Posts com a Tag ‘VALENTE Matheus (Res)’
About Oneself: De Se Thought and Communication – GARCÍA-CARPINTERO (M)
GARCÍA-CARPINTERO, Manuel; TORRE, Stephan (eds.). About Oneself: De Se Thought and Communication. Oxford: Oxford University Press, 2016, 368p. Resenha de: VALENTE, Matheus. Manuscrito, Campinas, v.40 n.2 Apr./June 2017.
About Oneself: De Se Thought and Communication is a recently published collection of eleven papers on de se thought, i.e. thoughts about oneself as oneself, and its implications for a theory of communication. Edited by Manuel García-Carpintero and Stephan Torre, this volume contains contributions from many distinguished experts and presents the state-of-the-art discussions on this important field.
The issue of de se thought dates, at least, as far back as the late 1960s1, when some noticed that, in order to characterize the information encoded in a de se thought, one must reject some traditional assumptions about propositional attitudes. Take, for example, Perry’s famous story of when he tried to find the person making a mess in the supermarket by following a trail of spilled sugar only to subsequently realize that he himself was the culprit. It seems that, whatever the content of Perry’s epiphany is – the one he could express by uttering “I am making a mess” – it resists characterization by traditional conceptions of propositions (i.e. as sets of possible worlds or structured Russellian propositions).
Most of the chapters in this volume are primarily concerned to defend one or another theory of de se thought and to examine their implications for an account of communicative success. Due to shortage of space, this review will focus on the papers that are directly involved with these questions. Our main objective will be weaving these papers together such as to make explicit their points of agreement and disagreement.
What, after all, is so special about de se content? This is not an easy question to answer. Indeed, some philosophers even got as far as declaring that there is no real problem of de se content over and above the typical issues that singular thought (in general) brings about, such as Frege’s Puzzle2. Dilip Ninan’s paper – What is the Problem of De Se Attitudes? – intents to reach a verdict about the extent to which some content is essentially indexical. According to Ninan, only de se attitudes (as opposed to other de re attitudes) are such that they give rise to cases where two subjects agree about all the objective properties of a situation while still diverging in their behavior. This happens, for example, in Perry’s bear scenario (1979), in which I am being chased by a bear while you are watching from a safe distance. Even though we may agree on our objective beliefs about the situation (e.g. that I am being chased by a bear and you are not) as well as in our desires (e.g. we both desire that I don’t get killed), it is still true that we will be motivated to behave differently (e.g. I will curl up into a ball and you will run to get help). That is, only when de se attitudes are concerned, there can be full belief-desire agreement concomitant with divergent behavior. That conclusion leads to an outright denial of Explanation:
(Explanation) If a subject’s behaving in a certain way is explained by his set of belief-desire pairs, then any other subject possessing the same set of belief-desire pairs will be disposed to behave identically.
Ninan’s paper help us see how most theorists of de se thought are trying to hold onto Explanation in the face of conflicting evidences by rejecting one of the following two theses:
(Absoluteness) The contents of attitudes are absolute, i.e. contents do not vary in truth-value across individuals or times.
(Publicity) The contents of attitudes are public or shareable, i.e. if an agent x can entertain a content p, then so can any other agent y. (p. 111)
If Explanation and Publicity are true, Ninan claims, one must agree that someone could possess one of my de se beliefs, e.g. that I am being chased by a bear. Per Explanation, we would then be disposed to behave identically – we would both be disposed to, say, curl up into a ball. However, since it is possible that our beliefs diverge in truth-value – one of us could just be overly paranoid – we would then have to dispose of Absoluteness. This is the path (Lewis, 1979) famously took by defending that the content of de se attitudes are properties (or, equivalently, centred propositions), entities which vary in truth-value relative to non-worldly parameters.
Clas Weber – in Being at the Centre: Self-location in Thought and Language – explicitly sets out to defend a Lewisian theory of propositional attitudes and to show how the communication of de se thoughts would be possible inside that framework. In order to do this, Weber advances the Transform-and-Recenter Model of communication, according to which there is no single content being replicated from speaker to hearer in successful instances of de se communication. Since assertions present their contents as being essentially from a particular perspective, Weber claims, we must perform a series of transformations on other people’s asserted contents, so that a piece of information that was originally presented from the speaker’s perspective becomes a piece of information relative to the hearer’s.
