The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a (...) consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

How is moral knowledge possible? This paper defends the anti-Humean thesis that we can acquire moral knowledge by deduction from wholly non-moral premises. According to Hume’s Law, as it has become known, we cannot deduce an ‘ought’ from an ‘is’, since it is “altogether inconceivable how this new relation can be a deduction from others, which are entirely different from it” (Hume, 1739, 3.1.1). This paper explores the prospects for a deductive theory of moral knowledge that (...) rejects Hume’s Law. (shrink)

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. (...) We also show that some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion. (shrink)

Description: Contents: Preface 1. General Remarks on the Vedanta 2. Fundamental Distinction Between The Self and the Ego 3. The Vital Centre of the Human Being, Seat of Brahma 4. Purusha and Prakriti 5. Purusha Unaffected by Individual Modifications 6. The Degrees of Individual Manifestation 7. Buddhi or the Higher Intellect 8. Manas or the Inward Sense : The Ten External Faculties of Sensation and Action 9. The Envelopes of the Self ; The Five Vayus or Vital Functions 10. The (...) Essential Unity and Identity of the Self in all the States of the Being 11. The Different Conditions of Atma in the Human Being 12. The Waking State or the Condition of Vaishwanara 13. The Dream State or the Condition of Taijasa 14. The State of Deep Sleep or the Condition of Prajna 15. The Unconditioned State of Atma 16. The Symbolical Representation of Atma and its Conditions by the Sacred Monosyllable Om 17. The Posthumous Evolution of the Human Being 18. The Reabsorption of the Individual Faculties 19. Differences in the Posthumous Conditions According to the Degrees of Knowledge 20. The Coronal Artery and the Solar Ray 21. The Divine Journey of the Being on the Path of Liberation 22. Final Deliverance 23. Videha-mukti and Jivana-mukti 24. The Spiritual State of the Yogi : The Supreme Identity. (shrink)

Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from the fact (...) that a subject knows that he is sitting in a room, and the fact that the subject’s sitting in a room entails his bodily existence, it does not follow that the subject also knows that he is not an envatted brain. This paper rejects Pritchard’s non-belief reading of hinge commitments. I start by showing that the non-belief reading fails to solve the skeptical paradox because the reasons that Pritchard uses to support the non-belief reading do not exempt hinge propositions from closure principles. I then proceed to argue that the non-belief reading is false as it claims that hinge commitments, unlike ordinary beliefs, are rationally unresponsive—with the help of a scenario in which a subject’s experience is internally chaotic, we can safely conclude that the hinge commitment that one is not systematically mistaken about the world is equally responsive to one’s evidential situations. (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)

While working on various medieval philosophers, I have noticed an affinity between their remarks on the reasonableness of accepting propositions that are not matters of proof and strict deduction and St. John Henry Newman’s remarks that we accept unconditionally and rightly everyday ordinary propositions without calibrating them to demonstrable arguments. In particular, Cardinal Matthew of Aquasparta and Blessed John Duns Scotus both claim there is a sense in which assent to everyday propositions is tantamount to knowledge, even though there (...) is no adequate argumentation or demonstrative reasoning compelling us to assent to such propositions. Newman’s distinction between notional and real apprehension of propositions, notional and real assents, and his insistence on the existence of real assents to propositions that are not necessarily proved, or in some cases provable, seem, at first glance, a case parallel to that of the medieval philosophers we have mentioned. (shrink)

Abstract Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in (...) a Reducibility-based reply to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9784-4 Authors Juhani Yli-Vakkuri, Wolfson College, Oxford University, Oxford, OX2 6UD UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (shrink)

The term "non-monotonic logic" covers a family of formal frameworks devised to capture and represent defeasible inference , i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called "non-monotonic" because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. (...) This is in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be "undone" by new information. (shrink)

In the process of scientific discovery, knowledge ampliation is pursued by means of non-deductive inferences. When ampliative reasoning is performed, probabilities cannot be assigned objectively. One of the reasons is that we face the problem of the unconceived alternatives: we are unable to explore the space of all the possible alternatives to a given hypothesis, because we do not know how this space is shaped. So, if we want to adequately account for the process of knowledge ampliation, (...) we need to develop an account of the process of scientific discovery which is not exclusively based on probability calculus. We argue that the analytic view of the method of science advocated by Cellucci is interestingly suited to this goal, since it rests on the concept of plausibility. In this perspective, in order to account for how probabilities are in fact assigned in uncertain contexts and knowledge ampliation is really pursued, we have to take into account plausibility-based considerations. (shrink)

