Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

In this issue, Pila (2009) has criticised the recommendations made by requirements engineers involved in the design of a grid technology for the support of distributed readings of mammograms made by Jirotka et al. (2005). The disagreement between them turns on the notion of “biographical familiarity” and whether it can be a sound basis for trust for the performances of professionals such as radiologists. In the first two sections, this paper gives an interpretation of the position of each side in (...) this disagreement and their recommendation for the design of technology for distributed reading, and in the third the underlying reasons for this disagreement are discussed. It is argued that Pila, in attempting to make room for mistrust as well as trust, brings to the fore the question of having and reflecting upon reasons for trust or mistrust. Pila holds that biographical familiarity is not a sound reason for trust/mistrust, as it seems to obliterate the possibility of mistrust. In response to her proposal, an analysis is proposed of the forms of trust involved in biographical familiarity. In particular, implicit trust is focused upon—as a form of trust in advance of reasons, and as a form of trust contained (in the logical sense) within other reasons. It is proposed that implicit trust has an important role in establishing an intersubjectively shared world in which what counts as a reason for the acceptability of performances such as readings of X-rays is established. Implicit trust, therefore, is necessary for professionals to enter into a “space of reasons”. To insist upon judgements made in the absence of the form of implicit trust at play in biographical familiarity is to demand that radiologists (and other relevantly similar professionals) make judgements regarding whether to trust or mistrust on the basis of reasons capable of being reflected upon, but at the same time leave them without reasons upon which to reflect. (shrink)

This paper defends Hegel’s positive contribution in the Subjective Logic and argues that it can be understood as presenting a compelling account of the space of reasons as a form of second nature. Taking Hegel’s praise of Kant’s conception of internal purposiveness and its connection to what he calls the Idea as a point of departure, I argue that Hegel’s theory of the Idea that concludes theLogicmust be understood in direct reference to Kant’s argument in the thirdCritiquethat purposiveness (...) defines the space of judgement’s power. I take up two arguments that help to understand Hegel’s appropriation and transformation of Kant’s purposiveness thesis: first, Hegel’s contention that internal purposiveness must have primacy over external purposiveness when considered in relation to judgement; and second, Hegel’s presentation of a logical concept of life as the immediate form of the Idea. (shrink)

Pila (2009) has criticised the recommendations made by requirements engineers involved in the design of a grid technology for the support of distributed readings of mammograms made by Jirotka et al. (2005). The disagreement between them turns on the notion of “biographical familiarity” and whether it can be a sound basis for trust for the performances of professionals such as radiologists. In the first two sections, this paper gives an interpretation of the position of each side in this disagreement and (...) their recommendation for the design of technology for distributed reading, and in the third the underlying reasons for this is agreement are discussed. It is argued that Pila, in attempting to make room for mistrust as well as trust, brings to the fore the question of having and reflecting upon reasons for trust or mistrust. Pila holds that biographical familiarity is not a sound reason for trust/mistrust, as it seems to obliterate the possibility of mistrust. In response to her proposal, an analysis is proposed of the forms of trust involved in biographical familiarity. In particular, implicit trust is focused upon — as a form of trust in advance of reasons, and as a form of trust contained (in the logical sense) within other reasons. It is proposed that implicit trust has an important role in establishing an intersubjectively shared world in which what counts as a reason for the acceptability of performances such as readings of X-rays is established. Implicit trust, therefore, is necessary for professionals to enter into a “space of reasons”. To insist upon judgements made in the absence of the form of implicit trust at play in biographical familiarity is to demand that radiologists (and other relevantly similar professionals) make judgements regarding whether to trust or mistrust on the basis of reasons capable of being reflected upon, but at the same time leave them without reasons upon which to reflect. (shrink)

The paper investigates the `logical space of reasons' as a social space in which rational agents operate and persons in an important sense come to be. Building from an investigation of argumentative agents in Aristotle's Rhetoric, I discuss both interior and exterior criteria for personhood and propose that the latter shows how argumentation, as a principal activity of the space of reasons, results in the particular kinds of persons we recognize there as rational agents. (...) The overall analysis is indebted to Robert Brandom's centralizing of the practice of giving and receiving reasons and the suggestive ways this can be applied to the realm of argumentation. (shrink)

