The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present (...) and justify the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

The negative zombie argument concludes that physicalism is false from the premises that p ∧¬q is ideally negatively conceivable and that what is ideally negatively conceivable is possible, where p is the conjunction of the fundamental physical truths and laws and q is a phenomenal truth (Chalmers 2002; 2010). A sentence φ is ideally negatively conceivable iff φ is not ruled out a priori on ideal rational reflection. In this paper, I argue that the negative zombie argument is neither a (...) priori nor conclusive. First, I argue that the premises of the argument are true only if there exists an adequate finite ideal reasoner R that believes ◊(p ∧ ¬q) on the basis of not believing p→q on a priori basis. Roughly, a finite reasoner is a reasoner with cognitive limitations (e.g. finite memory). I argue that R is finite only if R reasons nonmonotonically and only approach ideal reflection at the limit of a reasoning sequence. This would render the argument nonconclusive. Finally, I argue that, for some q, R does not believe ◊(p ∧ ¬q) on the basis of not believing p→q on a priori basis (e.g. for q =‘something is conscious’). This would render the choice of an adequate q dependent on empirical information (and the argument a posteriori). I conclude that the negative zombie argument (and, maybe, all zombie arguments) is neither a priori nor conclusive. (shrink)

Moral particularists argue that because reasons for action are irreducibly context-dependent, the traditional quest in ethics for true and exceptionless moral principles is hopelessly misguided. In making this claim, particularists assume a general framework according to which reasons are the ground floor normative units undergirding all other normative properties and relations. They then argue that there is no cashing out in finite terms either (i) when a given non-normative feature gives rise to a reason for or against action, or (...) (ii) how the reasons that are present in a given context play off each other to determine one’s overall duties. However, the conjunction of these two theses leaves particularists without a coherent notion of a reason for action: posit too much irreducible context-dependence in the behavior of reasons, and the reasons-based framework breaks down. One upshot is that the particularists’ challenge to principle-based approaches to ethics has not, at present, been successfully made out; another upshot is that perhaps the best way to formulate that challenge involves renouncing the reasons-based framework all together. (shrink)

The article explores the idea that according to Spinoza finite thought and substantial thought represent reality in different ways. It challenges “acosmic” readings of Spinoza's metaphysics, put forth by readers like Hegel, according to which only an infinite, undifferentiated substance genuinely exists, and all representations of finite things are illusory. Such representations essentially involve negation with respect to a more general kind. The article shows that several common responses to the charge of acosmism fail. It then argues that (...) we must distinguish the well-founded ideality of representations of finite things from mere illusoriness, insofar as for Spinoza we can have true knowledge of what is known only abstractly. Finite things can be seen as well-founded beings of reason. The article also proposes that within Spinoza's framework it is possible to represent a finite thing without drawing on representations of mind-dependent entities. (shrink)

All reasoners described in the most widespread models of a rational reasoner exhibit logical omniscience, which is impossible for finite reasoners (real reasoners). The most common strategy for dealing with the problem of logical omniscience is to interpret the models using a notion of beliefs different from explicit beliefs. For example, the models could be interpreted as describing the beliefs that the reasoner would hold if the reasoner were able reason indefinitely (stable beliefs). Then the models would describe maximum (...) rationality, which a finite reasoner can only approach in the limit of a reasoning sequence. This strategy has important consequences for epistemology. If a finite reasoner can only approach maximum rationality in the limit of a reasoning sequence, then the efficiency of reasoning is epistemically (and not only pragmatically) relevant. In this paper, I present an argument to this conclusion and discuss its consequences, as, for example, the vindication of the principle 'no rationality through brute-force'. (shrink)

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

Darwin famously held that his use of the term "chance" in evolutionary theory merely "serves to acknowledge plainly our ignorance of the causes of each particular variation". Is this a tenable view today? Or should we revise our thinking about chance in evolution in light of the more advanced, quantitative models of Neo-Darwinian theory, which make substantial use of statistical reasoning and the concept of probability? Is determinism still a viable metaphysical doctrine about biological reality after the quantum revolution (...) in physics, or dowe have to abandon it in favor of an objective indeterminism? In light of such reflections, what is the relevant interpretation of probability in evolutionary theory? Do biologists use the concept of probability because they are finite cognitive agents or because the evolutionary process is fundamentally probabilistic? In this paper, I will show that we do not yet fully understand the nature of chance in evolution. (shrink)