This article examines the current justifications of deductive inferences, and finds them wanting. It argues that this depends on the fact that all such justification take no account of the role deductive inferences play in knowledge. Alternatively, the article argues that a justification of deductive inferences may be given in terms of the fact that they are non-ampliative, in the sense that the content of the conclusion is merely a reformulation of the content of the premises. (...) Some possible objections to this view are discussed and found inadequate. (shrink)

In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk and Stokhof [1991: 39–100] with assignment and with generalized quantifiers. The use of this dynamic assignment language for natural language analysis, along the lines of o.c. and [Barwise, 1987: 1–29], is demonstrated by examples. We show that our representation language permits us to treat a wide variety of donkey sentences: conditionals with a donkey pronoun in their consequent and quantified sentences with donkey pronouns (...) anywhere in the scope of the quantifier. It is also demonstrated that our account does not suffer from the so-called proportion problem.Discussions about the correctness or incorrectness of proposals for dynamic interpretation of language have been hampered in the past by the difficulty of seeing through the ramifications of the dynamic semantic clauses (phrased in terms of input-output behaviour) in non-trivial cases. To remedy this, we supplement the dynamic semantics of our representation language with an axiom system in the style of Hoare. While the representation languages of barwise and Groenendijk and Stokhof were not axiomatized, the rules we propose form a deduction system for the dynamic assignment language which is proved correct and complete with respect to the semantics. (shrink)

This chapter contains sections titled: The Key Ingredients of Logic Non‐Deductive Reasoning Forms Plausible Reasoning Induction and Abduction Confirmatory Induction Concluding Remarks.

This paper argues that a necessary condition on inferential knowledge is that one knows all the propositions that knowledge depends on. That is, I will argue in support of a principle I call the Knowledge from Knowledge principle: (KFK) S knows that p via inference or reasoning only if S knows all the propositions on which p depends. KFK meshes well with the natural idea that (at least with respect to deductively valid or induc- tively strong (...) arguments) the epistemic status of one’s belief in the conclusion of an argument is a function of the epistemic status of the attitudes one has to the premises of that argument. One gets what one puts in: S’s belief in the conclusion C of an argument A has epistemic status E for S only if S’s belief in each of the premises C depends on also has epistemic status E.1 This is compatible, of course, with the epistemic status of S’s conclusion being greater than the epistemic status of the premises on which the conclusion of her reasoning depends. Furthermore, even though KFK applies more straightforwardly to non-suppositional inferences, we can also plausibly apply the principle to sup- positional reasoning if we treat S’s assuming for the sake of argument that p,2 as S assuming for the sake of argument that she knows that p.3 Although extremely plausible, philosophers have failed to present a concerted case in support of KFK. Most of their energy goes to articulating and/or defending some form of closure principle for knowledge.4 What is more, recently versions of this principle have been dismissed as problematic but I think without the reasons in its support been fully appreciated. This paper is an e fort to change the current state of affairs. Its focus is positive, however: my goal is to make the best case I can in support of KFK.5 To that end, the paper presents the reasons we have to accept KFK (§1), consid- ers an objection to the principle (§2), and situates the principle in the broader normative context of knowledge norms (§3). (shrink)

This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition’s truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we (...) can justly expect that if the mathematical proposition is actually false, despite the evidence for its truth, then this fact has an explanation. (shrink)

I argue for a novel, non-subjectivist interpretation of Kant’s transcendental idealism. Kant’s idealism is often interpreted as specifying how we must experience objects or how objects must appear to us. I argue to the contrary by appealing to Kant’s Transcendental Deduction. Kant’s Deduction is the proof that the categories are not merely subjectively necessary conditions we need for our cognition, but objectively valid conditions necessary for objects to be appearances. My interpretation centres on two claims. First, Kant’s method of self- (...) class='Hi'>knowledge consists in his determining what makes our cognitive faculty finite in contrast to God’s infinite cognitive faculty. Second, Kant’s limitation of our knowledge to appearances consists in his developing an account according to which appearances and our finite cognitive faculty are conceived of in terms of each other and in contrast to noumena in the positive sense and God’s infinite cognitive faculty. (shrink)