In his contribution, De Se Communication: Centered or Uncentered?, Peter Pagin argues that no Lewisian theory positing centered contents can give a suitable account of de se communication, since “the connection between a [centered] content and its thinker is not representational” (p. 275). In a Lewisian theory, the content of de se thoughts are impersonal properties, e.g. the property of being chased by a bear. Only when a thinker believes that property, i.e. self-ascribes it, a connection between her and the content of her thought is drawn. Pagin argues that this entails that a thinker may never merely entertain a thought, e.g. that she is being chased by a bear; what she entertains is just the property of being chased by a bear, not that she is being chased by a bear. After considering various recent incarnations of the Lewisian theory, Pagin goes on to advance his own Fregean-inspired view, maintaining Absoluteness in exchange for Publicity, and thus, giving rise to the famous issue of ‘limited accessibility’. Pagin claims the denial of Publicity should be seen as non-problematic since (i) it is an independently motivated thesis that subjects rarely have the same conception of the concepts they employ and that (ii) this should not harm communicative success in the least.
In opposition to both Lewisian and Fregean theories, some philosophers argue, following (Perry, 1979), that sameness of behavior between A and B should not be explained by them believing a common content, but by them believing possibly distinct contents under the same guise. François Recanati and Manuel García-Carpintero both identify themselves as developing their own Perrian accounts of de se thought. These two authors argue that, in order to clarify these issues, one has to take into account two distinct semantic levels about which one’s attitudes and assertions are accountable: the presuppositional content that one’s representations carry and the content that they properly expresses. The former accounts for the cognitive significance of a thought, whereas the latter accounts for our intuitions on (dis)agreement and sameness of subject matter. Recanati, in Indexical Thought: The Communication Problem, presents his version of a Perrian two-factor theory by means of his independently motivated framework of Mental Files, i.e. psychological guises by means of which we produce and retain singular thoughts. Recanati considers multiple accounts of de se communication before settling for an improved variant of Weber’s Transform-and-Recenter model. Differently from Weber, who frames his model by means of metarepresentations, Recanati fleshes it out in terms of Mental Files. For this reason, he claims to be able to overcome the aforementioned objections from Pagin. One interesting consequence of Recanati’s account of de se communication is that the idea of the thought expressed by an utterance, over and above the thoughts of the speaker and her interlocutor, comes out as otiose. As the author emphasizes, as long as we have our hands on the thought of the speaker, the thought of the hearer, and a suitable relation of coordination between them, there remains no theoretical role to be played by a neutral notion of the thought expressed by the utterance.
Manuel García-Carpintero’s paper, Token-Reflexive Presuppositions and the De Se, agrees with Recanati’s in that both argue that the cognitive state of a subject undergoing a de se thought must be characterized not only by (i) that subject (mentally) asserting a certain content but also by (ii) her thought triggering certain reference-fixing presuppositions. Thus, even if the content of de se attitudes are to be fleshed out as familiar singular propositions, “when I judge I am hungry I [also] presuppose that the person of whom I am predicating being hungry is the thinker of this very judgement” (p. 191). García-Carpintero points out the importance of distinguishing the attitude a subject holds towards an asserted content from the attitude held towards a content that she presupposes in virtue of having made that assertion. The author claims that the attitude towards a presuppositional content cannot be that of belief, since anyone else could believe a certain presuppositional content without being motivated to act in the special way de se attitudes motivate us to act. Because of these reasons, García-Carpintero notes, even a Perrian theory is bound to posit some kind of limited accessibility to de se thoughts. In his own framework, the limited accessibility arises from the fact that, while anyone can have a belief about the owner of a certain thought of mine (e.g. that the owner of that thought is hungry) only I can have a thought about myself by correctly presupposing that the owner of that thought is hungry. One shortcoming of that paper, as the author himself admits, is that it does not provide a deeper development of the attitude of presupposition. More particularly, it would be enlightening to know more about a subject’s understanding of her own presuppositions besides the fact that it should be merely implicit. Should it, for example, be characterized as dispositional knowledge that one would be able to manifest given sufficient time and reflection or is it something even less substantial, such as, perhaps, a matter of knowledge-how? These questions remain open for further inquiry.