This quoted passage makes a negative claim – a claim about what we are not doing when we characterize an episode or state as that of knowing – and it also makes a positive claim – a claim about what we are doing when we characterize an episode or state as that of knowing. Although McDowell has not endorsed the negative claim, he has repeatedly and explicitly endorsed the positive claim, i.e., that “in characterizing an episode or a state as (...) that of knowing… we are placing it in the logical space of reasons, of justifying and being able to justify what one says.” This is what I will henceforth call “the positive Sellarsian claim”. (shrink)

Wilfrid Sellars employs the metaphor of the space of reasons to express a certain conception of knowledge: “in characterising an episode or state as that of knowing … one is placing it in the logical space of reasons, of justifying and being able to justify what one says”.1 A growing number of philosophers employ the same metaphor to express a conception of at least some (other) mental states: in characterising a state as that of belief, (...) or intention, one is placing it in the same logical space.2 The burden of Alan Millar’s characteristically careful and thought-provoking book is to tell us what this conception amounts to, and to argue for its truth. Its central claim is that the concepts of belief and intention, and what they are concepts of, are (in a sense to be explained) normative. Chapter four – “the heart of the book”, in Millar’s view3 – is devoted to explaining, and defending this claim. (shrink)

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘_p_ is a reason for _q_’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most (...) extant accounts of conditionals. (shrink)

It is no secret that Hegel, along with Vico, whom he never read, and Rousseau, whom he read with enthusiasm, regarded poetic meaning as historically prior to prosaic meaning - the figurative preceded the literal, the tropological antedated the logical per se. Indeed, Hegel went so far, in his Aesthetic, as to qualify poetry as “Man’s original grasp of truth”. Since, as we know, for Hegel the true is the whole, it would seem that this original grasp of the (...) truth would have to be accounted for in any speculative account of truth. (shrink)

Robert Brandom's normative-pragmatic theory is intended to represent the minimal set of practical abilities whose exhibition qualifies creatures as speaking a language. His model of a minimally discursive practice (MDP) is one in which participants, devoid of logical vocabulary, are only capable of making assertions and drawing inferences. This dissertation argues that Brandom's purely assertional practices are not MDPs and that speech acts of asking questions (queries) must be included in any practice that counts as an MDP. I propose (...) several novel alternations to Brandom's deontic scorekeeping model of discourse, which I then utilize to generate a normative-pragmatic analysis of inquisitive practices. This analysis supports the claim that agents who can assert need to be able to ask questions and vice versa. The upshot is that intentionality belongs to those who can ask and answer questions. (shrink)

State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn’s aboutness interpretation of fde, to the space of open sets of a spectral space. We show that these information structures induce (...) so-called hype models which were recently developed by Leitgeb. Conversely, we prove a representation theorem: roughly, hype models can be represented as induced by an information structure. Thus, the well-behaved logic hype is a sound and complete logic for reasoning about information in state spaces. As application of this framework, we investigate information fusion. We motivate two kinds of fusion. We define a groundedness and a separation property that allow a hype model to be closed under the two kinds of fusion. This involves a Dedekind–MacNeille completion and a fiber-space like construction. The proof-techniques come from pointless topology and universal algebra. (shrink)

It is not difficult to make sense of the idea that beliefs may derive their justification from other beliefs. Difficulties surface when, as in certain epistemological theories, one appeals to sensory experiences to give an account of the structure of justification. This gives rise to the so-called problem of ‘nondoxastic justification’, namely, the problem of seeing how sensory experiences can confer justification on the beliefs they give rise to. In this paper, I begin by criticizing a number of theories that (...) are currently on offer. Finding them all wanting, I shall then offer a diagnosis of why they fail while gesturing towards a promising way of resolving the dispute. It will be argued that what makes the problem of nondoxastic justification a hard one is the difficulty of striking the right balance between a notion of normative justification that is content-sensitive and truth conducive and the possibility of error while acknowledging the fact that our experiences can justify our beliefs in cases we are hallucinating. (shrink)

I try to lay bare some of the conceptual space in which one may be a Social Trinitarian. I organize the paper around answers to five questions. These are: (1) How do the three Persons of the Trinity relate to the Godhead? (2) How many divine beings or gods are there? (3) How many distinct centers of consciousness are there in the Godhead? (4) How many omnicompetent beings are there? (5) How are the Persons of the Trinity individuated? I (...) try to make clear costs and benefits of various answers to these questions. (shrink)

Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...) two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts. (shrink)