The paper discusses a four-valued propositional logic FOUR≤, similar to Belnap's logic, which can be used to describe incomplete or inconsistent knowledge. In addition to the two classical logical values tt, ff, FOUR≤ features also two nonclassical values: ⊥, representing incomplete information, and ⊤, representing inconsistency. The nonclassical values are incomparable, and together with the classical ones they form a diamond-shaped lattice L4 known from Belnap's logic, which underlies the semantics of FOUR≤. The set of connectives contains those of (...) Belnap's logic, together with an additional operator representing the lattice order, which decisively increases the expressive power of the logic. In the paper we develop a complete decompositional deduction system in Rasiowa-Sikorski style for FOUR≤. (shrink)

Every artificial-intelligence research project needs a working definition of "intelligence", on which the deepest goals and assumptions of the research are based. In the project described in the following chapters, "intelligence" is defined as the capacity to adapt under insufficient knowledge and resources. Concretely, an intelligent system should be finite and open, and should work in real time. ;If these criteria are used in the design of a reasoning system, the result is NARS, a non-axiomatic reasoning system. ;NARS uses (...) a term-oriented formal language, characterized by the use of subject-predicate sentences. The language has an experience-grounded semantics, according to which the truth value of a judgment is determined by previous experience, and the meaning of a term is determined by its relations with other terms. Several different types of uncertainty, such as randomness, fuzziness, and ignorance, can be represented in the language in a single way. ;The inference rules of NARS are based on three inheritance relations between terms. With different combinations of premises, revision, deduction, induction, abduction, exemplification, comparison, and analogy can all be carried out in a uniform format, the major difference between these types of inference being that different functions are used to calculate the truth value of the conclusion from the truth values of the premises. ;Since it has insufficient space-time resources, the system needs to distribute them among its tasks very carefully, and to dynamically adjust the distribution as the situation changes. This leads to a "controlled concurrency" control mechanism, and a "bag-based" memory organization. ;A recent implementation of the NARS model, with examples, is discussed. The system has many interesting properties that are shared by human cognition, but are absent from conventional computational models of reasoning. ;This research sheds light on several notions in artificial intelligence and cognitive science, including symbol-grounding, induction, categorization, logic, and computation. These are discussed to show the implications of the new theory of intelligence. ;Finally, the major results of the research are summarized, a preliminary evaluation of the working definition of intelligence is given, and the limitations and future extensions of the research are discussed. (shrink)

Formal ontologies are nowadays widely considered a standard tool for knowledge representation and reasoning in the Semantic Web. In this context, they are expected to play an important role in helping automated processes to access information. Namely: they are expected to provide a formal structure able to explicate the relationships between different concepts/terms, thus allowing intelligent agents to interpret, correctly, the semantics of the web resources improving the performances of the search technologies. Here we take into account a problem (...) regarding Knowledge Representation in general, and ontology based representations in particular; namely: the fact that knowledge modeling seems to be constrained between conflicting requirements, such as compositionality, on the one hand and the need to represent prototypical information on the other. In particular, most common sense concepts seem not to be captured by the stringent semantics expressed by such formalisms as, for example, Description Logics (which are the formalisms on which the ontology languages have been built). The aim of this work is to analyse this problem, suggesting a possible solution suitable for formal ontologies and semantic web representations. The questions guiding this research, in fact, have been: is it possible to provide a formal representational framework which, for the same concept, combines both the classical modelling view (accounting for compositional information) and defeasible, prototypical knowledge ? Is it possible to propose a modelling architecture able to provide different type of reasoning (e.g. classical deductive reasoning for the compositional component and a non monotonic reasoning for the prototypical one)? We suggest a possible answer to these questions proposing a modelling framework able to represent, within the semantic web languages, a multilevel representation of conceptual information, integrating both classical and non classical (typicality based) information. Within this framework we hypothesise, at least in principle, the coexistence of multiple reasoning processes involving the different levels of representation. (shrink)