Robert Stalnaker’s positions about de se thought have been usually understood as being in opposition to a Perrian two-factor theory. Be that as it may, in his contribution – Modeling a Perspective on the World – we see him getting closer and closer to that tradition. Stalnaker’s most immediate concern in that paper is proving that one does not need to add centers to possible worlds in order to model attitudinal content. According to him, the formal apparatus of centred possible worlds is theoretically useful, not for modeling contents, but for modeling belief states, i.e. the relation between particular thinkers and the set of doxastic alternatives accessible to them. More specifically, belief states are modeled by Stalnaker as pairs consisting of a base world (the world and time in which the subject is in that state) and a set of doxastic alternatives available to that subject (the worlds that might, for all that subject believe, be the actual one). As more than one author in this volume has noticed3, Stalnaker’s resulting theory resembles a typically Perrian theory with two levels of content, one playing the internal role of psychological rationalization (the doxastic alternatives) and the other, playing the external role of providing absolute truth-conditions for the relevant attitude (the base world). One might wonder, as García-Carpintero (p. 188 ff. 21) suggests, whether this means that Stalnaker’s theory is not concerned, as it used to be in earlier works, with providing a holistic individuation of a subject’s total belief state, but with characterizing specific parts of a subject’s belief states. Unfortunately, Stalnaker does not comment on that, so we are left to our own speculations.
No theory of de se thought has an easy way out of the problem of communication. In Varieties of Centering and De Se Communication, Dirk Kindermann claims that no variant of the Lewisian and Perrian accounts of de se thought4 allows us to maintain a simple picture of communication as the replication of thought from speaker to hearer. He takes that and related facts to motivate a neutral position on the issue of de se thought: “everything that can be done by one view can also be done by the others; the views cover exactly the same empirical data and do so in equally simple ways; the choice between the views is a matter of (theoretical) taste and prior commitments” (p. 309). Kindermann’s conclusion implies that, at least some disagreements between philosophers working on de se thought are not fundamental, such as those about which theory provides a simpler account of de se communication, propositional agreement/disagreement or of samesaying. Coming last in a volume about de se communication, Kindermann’s paper has a particularly anti-climactic feel. If, as this author suggests, there are no knock-down arguments waiting to be discovered in favor of this or that theory, philosophers might need to put the issue of de se thought into a new perspective in order to avoid reaching an argumentative dead-end.
There are four remaining papers. Isidora Stojanovic’s Speaking About Oneself investigates the concept of samesaying in relation to de se utterances and argues that it neither tracks the character nor the Kaplanian content of an utterance. In Why My I Is Your You, Emar Maier presents a formal model of de se communication using the apparatus of Discourse Representation Theory. Aidan McGlynn’s Immunity to Error Through Misidentification and the Epistemology of De Se Thought claims that de se thoughts are not epistemically special and that the phenomenon of IETM should be characterized as a matter of degree. Finally, Kathrin Glüer’s Constancy in Variation tackles the issue of perceptual content and defends the thesis that it does not need to be modeled by centered contents.
One may ask, what is the upshot of the discussions and arguments contained in this volume? Here’s a tentative answer: to account for de se intentionality, we need to explain (i) why two people who have identical de se beliefs are (ceteris paribus) disposed to behave identically while (ii) two people who seem to agree on all the objective properties of a scenario may nonetheless go on to act differently. This was, as we have seen, one of the lessons of Ninan’s contribution to that volume. Most authors seem to agree that, in order to explain (i), we need fine-grained representations of one’s beliefs and/or belief states; however, it is crucial to distinguish the attitude one has towards those fine-grained objects from the attitude one has towards one’s beliefs. On the other hand, there is not much consensus nor positive suggestions about how to explain (ii). Again, most authors point out that merely having beliefs with the same objective truth-conditions is not enough for two people (or two temporal stages of the same person) to count as being in agreement with each other. However, it is not clear what else is necessary. One interesting theoretical possibility is suggested by Recanati’s talk of “coordination” among different thoughts, but the idea is arguably underdeveloped as it stands. Another possibility is to see Weber’s Transform-and-Recenter model as providing a constraint on the agreement relations between two thoughts, e.g. two thoughts A and B agree with each other if and only if B would be the output of the Transform-and-Recenter operation on A and vice-versa. However, that route seems to lead one to conclude that communication and belief retention are highly intellectual inferential processes, whereas intuition has it that they are just the opposite.