Chains of causes appear when the existence of God is discussed. It is claimed by some that these chains must be finite and terminated by God. But these chains seem endless through our knowledge search. This endlessness for the physical reasons for any world event expresses the greatness and complexity of God’s creation and so the transcendence of God. So, only we can put our hands on physical reasons in an endless forage for knowledge. Yet, the endlessness of the (...) physical causes chains confirms the existence of God, and this is what our paper tries using Zorn’s lemma, an equivalent for one of the most celebrated axioms of mathematics, the Axiom of Choice. (shrink)

In this paper, I examine Wittgenstein’s conception of reason and rationality through the lens of his conception of reasons. Central in this context, I argue, is the image of the chain, which informs not only his methodology in the form of the chain-method, but also his conception of reasons as linking up immediately, like the links of a chain. I first provide a general sketch of what reasons are on Wittgenstein’s view, arguing that giving reasons consists in making thought and (...) action intelligible by delineating reasoning routes; that something is a reason not in virtue of some intrinsic property, but in virtue of its role; and that citing something as a reason characterises it in terms of the rational relations it stands in according to context-dependent norms. I then argue that on Wittgenstein’s view, we misconceive chains of reasons if we think of them on the model of chains of causes. Chains of reasons are necessarily finite, because they are anchored in and held in place by our reason-giving practices, and it is in virtue of their finitude that chains of reasons can guide, justify and explain. I argue that this liberates us from the expectation that one should be able to give reasons for everything, but that it limits the reach of reasons by tying them to particular reasoning-practices that they cannot themselves justify. I end by comparing and reconciling Wittgenstein’s dichotomy between chains of reasons and chains of causes with seemingly competing construals of the dichotomy, and I clarify its relation to the dichotomy between explanation and justification. (shrink)

This paper aims to show the significance of respect in revealing the normative structure of Kant’s ethics to the agent as a finite rational being. I argue that understanding the moral law as a fact of reason is insufficient for fully recognizing its absolute value and the normative consequences it entails. Indeed, the finiteness of the human agent requires the experience of the feeling of respect, which not only has a motivational role but also an epistemic one. I thus (...) start by clarifying the nature of feeling for Kant in a way that highlights its complex structure. Then, I show how respect – as a particular kind of feeling – gives the agent a deeper understanding of her relationship with the moral law, thereby allowing the unveiling of Kant’s normative theory. (shrink)

The article proposes a new solution to the long-standing problem of the universality of essences in Spinoza's ontology. It argues that, according to Spinoza, particular things in nature possess unique essences, but that these essences coexist with more general, mind-dependent species-essences, constructed by finite minds on the basis of similarities that obtain among the properties of formally-real particulars. This account provides the best fit both with the textual evidence and with Spinoza's other metaphysical and epistemological commitments. The article offers (...) new readings of how Spinoza understands not just the nature of essence, but also the nature of being, reason, striving, definitions, and different kinds of knowledge. (shrink)

Genevieve Lloyd’s Spinoza is quite a different thinker from the arch rationalist caricature of some undergraduate philosophy courses devoted to “The Continental Rationalists”. Lloyd’s Spinoza does not see reason as a complete source of knowledge, nor is deductive rational thought productive of the highest grade of knowledge. Instead, that honour goes to a third kind of knowledge—intuitive knowledge (scientia intuitiva), which provides an immediate, non-discursive knowledge of its singular object. To the embarrassment of some hard-nosed philosophers, intellectual intuition has an (...) affective component; it is a form of love, and ultimately given that human beings are finite modes of God/Nature (Deus sive Natura), it is a form of the intellectual love of God (amor Dei intellectualis). Some philosophers do not know what to make of this mysterious aspect of Spinoza’s philosophy, which is nonetheless firmly anchored in a reading of Part V of the Ethics. Nonetheless, this note will insist with Lloyd’s “Reconsidering Spinoza’s Rationalism” that such doctrine is an integral part of Spinoza’s philosophy. Moreover, it will be shown that Spinoza is well aware of the limitations of reason (ratio) in gaining scientific knowledge of the world and requires intuition precisely because of the inability of reason to represent individuals in their full particularity. Imagination too has a role to play in shaping scientific knowledge, although reason performs a vital critical role in disciplining and liberating the human mind from inadequate imaginary ideas. The result is an interpretation of Spinoza’s epistemology as both rationalist and intuitionist. DOI: 10.1080/24740500.2021.1962652. (shrink)