We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results on topologic relate (...) early work of McKinsey on topological interpretations of S4 with recent work of Georgatos on topologic. Some of the results of this paper were presented at the 1992 conference on Theoretical Aspects of Reasoning about Knowledge. (shrink)

In Logic, Watts address proper thinking under the four basic functions of the human mind: perception, judgment, reasoning, and disposition. In part one, Watts addresses human perception, the cultivation of ideas, and how we associate them with words. In part two, Watts treats human judgment and its ability to construct various kinds of propositions, while giving guidance for avoiding the formation of bad judgments. Part three covers our ability to reason, giving instruction on the use of syllogisms for constructing a (...) good argument. Part four discusses the mind's disposition as a method of arranging our thoughts for better understanding and memory. (shrink)

As Friedman has argued, Kant's argument for the ideality of space turns on the nondeductive character of geometrical reasoning in Euclid's system. Since geometry can be axiomatized, this argument fails. But ("pace" Russell) Leibniz's argument based on the unreality of constitutive relations is not thereby answered as well. I argue that what is needed in response to Leibniz is a properly post-Kantian conception of concepts as inferentially articulated. This conception, I suggest, is based on the same fundamental insight that (...) underlies the axiomatization of geometry. (shrink)

In his magnum opus, The Logic of Scientific Discovery (first published in German in 1934, English translation, 1959), Karl Popper make two fundamental philosophical moves. First, he relocates the center of gravity of the philosophical treatment of science around what he calls the problem of demarcation. This is the problem of distinguishing between science, on the one hand, and everything else on the other. (By contrast, his contemporaries of the Vienna Circle, whose positivism would prove the most influential brand of (...) empiricism of the day, located the center of gravity around the problem of linguistic meaning, and use a criterion according to which a statement is meaningful to the extent that one can identify verification conditions for it.) Popper excludes from science such things as logic, metaphysics, Freudian psychoanalysis, and Marx’s theory of history. Second, Popper propounds the doctrine of falsification, which handles the problem of demarcation, as well as answers David Hume’s shattering attack on science as the premier form of knowledge centuries before. The arguments he mounts for falsification would function also as an attack on any account of the scientific enterprise that, like positivism, adheres to the idea that science progresses logically from instances (given in observation or experience) to the high-order generalizations characteristic of mature scientific theory. In this small space I shall undertake neither to illuminate the nuances of Popper’s position, nor to trace the (numerous) lines of criticism that have accumulated against it some seventy years later. I shall busy myself instead with tracing a trajectory of thought on the subject of scientific reasoning and its relation to individual decision-making, reflecting on Popper’s contribution and on how his legacy might be further enlarged. (shrink)

Francis Fukuyama postulated that there are two powerful forces at work in human history. One, he calls, ‘the logic of modern science’ and the other, ‘the struggle for recognition’. I agree with Fukuyama that human developmental progression is propelled by these twin principles. It is my position that these principles have been the drivers of geopolitics. In this paper, I argue that, in addition, knowledge production is a major factor in geopolitics and that the Euro-American worldview has occupied the place (...) of hegemony by reason of knowledge production. Africa has been denied having any form of epistemic tradition by the Euro-American world to sustain itself in the position of hegemony. In the era of Fourth Industrial Revolution, it will be antithetical for Africa to continue to adopt or consume technologies driven by Eurocentrism without projecting its contribution to the global space. Hence, using a critical hermeneutical approach, I contend that Africa needs to make a unique African contribution in the era of Fourth Industrial Revolution. It is Africa’s unique contribution that will guarantee Africa a place in geopolitics. (shrink)

This book offers new insights into the nature of human rational capacities by engaging inferentialism with empirical research in the cognitive sciences. Inferentialism advocates that humans' unique kind of intelligence is discursive and rooted in competencies to make, assess and justify claims. This approach provides a rich source of valuable insights into the nature of our rational capacities, but it is underdeveloped in important respects. For example, little attempt has been made to assess inferentialism considering relevant scientific research on human (...) communication, cognition or reasoning. By engaging philosophical and scientific approaches in a productive dialogue, this book shows how we can better understand human rational capacities by comparing their respective strengths and weaknesses. In this vein, the author critically revisits and constructively develops central themes from the work of Robert Brandom and other language rationalists: the nature of the assertoric practice and its connection to reasoned discourse, the linguistic constitution of the shared space of reasons, the social nature and function of reasoning, the intersubjective roots of social-normative practices and the nature of objective thought. Practices of Reason will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language and philosophy of logic. (shrink)