In this paper, I discuss the debate on Kant and nonconceptual content. Inspired by Kant’s account of the intimate relation between intuition and concepts, McDowell (1996) has forcefully argued that the relation between sensible content and concepts is such that sensible content does not severally contribute to cognition but always only in conjunction with concepts. This view is known as conceptualism. Recently, Kantians Robert Hanna and Lucy Allais, among others, have brought against this view the charge that it neglects the (...) possibility of the existence of essentially nonconceptual content that is not conceptualised or subject to conceptualisation. Their critique of McDowell amounts to nonconceptualism. However, both views, conceptualist and nonconceptualist, share the assumption that intuition is synthesised content in Kant’s sense. My interest is not in the validity of the philosophical positions of conceptualism or nonconceptualism per se. I am particularly interested in the extent to which the views that McDowell and Hanna and Allais respectively advance are true to Kant, or can validly be seen as Kantian positions. I argue that although McDowell is right that intuition is only epistemically relevant in conjunction with concepts, Hanna and Allais are right with regard to the existence of essentially nonconceptual content (intuitions) independently of the functions of the understanding, but that they are wrong with regard to non-conceptualised intuition being synthesised content in Kant’s sense. Kantian conceptualists (Bowman 2011; Griffith 2012; Gomes 2014) have responded to the recent nonconceptualist offensive, with reference to A89ff./B122ff. (§13)—which, confusingly, the nonconceptualists also cite as evidence for their contrary reading—by arguing that the nonconceptualist view conflicts with the central goal of the Transcendental Deduction, namely, to argue that all intuitions are subject to the categories. I contend that the conceptualist reading of A89ff./B122ff. is unfounded, but also that the nonconceptualists are wrong to believe that intuitions as such refer strictly to objects independently of the functions of the understanding, and that they are mistaken about the relation between figurative synthesis and intellectual synthesis. I argue that Kant is a conceptualist, albeit not in the sense that standard conceptualists assume. Perceptual knowledge is always judgemental, though without this resulting in the standard conceptualist claim that, necessarily, all intuitions or all perceptions per se stand under the categories (strong conceptualism). I endorse the nonconceptualist view that, for Kant, perception per se, i.e. any mere or ‘blind’ intuition of objects (i.e. objects as indeterminate appearances) short of perceptual knowledge, does not necessarily stand under the categories. Perception is not yet perceptual knowledge. In this context, I point out the common failure in the literature on the Transcendental Deduction, both of the conceptualist and nonconceptualist stripe, to take account of the modal nature of Kant’s argument for the relation between intuition and concept insofar as cognition should arise from it. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...) `pragmatic', but that there must be an element of what it is rational to believe on the evidence, that is, of non-deductive logic. (shrink)

. Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other (...) conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. (shrink)

ABSTRACT This is a continuing attempt in a series of papers [KM 93, Mur 93, Mur 96] to show how computer-represented knowledge can be arranged as elements of an effectively represented semantic (or algebraic) domain in the sense of [GS 90]. We present a direct deductive description of the domain, which was defined semantically in [KM 93], via the Scott's notion of information system. Also, the internal structure of the continuous ampliative operations coordinated with the domain's effective basis (...) is established. Though we always remain in the paradigm of the toleration of contradictory information described in [Bel 75, Bel 76], the approach in question could be extended to include domains for consistency knowledge bases. (shrink)

Two theses are central to foundationalism. First, the foundationalist claims that there is a class of propositions, a class of empirical contingent beliefs, that are ‘immediately justified’. Alternatively, one can describe these beliefs as ‘self–evident’, ‘non–inferentially justified’, or ‘self–warranted’, though these are not always regarded as entailing one another. The justification or epistemic warrant for these beliefs is not derived from other justified beliefs through inductive evidential support or deductive methods of inference. These ‘basic beliefs’ constitute the foundations of (...) empirical knowledge. One can give a reason for the justification of a basic belief even though the justification for that belief is not based on other beliefs. Thus, according to Chisholm, if asked what one's justification was for thinking that one knew, presently, that one is thinking about a city one takes to be Albuquerque, one could simply say ‘what justifies me…is simply the fact that I am thinking about a city I take to be Albuquerque’. (shrink)

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and (...) that it is in good epistemic standing. (shrink)

[Significantly updated in Chapter 6 of Awareness and the Substructure of Knowledge] In order for a reason to justify an action or attitude it must be one that is possessed by an agent. Knowledge-centric views of possession ground our possession of reasons, at least partially, either in our knowledge of them or in our being in a position to know them. On virtually all accounts, knowing P is some kind of non-accidental true belief that P. This entails (...) that knowing P is a kind of non-accidental true representation that P. I outline a novel theory of the epistemic requirement on possession in terms of this more general state of non-accidental true representation. It is just as well placed to explain the motivations behind knowledge-centric views of possession, and it is also better placed to explain the extent of the reasons we possess in certain cases of deductive belief-updates and cases involving environmental luck. I conclude with three reflections. First, I indicate how my arguments generate a dilemma for Errol Lord’s view that possessing reasons is just a matter of being in a position to manifest one’s knowledge how to use them. Second, I explain how my view can simultaneously manage cases of environmental luck without falling prey to lottery cases. Finally, I sketch the direction for a further range of counterexamples to knowledge-centric theories of possession. (shrink)