All in all, the issue of de se thought is by now a firmly established area of philosophical research and this volume points the way future discussions should take. We recommend it to any reader who is interested in the latest discussions in the philosophy of language and their ramifications into the philosophy of mind and epistemology.
References
Castañeda, Hector-Neri ‘He’: A study in the logic of self-consciousness. Ratio 8 (December):130-157, 1966. [ Links ]
Perry, J. The problem of the essential indexical. Noûs 13 (December):3-21, 1979. [ Links ]
Lewis, D. Attitudes de dicto and de se. Philosophical Review 88 (4):513-543, 1979. [ Links ]
Prior, A. N. Thank Goodness That’s over. Philosophy 34 (128):12 – 17, 1959. [ Links ]
Frege, G. The thought: A logical inquiry. Mind 65 (259):289-311, 1956. [ Links ]
Cappelen, H. & Dever, J. The Inessential Indexical: On the Philosophical Insignificance of Perspective and the First Person. Oxford University Press, 2013. [ Links ]
Magidor, O. The Myth of the De Se. Philosophical Perspectives 29 (1):249-283, 2015. [ Links ]
Notas
1(Castañeda, 1966), (Perry, 1979) and (Lewis, 1979) are usually referred as the first authors to address the issue of de se thought. However, the origins of the argument in favor of essentially de se thoughts can be traced to even earlier works, such as (Prior, 1959) and (Frege, 1956).
2For some recent de se eliminativists, see (Cappelen and Dever, 2013) and (Magidor, 2015).
3García-Carpintero, p. 188 ff. 21; Recanati, p. 144 ff. 5; Weber, p. 249 ff. 5.
4lt seems that Kindermann could very well extend his argument to Fregean theories, although he does not go in that direction.
Matheus Valente – Universitat de Barcelona – Department of Logic, History and Philosophy of Science, Carrer de Montalegre 6 Barcelona 08001, Spain, [email protected]
Realizing Reason: A Narrative of Truth and Knowing – MACBETH (M)
MACBETH, Danielle. Realizing Reason: A Narrative of Truth and Knowing. Oxford: Oxford University Press, 2014. 494 p. Resenha de: VALENTE, Matheus; DAL MAGRO, Tamires. Manuscrito, Campinas, v.39 n.3 July/Sept. 2016.
Danielle Macbeth’s Realizing Reason is a tour de force about the history of mathematical knowledge from ancient Euclidean geometry to the late 19th century and early 20th century developments on mathematical logic. It is an ambitious work dealing with a vast array of subjects and philosophical themes while still being able to consistently display a high standard of erudition and originality in areas as diverse as the Philosophy of Mathematics, Language, Science and Mind.
The narrative of the book is complex and multifaceted, but its main thread is two-fold. On one hand, Macbeth aims to develop a novel account of “our being in the world” which gives room for the existence of normative facts in a world which is fully explained by mechanistic causal laws – a profound philosophical dilemma that stands at the center of many authors’ works such as Kant, and, more recently, Macbeth’s former Pittsburgh colleague, John (McDowell, 1994). On the other hand, Macbeth argues for a reparation on the perspective with which philosophers should see the practice of mathematics and the mode through which it attains knowledge. The author’s objective is primarily to show how the practice of mathematics, in each of its historical stages from the Greeks to the present, by means of its characteristic linguistic notations, enabled thinkers to literally amplify their knowledge, as opposed to merely making explicit what was already implicit in the information one had begun with. Furthermore, Macbeth aims to prove that this much is true even of mathematics as it is currently conceived, i.e. “the practice of reasoning deductively from concepts” (p. 5). One of the author’s main challenges is to show how there can be such a thing as an “ampliative deduction”, and in order to achieve this feat, Macbeth must break through Kant’s conceptual distinctions to open the way for the idea that the knowledge attained by some deductions, which is, per definition, analytic, can, at the same time, be synthetic.