Weak particularism about reasons is the view that the normative valency of some descriptive considerations varies, while others have an invariant normative valency. A defence of this view needs to respond to arguments that a consideration cannot count in favour of any action unless it counts in favour of every action. But it cannot resort to a global holism about reasons, if it claims that there are some examples of invariant valency. This paper argues for weak particularism, and presents a (...) framework for understanding the relationships between practical reasons. A central part of this framework is the idea that there is an important kind of reason-a 'presumptive reason'-which need not be conclusive, but which is neither pro tanto nor prima facie. /// [Richard Holton] Should particularists about ethics claim that moral principles are never true? Or should they rather claim that any finite set of principles will not be sufficient to capture ethics? This paper explores and defends the possibility of embracing the second of these claims whilst rejecting the first, a position termed 'principled particularism'. The main argument that particularists present for their position-the argument that holds that any moral conclusion can be superseded by further considerations-is quite compatible with principled particularism; indeed, it is compatible with the idea that every true moral conclusion can be shown to follow deductively from a finite set of premises. Whilst it is true that these premises must contain implicit ceteris paribus clauses, this does not render the arguments trivial. On the contrary, they can do important work in justifying moral conclusions. Finally the approach is briefly applied to the related field of jurisprudence. (shrink)

This dissertation examines Fichte's critical idealism in an effort to formulate a compelling model of how we can be said to be free, despite our subjection to both rational and nonrational constraints. ;Fichte grounds idealism in a "drive to freedom" that involves two disparate strands of thought: the standpoint of idealism is said to be both the result of an absolutely free adoption of the principle of self-determination and conditioned by reason, to which the finite I is necessarily subject. (...) However, if there is no reason prior to the choice of a first principle, the choice of idealism over dogmatism cannot be motivated, and so is not attributable to a responsible subject. And if there is a prior basis for the election of idealism, the constraints of reason already necessitate the I's attempt to consider itself to be independent and are, therefore, not self-legislated. Fichte's argument strategy thus yields the following question: How can there be an absolute election of the philosophical principle of one's life, when the adoption of such a standpoint is already a manifestation of who one is? Fichte confronts this issue by conceiving of the I as necessarily subject to an original limit and by radically subjectivizing the world in terms of the I's ethical and conceptual demands. ;By locating the tension between these positions, this dissertation reveals how philosophers indebted to Fichte as well as interpreters of the Wissenschaftslehre have mischaracterized Fichte's treatment of rational self-constraint. Fichte's synthesis of freedom and necessity constitutes a model of subjectivity according to which the normatively constrained structure of experience is impossible without my relating that experience to my practical activity, and the ways in which I am able to characterize that experience are answerable to what is practically required of me by that experience. Fichte shows the interdetermination of the givenness of the given and the autonomy of the I by qualifying each in terms of the other. As a description of this interdetermination, Fichte's striving doctrine establishes the tension involved in this mutually constitutive relation as a positive conception of human freedom. (shrink)

As analysis of Kant’s account of virtue in the Lectures on Ethics shows that Kant thinks of virtue as a form of moral self-mastery or self-command that represents a model of self-governance he compares to an autocracy. In light of the fact that the very concept of virtue presupposes struggle and conflict, Kant insists that virtue is distinct from holiness and that any ideal of moral perfection that overlooks the fact that morality is always difficult for us fails to provide (...) an appropriate model of human virtue. No matter how morally good we are or become, virtue remains a disposition to do one’s duty from duty, out of necessitation by practical reason. Yet, even though finite rational beings require a power of self-constraint in accordance with the commands of duty to comply with the law (which we obey reluctantly), the virtuous agent displays a unified soul that is at peace. This picture of virtue uncovered from the Lectures on Ethics thus reveals the way in which Kant’s conception of virtue accords with his foundational commitments in his moral theory, while at the same time representing a more complex theory of moral character and a life lived in accordance with practical reason. (shrink)

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the (...) three categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Leibniz endorses the world apart doctrine, according to which a substance is that which is independent of all other things except God. However, I will argue that in what appears to be a radical departure from the causal version of the world apart doctrine, Du Châtelet—whose metaphysics appears to be Leibnizian from a distance—embraces the causal connectedness of created substances. I further show that Du Châtelet’s rejection of Leibniz’s claim that a substance is causally independent of all other created substances (...) can be traced back to a more fundamental antiLeibnizian commitment on Du Châtelet’s part concerning the in-principle accessibility of natural (i.e., non-divine) sufficient reasons by finite minds and to her commitment to a causal theory of intentionality. (shrink)

