicit content that was generated by the respective step itself, which can thus be concretely grasped and which passes on the procedure through the resulting explication discrepancy.16 The dialectic is thus by no means subject to the – unfulfillable – condition that the Absolute must always be applied as an explicit criterion of the procedure. What is decisive is the self-referential recourse of the procedure to the respective preceding step with the aim of capturing the specific explicative discrepancy that occurs at each explicative step and resolving it by a new explicative act. One could characterize this as an act of reflexive self-assurance regarding the completeness of knowledge. But why should completeness be the goal of knowledge? Obviously because underhand the Absolute is asserting itself after all, which so to speak forms the secret motive of cognition. Logic – in the sense of fundamental logic –, so it had become clear, brings itself implicitly to validity; thinking nolens volens, we have always already subordinated ourselves to its absolute authority. All cunning of recognizing, to take possession of the Absolute, would be futile and useless, so Hegel's well-known formulation in the phenomenology, " if it were not actually already be and wanted to be with us " (Hegel 3.69). 5. Unassailability and fallibility of absolute knowledge The reference made at the beginning to the current discussion of the ultimate-grounding can now be further substantiated in methodological terms: Essential for the dialectical procedu- 15 The question of the conclusion of such an explication procedure must be left open at this point, as it required more far-reaching considerations. Cf. for this the critical considerations in Gloy 1981: 166 ff, 174 ff, and Hösle 1987: 196 ff. 16 Robert B. Brandom has shown in detail that the function of logical terms is to make explicit what is implicitly presupposed in the discourse: "The logical vocabulary has been characterized in this work as to make explicit constitutive features of discursive practice [...], features that were implicit in what was done before the introduction of that vocabulary. This is performed by terms "that qualify as logical by virtue of their role in making explicit". According to Brandom, what is made explicit hereby are "implicit inferential determinations" of terms (Brandom 2000: 737): Whoever understands the term 'dog' has also understood that from 'dog' the inference to 'mammal' is possible. "A theory of expression thus explains how that what is explicit emerges from that what is implicit" (Brandom 2000: 136). Brandom himself recognizes here a Hegelian perspective (e.g. Brandom 2000: 156 f; see also Brandom 2001). – Nevertheless: the difference to the considerations developed here cannot be overlooked either: Brandom is not concerned with the project of a systematic development of that what is implicit to be explicated, the procedural generation of which is the actual point in the present context. According to this (see above) exactly that implicit content is explained which was generated by the respective preceding procedural step itself, thereby can be concretely grasped and passes on the procedure through the newly resulting explanation discrepancy. Brandom's interest, on the other hand, is focussed on the inferential potential implicitly contained in empirical terms, which he understands as being socially constituted. The systematic development of fundamentallogic is not his issue. (For more detail see Wandschneider 2006.) 10 re is, as has been shown, the recourse on the respective implicit fact generated by the preceding explication step and thus to be understood as a transcendental condition of the following step of the procedure. This turning back of thinking to itself can, with a term introduced by Wolfgang Kuhlmann in a transcendental-pragmatic context, also be characterized as an act of strict reflection (Kuhlmann 1985: cf. e.g. 76 ff, 119). Kuhlmann understands by it the recollection of the respective directly performed linguistic action (insofar 'strict') and the 'action knowledge' implicitly determining this linguistic action ('hereby I claim [...]', 'I presuppose [...]' etc.). A similar reflection on the foregoing procedural step is also given in my argument, however not on presuppositions of speech acts, but on the respective procedural-generated semantic-logical constellation, i.e. the logical determinations made by the procedure itself in the immediately preceding explication step. With each step of the procedure a logical potential is generated, as it were, which, by being reflected upon, provides new material content for the argument and thereby drives the procedure further – a methodically regulated strict reflection, as it were. For Kuhlmann, however, the question of certainty is of primary importance: "When I make a claim, there can be no doubt that I have made an act of assertion, because that corresponds to my intention in making the claim. When I speak meaningfully, I must know what I mean when I speak: in this respect, the 'knowledge of action' associated with speech acts is indeed of immediate certainty for the speaker himself. This is of course a private certainty. Although, according to the 'private-languageargument', there can be no private language in the strict sense, but what is intentional intended is immedately certain only for me – the intentional speaker. The addressee of my speech can only indirectly realize its meaning and thus only have hypothetical certainty. Therefore, the aspect of private evidence is not relevant for the foundation of philosophy. What is decisive