Both issues dealt with in the book – the apparent incompatibility of reasons in a world of causes and the notion of ampliative mathematical knowledge – are foundational questions in Philosophy and each can be traced to the early beginnings of philosophical practice itself. It is noteworthy that Macbeth sets out to tackle both at the same time while also showing how the resolution of one question is tied to the resolution of the other (and vice-versa).
The book is divided into three main sections, each composed by three chapters, which chronologically tell the story of reason’s development and unfolding from the Ancient Greek’s mathematical practice to the present. The first section is entitled Perception, alluding to Macbeth’s claim that in the early stages of our intellectual development we have our “primary mode of intentional directedness in perception” (p. 17). This corresponds to a time before the Cartesian turn in the sixteenth century, where “pure intellection”, as opposed to the perception of an object, “becomes the paradigmatic mode of intentional directedness and the model even for perception” (p. 18). This intellectual revolution, which led us from bare perception to pure intellection, is the main theme weaving together the three first chapters.
In Chapter 1, Macbeth presents a story detailing how perceptually aware beings, like ourselves, have managed to progress from our ancestors’ rudimentary capacities of imitation and of synthesizing procedural knowledge to sophisticated self-consciousness and rationality. Crucial to Macbeth’s story is a profound anti-Cartesian stance, according to which we should not make a division between the merely physically describable stuff that is “outside” and the normatively significant, meaningful experiences that are “inside” (p. 20). In explicit opposition to Robert (Brandom, 1994), Macbeth suggests jettisoning altogether the idea that a world described by means of causes stands in contrast to a world described by means of reasons, as if these concepts were not applicable to things of the same nature. Just as nature acquires biological significance as animals evolve in their environments, e.g. a bunch of leaves becomes food, so does nature become socially and culturally significant as intelligent beings begin cooperating, sharing goals and engaging in practices and games among themselves. The last step in that progression is the transformation of social beings into “properly rational beings capable of distinguishing in principle between how things seem and how things are” (p. 56); that is, the acquisition of the capacity to step back from our natural inclinations and to realize that “anything we think can be called into question, and improved upon” (p. 49). This final stage of intellectual development, Macbeth claims, depends fundamentally on the coming into being of a natural language, which is, albeit contingent and historical, not an obstacle to objectivity, but constitutive of our access to it.
Notwithstanding their importance, natural languages are intrinsically grounded on our perceptual means of access to the world, and, for that reason, do not reach far enough so as to provide us with knowledge of all there is to be known about in the world. In chapter 2, Macbeth delves deeply into Ancient Greek mathematics – exemplified by Euclidean diagrammatical practice, a methodology that would be the unchallenged orthodoxy in Western mathematical thought for centuries until the Renaissance – in order to make clear how the unfolding of reason takes us ever more far from our immediate empirical reality. Macbeth’s central claim in this chapter is that, in Euclidean diagrammatical practice, we do not reason on diagrams, but in them; in other words, Macbeth claims that an Euclidean diagram does not merely describe a certain course of mathematical reasoning (as, for example, we could describe a mathematical demonstration on natural language), it “formulates the contents of concepts” in a mathematically tractable way and, for that reason, constitute – as opposed to merely picturing or describing – the reasoning itself. As Macbeth fleshes out that important distinction, it becomes ever clearer how demonstrations in Euclidean geometry managed to amplify our knowledge, often giving rise to discoveries that were not even implicit in what the demonstration had begun with. Differently from an Euler or Venn diagram (or any other types of “picture proofs”), in an Euclidean diagram “what is displayed are the contents of concepts the parts of which can be recombined with parts of other concepts”. So, for example, a certain mark in a diagram may be seen as either the side of a triangle or the radius of a circle, depending on the perspective that the reasoner impinges on the drawing. The possibility of this “gestalt-shift” (absent in, e.g. Euler and Venn diagrams) is what explains how figures often pop-up in an Euclidean proof – such as when an equilateral triangle appears as if from nowhere in the proof I.1 of the Elements – and thus, how “something new can emerge that was not there even implicitly”.