Finite agents such as human beings have reasoning and updating processes that are extended in time; consequently, there is always some lag between the point at which we gain new reasons and the point at which our attitudes have fully responded to those reasons. This phenomenon, which I call rational delay, poses a threat to the most common ways of formulating rational requirements on our attitudes, which do not allow rational beings to exhibit such delay. In this paper, (...) I show first how this problem undermines synchronic formulations of rational norms. Then I show how it likewise undermines the most natural diachronic modifications of these norms. Ultimately, I argue that a successful account of rational delay will reject norms that directly govern attitudes or states of mind like belief and intention altogether, in favor of norms that fundamentally concern temporally extended rational processes like deliberation. (shrink)

A number of philosophers have argued that it is hard for finite agents like us to reason and make decisions relying solely on our credences and preferences. They hold that for us to cope with our cognitive limitations, we need binary beliefs as well. For they think that such beliefs, by disposing us to treat certain propositions as true, help us cut down on the number of possibilities we need to consider when we reason. But using Ross and Schroeder (...) as my stalking horse, I argue that such an appeal to binary beliefs does not work. I begin by explaining why there’s supposedly a problem for an account of reasoning that invokes only credences and preferences. I then argue that Ross and Schroeder’s account of belief—as well as other similar accounts—does not help solve the problem. Finally, I consider an alternative approach to solving the problem. This approach, unlike the accounts I criticise, does not hold that having a disposition to treat a proposition as true is necessary for believing it. (shrink)

I show that unlike her rationalist predecessor Leibniz, Du Châtelet is committed to epistemic causal idealism about natural causes. According to this view, it is constitutive of natural causes that they are in principle knowable by us (i.e., finite intelligent beings). Du Châtelet’s causal idealism stems at least in part from the distinctive theoretical role played by the Principle of Sufficient Reason in her system (as presented in her _Institutions de physique_), as well as her argument for the Principle (...) of Sufficient Reason. I show that far from merely explicating Leibniz’s metaphysics, Du Châtelet develops a radical and novel rationalism that is in keeping with her core commitment to science. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability (...) of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of (...) automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation (...) are elaborated, and examples of cyclic and convergent causation are given. Soundness and completeness proofs are sketched. (shrink)

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of (...) automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

One of the central tasks of a theory of argumentation is to supply a theory of appraisal: a set of standards and norms according to which argumentation, and the reasoning involved in it, is properly evaluated. In their most general form, these can be understood as rational norms, where the core idea of rationality is that we rightly respond to reasons by according the credence we attach to our doxastic and conversational commitments with the probative strength of the reasons (...) we have for them. Certain kinds of rational failings are so because they are manifestly illogical – for example, maintaining overtly contradictory commitments, violating deductive closure by refusing to accept the logical consequences of one’s present commitments, or failing to track basing relations by not updating one’s commitments in view of new, defeating information. Yet, according to the internal and empirical critiques, logic and probability theory fail to supply a fit set of norms for human reasoning and argument. Particularly, theories of bounded rationality have put pressure on argumentation theory to lower the normative standards of rationality for reasoners and arguers on the grounds that we are bounded, finite, and fallible agents incapable of meeting idealized standards. This paper explores the idea that argumentation, as a set of practices, together with the procedures and technologies of argumentation theory, is able to extend cognition such that we are better able to meet these idealized logical standards, thereby extending our responsibilities to adhere to idealized rational norms. (shrink)

We analyze some normative relations as instances of a general schema of relations among a finite number of parties; in this schema parties can play various roles grouped into two main conceptual layers, called 'subject position' and 'object position'. Relying on the theoretical apparatus introduced, we develop a new symbolic representation for normative reasoning which constitutes an alternative to approaches available in the literature. Our contribution includes a semantic characterization for a series of logical systems built over the (...) proposed framework. (shrink)

Pascal’s wager uses decision theory to argue that it is rational to attempt to nurture belief in God, based on the expected utility of believing (infinite happiness) compared to not believing (at best, only finite happiness). A belief in an eternal conscious torment in hell (infinite suffering) for non-believers makes the differences in expected utility even more apparent, strengthening the argument. Similar reasoning can also be used to calculate the expected moral value of actions, including procreation. Under theism, (...) if possible future children might suffer eternal conscious torment, the expected moral value of procreation is extremely negative. This implies that theists have a moral obligation not to procreate, which for most theists, entails a moral obligation to be celibate or to undergo sterilisation surgery. (shrink)