Although Gregory wrote very little about this. he acknowledged that natural reason can lead us from the orderliness of the physical world to the existence of God; in this, he followed the tradition of Athanasius and other Greek fathers. Unlike Aquinas, he did not seek to present the argument a; deductive: in fact his argument is inductive, and of die same kind as - we now realize - scientists and historians use when they argue from phenomena to then explanatory (...) cause. Gregory wrote hardly anything about how one could obtain knowledge of the truths of the Christian revelation by arguments from non-question-beggining premises; but in his conversations with the Turks he showed that he believed that there are good arguments of this kind. Almost all of Gregory's writing about knowledge of God concerned how one could obtain this by direct access in prayer: this access, he held is open especially to monks, but to a considerable degree also to all Christians who follow the divine commandments. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:141 HUME AND DEMONSTRATIVE KNOWLEDGE Little could be clearer than that Hume's sceptical arguments concerning induction and causation depend to some considerable extent on his contention that there can be no demonstrative arguments for matters of fact. An understanding of his use of the terms 'demonstration', 'demonstrative reasoning' etc., would seem to be a prerequisite for a satisfactory appraisal of those arguments. What is almost as clear, however, (...) is that these terms have so far evaded much critical discussion and, with one notable exception, it seems to be assumed that we know well enough what they mean. That exception is David Stove, whose book on Hume contains, among many good things, a boldly provocative discussion of these terms in relation to the sceptical argument. Stove has interesting things to say about the terms: I don't think that he is quite right, but then neither is he straightforwardly wrong. I shall present his account, and the one to which he is opposed, and then, after criticising both, I shall try to show why the truth lies elsewhere, and why we begin to approach Hume correctly only when we temper our fascination with the purely formal structures of argument. Inductive scepticism is, of course, that scepticism which claims that there can be neither knowledge nor reasonable beliefs about unobserved matters of fact. Thus inductive arguments, those arguments which attempt to ground beliefs in unobserved matters of fact are, under this scepticism, claimed to 142 be bad arguments. Deductively valid arguments are, of course, often good, but it seems that they are unable to be utilised in justifying beliefs in unobserved matters of fact. The problem of induction is thus that of explaining how these non-valid inductive arguments can be forceful, and Hume's scepticism about induction resides in his believing and arguing, or appearing to believe and to argue, that they cannot. Hume himself does not, however, use the terms 'inductive', 'deductive' and their cognates. Some translation has therefore been employed in getting from his writings to the rough and ready sketch of the problem of induction as presented above. Stove spends some considerable time on this, and there is surely nothing wrong with his careful glossing of Humes 'moral' and 'probable' arguments by our term 'induetive '. There are, however, good reasons to tread carefully where 'demonstrative' is concerned. Stove's remarks here are somewhat contentious, and before giving his version of what Hume's term means, I shall present what may be accounted the standard view. While Hume does not use the term 'deductive', he does make freguent use of 'demonstration' and its derivatives, and he uses these in such a way as to suggest that a gloss via our term 'deduction' will not be far off the mark. Consider, for example, the following passage: Our foregoing method of reasoning will easily convince us, that there can be no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience. We can at least conceive a change in the course of nature; which sufficiently proves, that such a change is not absolutely impossible. To form a clear idea of anything, is an 143 undeniable argument for its possibility, and is alone a refutation of any pretended argument against it. (T 89) His point here seems to be that as alternative states of affairs remain possible, and are thus compatible with all the evidence upon which is based the hypothesis about continuing uniformity, it cannot be claimed that the persistence of such uniformity is established by argument. A similar account will be given of the following passage from the Enquiry: When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible gualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative.... (E 37) It is tempting to understand Hume here as once again... (shrink)