Chapter 3 leads us to the radical departure from Ancient thought that happens during the Renaissance with the rise of Modern philosophy, physics and mathematics. Macbeth is particularly concerned with Descartes’ influence in the emergence of a new mathematical practice by means of the introduction of the language of elementary algebra. The algebraic method adds a new degree of abstraction to the activity of reasoning, Macbeth argues, since its intentionality is not object-oriented, but directed to the merely potential relations which arbitrary objects may instantiate (p. 132). For example, one begins to interpret geometrical objects in a computationally tractable way, as the arithmetical relationship of some lengths (e.g. a square is some quantity multiplied by itself). By abstracting away from objects, and, thus, from any subject matter in particular, Descartes’ language allows “pure intellection to become (at least in intention) an actuality” (p. 149). Similarly to the language of Euclidean geometry, Descartes’ algebraic method is not to be conceived as merely a tool through which a course of reasoning can be described or pictured; instead, these symbolic languages present content in a mathematically tractable way, and, because of that, are the matter by means of which reasoning itself is constituted, or, to use Macbeth’s terminology, reasoning comes into existence in those symbolic languages, as opposed to being merely described on them.
The next triad of chapters is entitled “Understanding”, referencing the fact that Kant’s legacy to Philosophy entails that “pure reason is not and cannot be a power of knowing as Descartes had thought. Not reason but only understanding is a power of judgement, of knowing” (p. 151). This is precisely what chapter 4 is concerned about, more particularly, Kant’s Copernican revolution, by means of which our epistemic access to reality is turned upside-down, requiring “the philosopher […] to focus not unthinkingly on the object of knowing but self-consciously on the power of knowing, on what reason requires of objects as objects of knowledge” (p. 199). Macbeth’s argues that, as groundbreaking as Kant was, his thought was still pretty much restrained by the scientific, and, most importantly, the mathematical practice of his day, which, absent the revolution that would come in the nineteenth-century, could not ground a proper account of mathematical truth and knowledge – that is, an account of mathematical truth and knowledge answerable to things as they are in themselves, as opposed to things as they merely appear to us.
Chapters 5 and 6 present the new form that mathematics has come to be clothed in by means of the collective effort of intellectuals throughout the nineteenth-century. By means of the work of mathematicians such as Bolzano, Galois and Riemann, Macbeth tells us the story of how mathematics, after twenty-five centuries of development, finally becomes a self-standing discipline, “the work of pure reason wholly unfettered by the contingencies of our form of sensibility” (p. 244). However, not all is well with that sudden reshaping of mathematical practice, since, if mathematics answers to nothing outside of its own activity, as it came to be seen, it starts to look as if mathematics is nothing more than a linguistic game, completely disconnected of any struggle for objectivity.
Indeed, for much of the twentieth-century, Macbeth will go on to argue, a cluster of theses based on (i) the distinction of logical form and semantical content, (ii) a truth-theoretical account of meaning and (iii) a primacy of mathematical logic as the ruler of all formal disciplines will go on to become the orthodoxy in the understanding of mathematics and of its practice. This is, according to Macbeth, a very unfortunate event, since it seems force on us a picture of logic and mathematics as being merely formal disciplines, and, for that reason, completely deprived of intentional properties. Even worse, and this is one of the central points of the book, this is the picture that intellectuals born during the twentieth-century (even the best of them), have accepted without subjecting it to scrutiny, i.e. a picture of reasoning as being purely mechanistic, “nothing more than the rule-governed manipulation of signs with no regard for meaning” (p. 293).
In the last group of three chapters, aptly entitled “Reason”, Macbeth purports to analyze the philosophical problems that are engendered by the last great revolution in mathematics, i.e. when it came to be seen as “a practice of deductive reasoning on the basis of defined concepts” in nineteenth-century Germany. Most pressing to the author’s concerns is showing that this new conception of the mathematical practice is not purely formal in the sense that it came to be seen by philosophers, but, on the contrary, that it is intrinsically meaningful and often enables us to attain knowledge in the strongest sense of that concept, that is, objective knowledge about things in themselves.