is the validity of the argument, and that is solely a question of logic. With this proviso the principle of strict reflection in the sense of the developed considerations is justified: Each explication step is then only possible in recourse to the previous one, to the new constellation thus generated of explicit elements and their implicit logical structure. The dialectical procedure so indeed has the character of strict reflection, which here, however, is not to be understood as a recourse to a privately performed (and moreover contingent) linguistic act, but, as explained, as an objective procedural principle, which would thus be characterized as methodically regulated strict reflection. Thus the logic effective in all argumentation takes the place of the only privately accessible linguistic action knowledge. But, admittedly, in this way no direct knowledge and no direct evidence is possible, so that the possibility of error cannot be excluded in principle. This marks the obvious difference between the developed view and the transcendental-pragmatic position advocated by Kuhlmann – notwithstanding the undoubtedly common interest of both with regard to the possibility of ultimate-grounding From there also light is shed on the question of the fallibility of knowledge: Not that the intentions accompanying my speech actions are directly accessible and evident to me, can be regarded as criterion of knowledge, but only the logical justification of knowledge, accessible and objectively comprehensible to all – which as such is admittedly also prone to error. Hegel remarks that Plato reworked the 'Politeia' seven times; for an undertaking of the type of Hegelian logic it would have been desirable, according to Hegel, that "the free leisure to work through it seventy-seven times would have been granted" (Hegel 5.33). Ultimate-grounded, absolute knowledge' is indeed not synonymous with 'ultimate, absolute certainty': it cannot be 'ultimate' knowledge, since, as explained, it is knowledge that can be overtaken, i.e. further developed, forther specified. And the aspect of absolute subjective certainty is objectively irrelevant according to what has been said. If it is 'ultimately-groundable', this rather means that it can be shown to be 'absolute' for logical reasons, i.e. to negate it would be self-contradictory. But regarding the 'justification of logical reasons', errors of thought, i.e. subjective errors, cannot be excluded in principle. However, 'errors cannot be excluded in principle' is certainly not the same as 'errors are inevitable in principle', or, to put it more briefly: 'Error is possible' is not the same as 'error is necessary'. The latter is the pragmatically contradictory and thus untenable the11 sis of fallibilism,17 which must therefore be rejected. 6. Conclusion Altogether: Three main points have become visible for the outlined procedure of dialectical explication of fundamental-logic: (1) On the one hand, it has a strictly methodological character. Its results are not beheld, guessed or even subreptitiously obtained, but are generated in a methodically comprehensible way. In this sense they are principally justifiable and can therefore appear with a strictly scientific claim. Indeed they are also overtakable in the sense of 'further developable', i.e. 'specifiable'. But the overtakeability of the categories derived does not prevent the stringency of their dialectical reconstruction, and that also means: Overtakeable categories are not 'false' categories. The 'correct' meaning of a category is rather that which belongs to the respective state of the procedure. The category belonging to a more advanced stage of the procedure is not the more correct one, but only a more specific category.18 And the argument on which it is based is by no means more stringent than that in the case of a procedurally earlier category. (2) The direction of dialectical progression is determined by the procedure itself, in so far as the next step is logically determined by the previous one. In this sense, dialectics, as Hegel repeatedly emphasizes, is not a method that would be applied externally, i.e. arbitrarily, to an already ready given object. Rather, it produces its object itself, and in this sense, with Hegel, it can indeed be characterized as a self-movement of the concept.19 (3) Finally, the procedure also has a heuristic function: as a guideline for the systematic exploration and explication of the system of fundamental-logic. It is intuitively obvious that the procedure of dialectical category explication is always a progression towards higher conceptual complexity; for each element that is newly explicated expands the overall constellation of explicit elements. That the case of a mere iteration can be excluded can be derived from the specific structure of dialectical development, which, via antithetical terms, leads to synthetic categories, with which, as it were, a new conceptual level is reached, on which new antithetical terms appear, etc. At the same time, it is clear that this development would only be complete when it no longer generates new opposites and thus no longer poses a new explication task. Justifiability, self-movement and the heuristic character of dialectical category explication are thus closely connected and qualify it as the sought-after procedure of the self-explication of logic by logical means. Hegel's Science of Logic is – after proleptic approaches, for example with Plato (cf. e.g. Sophistes 251a ff, Parmenides 135c ff) and Leibniz – certainly the most elaborated draft of such a system to date: a gigantic, admirable construct of thought, which nevertheless also shows cracks and breaks20 and thus could rather be understood as a still unfinished metaphysical project, not yet as the elaborate system of fundamental-logic. The fact that this metaphysical claim has in fact not yet been fulfilled, neither in Plato's nor Hegel's work nor in current thinking, speaks neither against the sense nor against the feasibility of the project. With the initially punctual proof of ultimately-grounded truth, both meaning and feasibility can 17 Following the footsteps of Karl R. Popper, again discussed and vehemently represented by Hans Albert (31975), among others. 