Hostile epistemology is the study of how environmental features exploit our cognitive vulnerabilities. I am particularly interested in those vulnerabilities arise from the basic character of our epistemic lives. We are finite beings with limited cognitive resources, perpetually forced to reasoning a rush. I focus on two sources of unavoidable vulnerability. First, we need to use cognitive shortcuts and heuristics to manage our limited time and attention. But hostile forces can always game the gap between the heuristic and (...) the ideal. Second, we need to trust others, and trust makes us vulnerable. In particular, we need to trust experts whose expertise lies beyond our individual ability to vet. So we must rely on various imperfect signals and proxies, like institutional affiliation, to manage our trust. We are forced to use these imperfect and exploitable forms of reasoning, in order to cope with a cognitively overwhelming world. I present the hostile epistemology framework as a counterbalance to vice epistemology, which tends to locate responsibility for bad beliefs in the character of the believer. I draw two conclusions from my analysis. First: suppose we accept that that only communities and institutions can know about the world. This deeply social approach doesn’t solve the problem of expert identification. The individual still faces a problem: given their incomplete understanding, how should the individual pick which group to trust? Second: we might have hoped to get some kind of static picture of the right principles of reasoning — but hostile epistemology presents a different picture. We have to use risky heuristics and shortcuts, which hostile forces can game and exploit. We can respond by shifting to a different set of heuristics, but this simply shifts the location of our vulnerabilities. These new heuristics are also exploitable. There is no end to this, only a constant struggle to adapt. Limited beings in a hostile epistemic environment are locked in an unending epistemic arms race. (shrink)

The nature of the philosophical description of consciousness requires a mode of reflection that is different from ordinary understanding, including most of what transpires in the name of philosophy. Therefore, it will be helpful to review once again the basic development that has been covered thus far in previous articles. The consciousness of Understanding deals with the aspects or the “in-so-far-as” perspective of things. It does not deal with things in their contradictory wholeness. Rational consciousness, however, deals with wholes that (...) are only abstractly divided for the sake of Understanding. It is the task of Reason to determine how to deal with wholes as wholes. Most importantly, is that comprehension of the whole, even when that is attained, puts the comprehending consciousness outside the whole that it is comprehending. This is therefore not the whole as it is in and for itself. The whole must include the consciousness comprehending it as well as everything else, and it must have its own being beyond any finite conception of it, and in fact produce the finite conception of itself. It is perhaps one of the most significant achievements of Hegelian philosophy to be able to reach this goal—Truth in and for itself and not only for consciousness. Another is that Hegel is able to expound a scientific system that deals with a substantial Reality that is essentially Subject, i.e. a Truth that is rationally conscious of itself—God. And finally within his system he is able to deal with all the problems of philosophy in a consistently methodical way that proves to be both necessary and complete. All of this is the product and development of Reason which is the integrating and differentiating substance of Reality that is essentially Subject— viz., the Absolute Reason of God. (shrink)

In this paper we want to focus on Husserl’s critique of Kantian ethics and to develop the following questions. Against the merely empiristic orientation of Hume’s ethics, the Kantian foundation of ethics has an aprioristic character; but does this aprioristic character have to be identified with the origin of ethical principles in the pure subjectivity, and if not, which is its phenomenological signification? The sense of the Copernican revolution is that the structures of the objects are in accordance with the (...) universal structures of the finite subject; a contrario, Husserl refuses this Copernican principle and assumes that every sort of object determines a regulative structure in the subject; is it possible to apply this anticopernican principle to the ethical sphere? As opposed to the Kantian principle of the supremacy of practical reason, we find in Husserl’s thought a supremacy of the theoretical reason; but which is the sense of this inversion? The concept of foundation has in Husserlian phenomenology a cardinal importance: all sorts of truth of superior degree are founded on the inferior level of sensible truth; is it possible to apply this principle of foundation to the ethical sphere, so that ethical consciousness would be founded on feelings? At last the Kantian concept of liberty is not an empirical one, but a cosmological and practical idea; which is the phenomenological sense of liberty? (shrink)

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring (...) our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives. (shrink)