In chapter 7, Macbeth takes the reader to a confrontation, for the first time, with Gottlob Frege’s Begriffsschrift, a mathematical notation that “was explicitly designed as a notation within which to reason deductively from concepts in mathematics”. This long chapter goes at great lengths to explain Frege’s concept-script because, as Macbeth defends, one must understand the notation in order to be able to see the mode of reasoning embodied within it. The pinnacle of the chapter, however, is Frege’s proof of theorem 133 in Part III of the Begriffsschrift, which Macbeth presents as being a real example of a deduction that establishes a real extension of one’s knowledge. The particularity of that proof is the book’s central concern until its very end, namely, the fact that it joins content from two definitions, as opposed to merely joining content from two axioms. That operation of bridging the content from two previously unconnected definitions is precisely what enables that mathematical practice to amplify one’s knowledge. Just as figures often pop up in a Euclidean diagram, “as if from nowhere”, some deductive proofs link concepts that were independently introduced and which, absent that proof, would display no immediate connection among themselves.
That much gets clearer throughout chapter 8, where Macbeth argues that definitions, although they are, by nature, stipulative, are not epistemically vacuous, since they serve to articulate the inferential content of particular concepts, and that is something one might – objectively – succeed in doing correctly or not. Definitions, however, do not amplify one’s knowledge by themselves; it is only in the context of a proof that they are able to forge new links within one’s conceptual repertoire:
proofs without definitions are empty, merely the aimless manipulation of signs according to rules; and definitions without proofs are, if not blind, then dumb. Only a proof can actualize the potential of definitions to speak to one another, to pool their resources so as to realize something new. (p. 387)
The conception of reasoning that we reach by the end of the book is, contrary to the Early Modern simulacrum that we have unreflectively inherited, is neither reductive nor mechanistic. It does not purport to reduce the content of concepts to primitive notions, instead, those contents are displayed in a mathematically tractable way. It is also not mechanistic, Macbeth claims, since the knowledge attained by a deductive proof may be, at the same time, both analytic and synthetic – a fact that makes Kant’s dichotomies stand in need of a radical revision.
The book’s narrative comes full-circle by the end of chapter 8 and throughout chapter 9, where Macbeth studies the case of physics, about which she draws a parallel between the nineteenth-century revolutions in mathematics and the twentieth-century revolutions in theoretical physics. The underlying theme is that mathematics and physics have both recently undergone profound revolutions, while philosophy “has, until now, remained merely Kantian” (p. 453). The final blow on the Cartesian view that we have inherited from the early moderns involves disentangling the Sinn/Bedeutung distinction from that of concept and object (a disentanglement that was out of reach for Kant). Only by clarifying those distinctions, we can understand “how a radically mind-independent reality and an unconditioned spontaneity are not only compatible but in the end made for each other” (p. 451).
Realizing Reason suffers from a flaw that is an almost inevitable consequence of its virtues. Macbeth’s overambition, i.e. her attempt to leave no stone unturned, leads to her book having a certain bric-à-brac quality, since the thread that unites her narrative throughout highly distinct subject matters is usually, but not always, evident. Regardless of that, this book presents innovative theses in a multitude of areas, of special interest being its analysis of Frege’s work, which sees his accomplishments from a whole new perspective and as giving rise to a heterodox conception of ampliative deductive knowledge. All in all, Realizing Reason is a recommended read for anyone with interests in the broad set of areas encompassing the philosophy of mathematics, mathematical practice, history of mathematics and logic, and who is interested in seeing how the issues on those areas communicate with issues in the philosophy of mind, language and the history of philosophy.
References
BRANDOM, R. B. Making It Explicit: Reasoning, Representing, and Discursive Commitment. Harvard University Press. Link no philpapers: http://philpapers.org/rec/BRAMIE, 1994. [ Links ]
MCDOWELL, J. Mind and World. Cambridge: Harvard University Press. Link no philpapers: http://philpapers.org/rec/MCDMAW, 1994. [ Links ]
Matheus Valente – 1Universidade Estadual de Campinas 57 Monroe St, Campinas 13083-872, Brazil, [email protected]
Tamires Dal Magro – Universidade Estadual de Campinas Rua Cora Coralina, 100, Campinas 13083-872, Brazil, [email protected]