I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry based on certain algebraic objects, which regiments a mode of reasoning heuristically used by geometricists and physicists. I argue that SIG has the following utilities. It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. It generalizes a standard implementation of spacetime algebraicism called Einstein algebras. It solves (...) the long-standing problem of interpreting smooth infinitesimal analysis realistically, an alternative foundation of spacetime theories to real analysis, 277–392, 1980). SIA is formulated in intuitionistic logic and is thought to have no classical reformulations. Against this, I argue that SIG is such a reformulation. But SIG has an unorthodox mereology, in which the principle of supplementation fails. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this (...) contention and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)

According to the leading commentators and the author himself, Edmund Husserl's Formal and transcendental Logic is the most important work on phenomenological logic ever written. Nonetheless, it has, in general, gained far less attention than theLogical Investigations and the Ideas on a Pure Phenomenology and Phenomenological Philosophy. In particular, the argument of § 1 of the Logic, namely, that it is fruitful to start with the meanings of the expression “logos” in order to develop a genuinely transcendental logic, has received (...) virtually no consideration. This paper takes a step towards filling this empty space by analyzing and criticizing the argument of § 1 as a problem to which (a) solution(s) must be found: First, it offers an introduction to the problem per se, which is one of the relationship between speech and reason; second, it tries to bring the given senses of “logos” to a higher grade of conceptual clarity and distinctness than that in the text; third, it attempts to decide whether and how far these senses of the word can be documented according to principles of Classical philology; fourth, it endeavors to determine exactly the relationship between the meanings of “logos” in § 1 and the senses of “logic” in §§ 1–107; finally, it strives to show that, with respect to the account of the relationship between speech and reason provided by Husserl in the Logic, there is, at best, a conflict and, at worst, a contradiction between the strategy outlined in § 1 and the tactics adopted in § 2ff. Throughout, the paper reads Husserl's “descriptions” as ‘arguments’ for his positions, thereby avoiding any of the obscurity sometimes infecting work in “Continental philosophy”. (shrink)

How do you tell what’s right from what’s wrong? Can you always? What’s the difference between deduction, induction, and abduction? What are the best techniques for making an argument logically sound? In this fascinating little book, the smallest on its subject ever produced, philosopher Earl Fontainelle explores the ancient art of discursive Logic and demonstrates some of the techniques that have long been used to triumph over the debates and deceptions that assail us every day. Filled with helpful examples of (...) good and bad reasoning, Logic is an invaluable introduction to a defining human characteristic. (shrink)

This paper shows that the non-Boolean logic of quantum measurements is more naturally represented by a relatively new 4-operation system of Boolean fractions—conditional events—than by the standard representation using Hilbert Space. After the requirements of quantum mechanics and the properties of conditional event algebra are introduced, the quantum concepts of orthogonality, completeness, simultaneous verifiability, logical operations, and deductions are expressed in terms of conditional events thereby demonstrating the adequacy and efficacy of this formulation. Since conditional event algebra is (...) nearly Boolean and consists merely of ordered pairs of standard events or propositions, quantum events and the so-called “superpositions” of states need not be mysterious, and are here fully explicated. Conditional event algebra nicely explains these non-standard “superpositions” of quantum states as conjunctions or disjunctions of conditional events, Boolean fractions, but does not address the so-called “entanglement phenomena” of quantum mechanics, which remain physically mysterious. Nevertheless, separating the latter phenomena from superposition issues adds clarity to the interpretation of quantum entanglement, the phenomenon of influence propagated at faster than light speeds. With such treacherous possibilities present in all quantum situations, an observer has every reason to be completely explicit about the environmental–instrumental configuration, the conditions present when attempting quantum measurements. Conditional event algebra allows such explication without the physical and algebraic remoteness of Hilbert space. (shrink)