In this paper, we present an intelligent tutoring system developed to help students in learning Computer Theory. The Intelligent tutoring system was built using ITSB authoring tool. The system helps students to learn finite automata, pushdown automata, Turing machines and examines the relationship between these automata and formal languages, deterministic and nondeterministic machines, regular expressions, context free grammars, undecidability, and complexity. During the process the intelligent tutoring system gives assistance and feedback of many types in an intelligent manner according (...) to the behavior of the student. An evaluation of the intelligent tutoring system has revealed reasonably acceptable results in terms of its usability and learning abilities are concerned. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

The concept of practical knowledge is central to G.E.M. Anscombe's argument in Intention, yet its meaning is little understood. There are several reasons for this, including a lack of attention to Anscombe's ancient and medieval sources for the concept, and an emphasis on the more straightforward concept of knowledge "without observation" in the interpretation of Anscombe's position. This paper remedies the situation, first by appealing to the writings of Thomas Aquinas to develop an account of practical knowledge as a distinctive (...) form of thought that "aims at production" of things that lie within an agent's power; and then by showing how this Thomistic understanding of practical cognition seems to have been Anscombe's, too. Having done this, I question whether the thesis that agential knowledge is practical knowledge entails that an agent always has non-observational knowledge of what she is intentionally doing. I answer "Not": Anscombe's claims to the contrary rest on a misleading assimilation of human beings' finite agency to that of an infinite agent like God. (shrink)

Spinoza’s celebrated doctrine of the conatus asserts that “each thing, as far as it can by its own power, strives to persevere in its being” (E3p6). Shortly thereafter Spinoza makes the further claim that the (human) mind strives to increase its power of acting (E3p12). This latter claim is commonly interpreted as asserting that human beings (and their associations) not only strive to persevere in their existence, but also always strive to increase their power. Spinoza’s justification for E3p12 relies (among (...) others) on E3p6. For this reason, it seems reasonable that we strive to increase our power because having more power is likely to help us persevere in our being. The more power we have, the less likely we are to be out-powered by external causes that may conflict with our striving for persevering in our existence. The logic here is quite sound. Insofar as human beings are mere finite modes, i.e., entities whose existence is not guaranteed by their mere essence, and are distinct from other finite modes with whom we interact in various manners, it would seem that our striving for power should be insatiable. No finite degree of power can ever guarantee the continuation of our existence. On one occasion, Spinoza even defines good and evil as “what increases or diminishes, aids or restrains, our power of acting” (E4p8d). Having this sound logic in mind, we should be taken aback by a brief claim Spinoza makes in passing in the seventh chapter of Political Treatise. In this passage, Spinoza seems to assert that the stability of a state – which is one of the chief political virtues for Spinoza – is a function of having just the right degree of power, not less, but also, not more. The passage seems to imply that having too much power might be detrimental to the state. But how can such a view be consistent with Spinoza’s assertion and approval of our constant “will to power” in the Ethics? In the current paper, I will explain the tension between these two strands in Spinoza’s thought, and attempt to reconcile them. I will begin with a close examination of the passage from the seventh chapter of the TP, and its apparent contrast with Spinoza’s claim in the Ethics about our striving to increase our power of acting. I will then turn, in the second part, to consider whether Spinoza’s claims in TP Ch. 7 – a chapter dedicated to the exploration of the nature of non-tyrannical monarchy – are valid only with regard to a monarchic state, or whether we may generalize the claim that having too much power might be harmful to other forms of the state or even other kinds of individuals. In the third and final part I will attempt to solve the tension between Spinoza’s apparently conflicting claims by looking more closely at Spinoza’s understanding of human power, and its political dimensions. (shrink)

Sam Harris (2010) argues that, given our neurology, we can experience well-being, and that seeking to maximize this state lets us distinguish the good from the bad. He takes our ability to compare degrees of well-being as his starting point, but I think that the analysis can be pushed further, since there is a (non-religious) reason why well-being is desirable, namely the finite life of an individual organism. It is because death is a constant possibility that things can be (...) assessed as “for” or “against” one (Champagne 2011a; Smith 2000). Such an account lets us objectively adjudicate moral questions, as Harris desires. However, by anchoring itself in the mortal body as a whole and not just the brain, such an account dampens the claim that neuroscience would have all the answers. Moreover, it pivots on an affirmation of one’s life that can seem mysterious by regular scientific standards. This chapter thus explains why the trade-off is worthwhile. (shrink)

I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of (...) all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals. (shrink)