18 For this reason, as explained in the introduction, it is possible to argue stringently with a still largely undefined concept of truth (even with regard to the possibility of absolute truth), without having to have definitively solved the problem of truth negotiated in most diverse theories of truth beforehand. As has been shown, it is sufficient to know that a statement is always associated with a claim to truth. 19 From Hegel's Science of Logic here a formulation that also expresses the turning back of the argumentation to itself: "Movement as progressing turns directly to itself and is only in this way self-motion – movement that comes from itself" (Hegel 6.28). 20 Cf. e.g. the extension of the Hegelian logic by the category of intersubjectivity, asserted by Vittorio Hösle, which is to be necessary for a sufficient foundation of philosophy of mind. Hösle argues that "the realphilosophy is not completely 'covered' by logic, because objective mind and absolute mind contain categories of intersubjectivity and thus open a real-philosophical sphere that is no longer principiated by the logic as it is. [...] So in the divergence of logic and real-philosophy there seems to be a real inconsistency – an inconsistency that probably points to an incompleteness of the logic" (Hösle 1987: 646). 12 rather be regarded as secured in advance. What is lacking is the comprehensive, systematic elaboration of what has been outlined here. References Albert, Hans (31975), Traktat über kritische Vernunft, Tübingen (Reclam) Apel, Karl-Otto (1973), Transformation der Philosophie (Bd. 2), Frankfurt/M. (Suhrkamp) Aristoteles: Metaphysik Blau, Ulrich (1985), Die Logik der Unbestimmtheiten und Paradoxien, in: Erkenntnis (Bd. 22), 369–459 Brandom, Robert B. (2000), Expressive Vernunft. Begründung, Repräsentation und diskursive Festlegung, Frankfurt/M. (Suhrkamp) Brandom, Robert B. (2001) Begründen und Begreifen. Eine Einführung in den Inferentialismus, Frankfurt/M. (Suhrkamp) Düsing, Klaus (1997), Dialektikmodelle. Platons 'Sophistes' sowie Hegels und Heideggers Umdeutungen, in: Wandschneider, Dieter (Hg.) Das Problem der Dialektik, Bonn (Bouvier), 4–18 Gloy, Karen (1981), Einheit und Mannigfaltigkeit. Eine Strukturanalyse des 'und'. Systematische Untersuchungen zum Einheitsund Mannigfaltigkeitsbegriff bei Platon, Fichte, Hegel sowie in der Moderne, Berlin/ New York Hegel, G.W.F., Werke, 20 Bände, ed. E. Moldenhauer/ K.M. Michel, Frankfurt/M. 1969 ff (Suhrkamp) Hösle, Vittorio (1987), Hegels System. Der Idealismus der Subjektivität und das Problem der Intersubjektivität, Hamburg (Meiner) Hösle, Vittorio (1990), Die Krise der Gegenwart und die Verantwortung der Philosophie. Transzendentalpragmatik, Letztbegründung, Ethik, München (Beck) Kesselring, Thomas (1984), Die Produktivität der Antinomie. Hegels Dialektik im Lichte der genetischen Erkenntnistheorie und der formalen Logik, Frankfurt/M. (Suhrkamp) Kuhlmann, Wolfgang (1985), Reflexive Letztbegründung. Untersuchungen zur Transzendentalpragmatik, Freiburg/München (Alber) Platon: Politeia, Theaitetos, Sophistes, Parmenides Thiel, Christian (1972), Grundlagenkrise und Grundlagenstreit. Studie über das normative Fundament der Wissenschaften am Beispiel von Mathematik und Sozialwissenschaft, Meisenheim am Glan (Anton Hain) Wandschneider, Dieter (1985), Die Absolutheit des Logischen und das Sein der Natur. Systematische Überlegungen zum absolut-idealistischen Ansatz Hegels, in: Zeitschrift für philosophische Forschung (Bd. 39), 331–351 Wandschneider, Dieter (1993), Das Antinomienproblem und seine pragmatische Dimension, in: Stachowiak, Herbert (Hg.) PRAGMATIK (Bd. IV), Hamburg (Meiner), 320–352 Wandschneider, Dieter (1994), Letztbegründung und Logik, in: Klein, Hans-Dieter (Hg.), Letztbegründung als System? Bonn (Bouvier), 84–103 Wandschneider, Dieter (1996), Letztbegründung und Dialektik, in: Fornet-Betancourt, Raúl (Hg.), Diskurs und Leidenschaft. Festschrift für Karl-Otto Apel zum 75. Geburtstag, Aachen (Verlag der Augustinus-Buchhandlung), 317–336 Wandschneider, Dieter (2006) 'In-expressive Vernunft'. Abschied vom 'sich vollbringenden Skeptizismus' in Robert B. Brandoms pragmatistischem Positivismus, in: Bowman, Brady/ Vieweg, Klaus (ed. 2006) Die freie Seite der Philosophie. Skeptizismus in Hegelscher Perspektive. Würzburg: Königshausen & Neumann 2006, 199–216 Wandschneider, Dieter (2010) Dialectic as the 'Self-Fulfillment' of Logic, in: Limnatis, Nectarios G. (ed. 2010) The Dimensions of Hegel's Dialectic. London, New York: Continuum International Publishing Group 2010, 31–54 Wandschneider, Dieter (2013) Grundzüge einer Theorie der Dialektik. Rekonstruktion und Revision dialektischer Kategorienentwicklung in Hegels 'Wissenschaft der Logik'. Würzburg 13 2013 (Königshausen & Neumann) – unveränderter Nachdruck der Originalausgabe (1995, Klett-Cotta) Wieland, Wolfgang (1978), Bemerkungen zum Anfang von Hegels Logik, in: Horstmann, RolfPeter (Hg.), Seminar: Dialektik in der Philosophie Hegels, Frankfurt/M. (Suhrkamp), 194–