Osobliwość takich doznań, jak ból, głód i pragnienie. Reliabilizm w drugiej części szóstej Medytacji Kartezjusza Artykuł omawia epistemiczny status cielesnych doznań takich, jak ból, głód i pragnienia, o których mowa w drugiej części szóstej Medytacji Kartezjusza. Argumentuję, że ów fragment stanowi integralny komponent epistemologicznego programu, który można znaleźć w Medytacjach. Na ogół widzi się Kartezjusza jako zwolennika infallibilizmu, internalizmu oraz fundacjonalizmu. Tymczasem w odniesieniu do wiedzy i przekonań opartych na doznaniach cielesnych przyjmuje on fallibilizm, eksternalizm i reliabilizm. Na rzecz tego (...) wniosku przemawia z jednej strony, analiza tego, czego naucza nas – według Kartezjusza – natura przez wrażenia bólu, głodu i pragnienia, z drugiej strony jego analiza błędów, którym podlega nasza natura, przeprowadzona przeze mnie z wykorzystaniem zaproponowanego przez Wilfrida Sellarsa podziału na logiczną przestrzeń rozumu oraz empiryczną przestrzeń przyczyn. (shrink)

In a recent paper, Pila has criticised the recommendations made by requirements engineers involved in the design of a grid technology for the support of distributed readings of mammograms made by Jirotka et al. The disagreement between them turns on the notion of ‘biographical familiarity’ and whether it can be a sound basis for trust for the performances of professionals such as radiologists. In the first two sections, the paper gives an interpretation of the position of each side in this (...) disagreement and their recommendation for the design of technology for distributed reading, and in the third the underlying reasons for this disagreement are discussed. It is argued that Pila, in attempting to make room for mistrust as well as trust, brings to the fore the question of having and reflecting upon reasons for trust or mistrust. Pila holds that biographical familiarity is not a sound reason for trust/mistrust, as it seems to obliterate the possibility of mistrust. In response to her proposal, an analysis is proposed of the forms of trust involved in biographical familiarity. In particular, implicit trust is focused upon, as a form of trust in advance of reasons, and as a form of trust contained within other reasons. It is proposed that implicit trust has an important role in establishing an intersubjectively shared world in which what counts as a reason for the acceptability of performances such as readings of x-rays is established. Implicit trust, therefore, is necessary for professionals to enter into a ‘space of reasons’. To insist upon judgements made in the absence of the form of implicit trust at play in biographical familiarity is to demand that radiologists make judgements regarding whether to trust or mistrust on the basis of reasons capable of being reflected upon, but at the same time to leave them without reasons upon which to reflect. (shrink)

In this paper, I make explicit some implicit commitments to realism and conceptualism in recent work in social epistemology exemplified by Miranda Fricker and Charles Mills. I offer a survey of recent writings at the intersection of social epistemology, feminism, and critical race theory, showing that commitments to realism and conceptualism are at once implied yet undertheorized in the existing literature. I go on to offer an explicit defense of these commitments by drawing from the epistemological framework of John McDowell, (...) demonstrating the relevance of the metaphor of the “space of reasons” for theorizing and criticizing instances of epistemic injustice. I then point out how McDowell’s own view requires expansion and revision in light of Mills' concept of 'epistemologies of ignorance'. I conclude that, when their strengths are used to make up for each others' weaknesses, Mills and McDowell’s positions mutually reinforce one another, producing a powerful model for theorizing instances of systematic ignorance and false belief. (shrink)

This paper outlines an Husserlian, phenomenological account of the first stages of the acquisition of empirical knowledge in light of some aspects of Wilfrid Sellars’ critique of the myth of the given. The account offered accords with Sellars’ in the view that epistemic status is attributed to empirical episodes holistically and within a broader normative context, but disagrees that such holism and normativity are accomplished only within the linguistic and conceptual confines of the space of reasons, and rejects (...) the limitation of the relevant normativity to the cognitive domain. Attention to the phenomenological notion of motivations in our mapping of the structure and acquisition of empirical knowledge reveals a form of weak categoriality given in experience, one outside exclusive mediation by language and concepts but also not merely causal. Section 1 outlines some basic aspects of Sellars’ account of empirical knowledge in Empiricism and the Philosophy of Mind, including a regress objection that arises due to his claim that empirical knowledge presupposes knowledge of general facts about perception. Section 2 examines Sellars’ later revisiting of the objection, via his critique of Roderick Firth, in “The Lever of Archimedes,” focusing on his analysis of the “Myth of the Categorial Given” and his use of the notion of ur-concepts. Section 3 looks at Sellars’ psychological nominalism and his rejection of the explanatory primacy of experience in light of the strict dichotomy between the space of causes and the space of reasons, and shows how Firth’s account aligns with phenomenology in its advocating for an irreducible and non-inferential role for experience. It also raises an important objection to Sellars’ account concerning the categorial givenness of causality. Section 4 turns to Husserl, arguing that his conception of motivation in the Logical Investigations and Ideas II reveals a third explanatory or logical space “between” that of causes and that of reasons. Section 5 further develops this account with regard to the explanatory role of lived experience. Section 6 revisits the regress objection to Sellars from the phenomenological standpoint developed earlier in the paper, and argues that an Husserlian account of empirical knowledge offers a viable alternative to Sellars’ that overcomes the regress objection and gives proper explanatory weight to the evidence of lived experience vis-à-vis scientific presuppositions about causality. (shrink)