I examine the extent to which God is inscrutable to human reason in Kant's critical philosophy. I argue that Kant's view here is much more radical than the rationalist commonplace that we cannot grasp how divine perfection is compatible with the existence of (apparent) imperfections. In Kant's considered view, we are absolutely incapable of accurately representing God's nature in any minimally determinate way: when we try to go beyond the empty idea of a mere 'something', we inevitably distort the nature (...) of God in an anthropomorphic fashion. The reason for this radical inscrutability of God is that our discursive intellect with its finite conceptual resources cannot capture the nature of a supremely perfect being. Our only way to form a legitimate, positive notion of God is by means of an analogy with the features that we objectively cognize in finite beings. (shrink)

Both Martin Heidegger and Harry Frankfurt have argued that the fundamental feature of human identity is care. Both contend that caring is bound up with the fact that we are finite beings related to our own impending death, and both argue that caring has a distinctive, circular and non-instantaneous, temporal structure. In this paper, I explore the way Heidegger and Frankfurt each understand the relations among care, death, and time, and I argue for the superiority of Heideggerian version of (...) this nest of claims. Frankfurt claims that we should conceive of the most basic commitments which practically orient a person in the world and define his identity (“volitional necessities”) as naturalistic facts, foundational for and located completely without the normative space of reasons. In support of this he appeals to the supposedly foundational role played in human life by the instinct for self-preservation, what Frankfurt calls the “love of living.” The claim is that in questions of practical identity there is a definite priority of the factual over the normative. Frankfurt’s naturalistic model of volitional necessity is motivated by a misunderstanding of the temporal structure of care, a misunderstanding that helps lead him to an implausible conception of the basic structures of human identity. Heidegger advances an anti-naturalistic conception of caring, one bound up with his way of understanding how human beings relate to their own future. I argue that the existential, temporal, and normative significance that Frankfurt attributes to the naturalized “love of living” is better captured by the Heideggerian claim that human identity is defined by being “for-the-sake-of” certain projects and commitments, a way of being lived out in the way Heidegger calls “being-towards-death.”. (shrink)

This essay aims to provide a self-contained introduction to time in relativistic cosmology that clarifies both how questions about the nature of time should be posed in this setting and the extent to which they have been or can be answered empirically. The first section below recounts the loss of Newtonian absolute time with the advent of special and general relativity, and the partial recovery of absolute time in the form of cosmic time in some cosmological models. Section II considers (...) the beginning and end of time in a broader class of models in which there is not an analog of Newtonian absolute time. As we will see, reasonable physical assumptions imply that the universe is finite to the past, and Section III turns to consideration of the “beginning” itself. We critically review conventional wisdom that a “singularity” reveals flaws in general relativity and briefly assess ways of avoiding the singularity. (shrink)

This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value (...) of sophisticated mathematical structures employed in applied sciences like decision theory. In the last part, I introduce countable additivity into Savage's theory and explore some technical properties in relation to other axioms of the system. (shrink)

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should be replaced (...) by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (shrink)

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical (...) mathematician Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

I discuss the view, increasingly common in physics, that the foundational level of our physical reality is a network of computing machines (so that our universe is ultimately like a cellular automaton). I discuss finitely extended and divided (discrete) space-time and discrete causality. I examine reasons for thinking that the foundational computational complexity of our universe is finite. I discuss the emergence of an ordered complexity hierarchy of levels of objects over the foundational level and I show how the (...) special sciences study these emergent objects. (shrink)

This paper deals with Gärdenfors’ theory of conceptual spaces. Let \({\mathcal {S}}\) be a conceptual space consisting of 2-type fuzzy sets equipped with several kinds of metrics. Let a finite set of prototypes \(\tilde{P}_1,\ldots,\tilde{P}_n\in \mathcal {S}\) be given. Our main result is the construction of a classification algorithm. That is, given an element \({\tilde{A}}\in \mathcal {S},\) our algorithm classifies it into the conceptual field determined by one of the given prototypes \(\tilde{P}_i.\) The construction of our algorithm uses some physical (...) analogies and the Newton potential plays a significant role here. Importantly, the resulting conceptual fields are not convex in the Euclidean sense, which we believe is a reasonable departure from the assumptions of Gardenfors’ original definition of the conceptual space. A partitioning algorithm of the space \(\mathcal {S}\) is also considered in the paper. In the application section, we test our classification algorithm on real data and obtain very satisfactory results. Moreover, the example we consider is another argument against requiring convexity of conceptual fields. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential (...) to broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various topological (...) properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe. (shrink)