We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form $$\langle H, \mu \rangle $$ that needs not be a probability space. More precisely, though H needs not be a Boolean algebra, the corresponding monotone function (we call it measure) $$\mu : H \longrightarrow [0,1]_{\mathbb {Q}}$$ satisfies the following condition: if $$\alpha $$, $$\beta $$, $$\alpha \wedge \beta (...) $$, $$\alpha \vee \beta \in H$$, then $$\mu (\alpha \vee \beta ) = \mu (\alpha ) + \mu (\beta ) - \mu (\alpha \wedge \beta )$$. Since the range of $$\mu $$ is the set $$[0,1]_{\mathbb {Q}}$$ of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability. (shrink)

And yet, in these very texts Sallis identifies outbreaks of spacing that would disrupt the tranquil space of reason. Rather than closure, he finds an opening of reason to imagination.

Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, (...) medicine, forensics, and law. -/- This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily. -/- The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. (shrink)

This chapter contains sections titled: McDowell on the Space of Reasons Brandom's Inferentialism Ilyenkov on the Ideal Conclusion.

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘p is a reason for q’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most (...) extant accounts of conditionals. (shrink)

Two questions are central to the “rationality debate” in the philosophy of social science. First, should we acknowledge differences in basic norms of epistemic and agential rationality, or in the content of perceptual experience, as the “best explanation” of radical differences in belief and practice? Second, can genuine understanding be achieved between cultures and research traditions that so differ in their beliefs and practices? I survey a number of responses to these questions, and suggest that one of these, “dialogical optimism”, (...) while attractive, is in need of further clarification. Such clarification may be forthcoming if we attend to recent work by John McDowell. McDowell claims that perceptual experience, as our primary mode of epistemic access to the world, must be located within what Sellars termed the “space of reasons” if we are to make sense of our conception of ourselves as thinking creatures. I develop a reading of this claim in terms of a fundamental duality in human perceptual experience, and use this conception of experience to illuminate the dialogical optimist strategy in the rationality debate. (shrink)

This paper aims to show how Kant’s account of theoretical reason can inform the contemporary debate over unity and pluralism of science. Although the unity of science thesis has been severely criticized in recent decades, I argue that pluralism as the sole epistemic principle guiding science is both too strong and too weak a principle. It is too strong because it does not account for the process of theory unification in science. It is too weak because it does not answer (...) the question of how science ought to be done. I then look at a promising ‘perspectival’ (i.e., epistemically situated) approach to the problem Kant presents in the Appendix to the Transcendental Dialectic. I argue that the logical principles of systematicity (homogeneity, specification, continuity) form a ‘perspectival space’ within which scientists can pursue both unity and disunity of cognition. Finally, I suggest that the existing conflict between pluralism and unity ultimately resides in a metaphysical characterization of unity that does not correctly capture its epistemic significance in science. Looking at Kant’s ‘perspectivism’ not only allows us to resolve this apparent antinomy, but also to rethink unity and pluralism as mutually inclusive regulative principles. (shrink)

I defend the view that we should not overintellectualize the mind. Nonhuman animals can occupy islands of practical rationality: they can have contextbound reasons for action even though they lack full conceptual abilities. Holism and the possibility of mistake are required for such reasons to be the agent's reasons, but these requirements can be met in the absence of inferential promiscuity. Empirical work with animals is used to illustrate the possibility that reasons for action could be (...) bound to symbolic or social contexts, and connections are made to simulationist accounts of cognitive skills. (shrink)

We critically examine Bermejo-Luque’s account of the logical dimension of argumentation and its logical or semantic evaluation. Our considerations concern her views on inference claims, validity, logical normativity, warrants, necessity, warrants and the justification of inferences, ontological versus epistemic modal qualifiers, ontological versus epistemic probability, and ontological versus conditional probability.

In reasoning, we draw conclusions from multiple premises. But thinkers can be fragmented. And if there is no single fragment of the agent that thinks all of the premises, then the agent cannot draw any conclusions from them. It follows that reasoning from multiple premises depends on their being thought together. But what is it to think premises together? What is the condition that contrasts with fragmentation? This paper provides an answer to this question that is simple but compelling: to (...) think premises together is to attribute those very thoughts to one and the same self. The ability to reason depends on the ability to attribute the thoughts from which one reasons to oneself. Reasoning—at least the sort of reasoning that we do—requires de se thought. (shrink)

Ordinarily, if you say something like “I see a comet,” you might make a mistake about whether it is a comet that you see, but you could not be right about whether it is a comet but wrong about who is seeing it. There cannot be an “error of identification” in this case. In making a judgement like, “I see a comet,” there are not two steps, finding out who is seeing the thing and finding out what it is that (...) is being seen, so that you could go wrong at either step. The only place to go wrong is in your description of what is being seen. We usually take it that the same point applies to present-tense ascriptions to oneself of psychological states in general. You can get it wrong about which psychological state you are in, but you cannot get it right about the psychological state but wrong about whose psychological state it is. In contrast, in a room full of people, I might hear a noise and conclude, “Bill sneezed,” and in this case I could be wrong either about who it was that sneezed or about whether it was a sneeze, rather than say a death-rattle. (shrink)

In this paper, we use some elements of the philosophical theories of Wilfrid Sellars and Robert Brandom for examining the interactions between humans and machines. In particular, we adopt the concept of the space of reasons for analyzing the status of artificial intelligent agents. One could argue that AIAs, like the widely used recommendation systems, have already entered the space of reasons, since they seem to make knowledge claims that we use as premises for further claims. (...) This, in turn, can lead to a sense of alienation because AIAs do not quite play by the rules of the space of the reason. We, therefore, ask somewhat pointedly whether aliens have entered the space of reasons. A closer look reveals that it is a misconception to consider AIAs as being in the space of reasons. In fact, they should be seen as very sophisticated tools. Since these tools affect our own acting in the space of reasons, special regulations are required for their proper use. (shrink)

Inference and meaning -- Some reflections on language games -- Language as thought and as communication -- Meaning as functional classification : a perspective on the relation of syntax to semantics -- Naming and saying -- Grammar and existence : a preface to ontology -- Abstract entities -- Being and being known -- The lever of Archimedes -- Some reflections on thoughts and things -- Mental events -- Phenomenalism -- The identity approach to the mind-body problem -- Philosophy and the (...) scientific image of man -- "...this I or he or it (the thing) which thinks..." -- Some remarks on Kant's theory of experience -- The role of imagination in Kant's theory of experience. (shrink)

I defend the view that we should not overintellectualize the mind. Nonhuman animals can occupy islands of practical rationality: they can have context‐bound reasons for action even though they lack full conceptual abilities. Holism and the possibility of mistake are required for such reasons to be the agent's reasons, but these requirements can be met in the absence of inferential promiscuity. Empirical work with animals is used to illustrate the possibility that reasons for action could be (...) bound to symbolic or social contexts, and connections are made to simulationist accounts of cognitive skills. (shrink)

This paper explores ‘reasonable doubt’ as an enlightening notion to think of reasoning and decision-making generally, beyond the judicial domain. The paper starts from a decision-theoretic understanding of the notion, whereby it can be defined in terms of degrees of belief and a probabilistic confirmation threshold for action. It then highlights some of the limits of this notion, and proposes a richer analysis of epistemic states and reasoning through the lens of ‘reasonable doubt’, which in turn is likely to supplement (...) the DT framework. The strategy consists in fighting on two fronts: with DT, the paper claims that there is no absolute notion of ‘reasonable doubt’ but, pace DT, it shows that reasonable doubt cannot be accounted for only in terms of degrees of belief and probabilistic threshold. We argue that the lens of reasonable doubt sheds light on aspects of belief dynamics, as well as of the nature of epistemic attitudes, which are often obscured by belief-centred approaches. In particular, when it comes to acknowledging the necessary ignorance and irreducible uncertainty that we face in our everyday-life decisions, studying the various facets of doubt rather than focusing on what can be believed, enables one to do justice to the richness and diversity of the mental states in play. (shrink)