Phenomenology is the study of appearance as such. It is a branch of both Ontology and Epistemology, since appearing is being known. By an ‘appearance’ is meant any existent which impinges on consciousness, anything cognized, irrespective of any judgment as to whether it be ‘real’ or ‘illusory.’ The evaluation of a particular appearance as a reality or an illusion is a complex process, involving inductive and deductive logical principles and activities. Opinion has to earn the status of strict (...) class='Hi'>knowledge. Knowledge develops from appearances, which may be: (a) objects of perception, i.e. concrete phenomena in the physical or mental domains; (b) objects of intuition, i.e. one’s subjective self, cognitions, volitions and valuations (non-phenomenal concretes); and/or (c) objects of conception, i.e. simple or complex abstracts of preceding appearances. Abstraction relies on apprehensions of sameness and difference between appearances (including received or projected appearances, and projected negations of appearances). Coherence in knowledge (perceptual, intuitive and conceptual) is maintained by apprehensions of compatibility or incompatibility. Words facilitate our construction of conceptual knowledge, thanks to their intentionality. The abstract concepts most words intend are common characters or behaviors of particulars (concrete material, mental or subjective experiences). Granting everything in the world is reducible to waves, ‘universals’ would be equalities or proportionalities in the measures of the features, motions and interrelations of particular waves. Such a theory of universals would elucidate sensation and memory. In attempting to retrace the development of conceptual knowledge from experience, we may refer to certain major organizing principles. It is also important to keep track of the order of things in such development, interrelating specific concepts and specific experiences. By proposing a precise sequence of events, we avoid certain logical fallacies and are challenged to try and answer certain crucial questions in more detail. Many more topics are discussed in the present collection of essays, including selfhood, adduction and other logical issues, the status of mathematical concepts and theology. (shrink)

Intuitively, the knowledge of one’s own intentional actions is different from the knowledge of actions of other sorts, including those of other people and unintentional actions of one's own. But how are we to understand this phenomenon? Does it pertain to all actions, under every description under which they are known? If so, then how is this possible? If not, then how should we think about cases that are exceptions to this principle? This paper is a critical survey (...) of recent attempts to answer these questions. I consider views under three headings: "special source" views, which hold that the knowledge of one's intentional actions has a non-perceptual source; "special domain" views, which hold that some but not all aspects of one's intentional actions are known in a special way; and "special character" views, which hold that the knowledge of intentional actions is special not because of where it comes from, but because of some other respect in which it is different in kind from the knowledge of other things. (shrink)

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended (...) herein and the Trudy Govier's account are discussed as well. (shrink)

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended (...) herein and the Trudy Govier's account are discussed as well. (shrink)

The central argument in this paper is the following: if we agree that one of the aims of explanation is to provide or increase understanding, and if we assess understanding on the basis of the inferences one can draw from the knowledge of the phenomenon which is understood, then the value of an explanation, i.e. its capacity to provide or increase understanding of the explained phenomenon, should be assessed on the basis of the extra-inferences which this explanation allows for. (...) The extra-inferences which a given explanation allows for constitute its inferential content. The analysis of the explanation’s inferential content could be applied to all kinds of explanations with the aim of assessing their goodness. I show how such an analysis helps us to better understand a number of difficulties that have puzzled contemporary philosophers of explanation: the flagpole counterexample to the deductive-nomological model of explanation, the conjunction problem, the difference between good and bad circular explanations. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

What Mamardašvili meant by “process of knowledge” is not an all-embracing vision of reality accomplished “once-and-for-all”; it is not a step by step procedure of deduction; rather it is an anti-dialectical reconstruction of a constellation of signs put together over and over again by the subject by an act of non-premeditated genius. It is a kind of aesthetic act that makes the sense appear, like a vertical cut in the sequential line of space and time.

Dogmatism holds that an experience or seeming that p can provide prima facie immediate justification for believing p in virtue of its phenomenology. Dogmatism about perceptual justification has appealed primarily to proponents of representational theories of perceptual experience. Call dogmatism that takes perceptual experience to be representational "representational phenomenal dogmatism." As we show, phenomenal seemings play a crucial role in dogmatism of this kind. Despite its conventional appeal to representational theorists, dogmatism is not by definition committed to any particular view (...) of perceptual experience. Naive realists and disjunctivists who hold that perceptual experience is a perceptual relation of direct acquaintance can also endorse dogmatism. Indeed, we argue that they ought to do so. Otherwise, they cannot maintain that relationalism about perceptual experience has an epistemic advantage compared to the representational view. We then show that even if we grant that relationalism has this advantage, only dogmatism that takes perceptual experience to be representational can be extended to account for non-deductive inferential justification. As an account of the latter is required to avoid succumbing to skepticism, relationalism, we argue, does not have the epistemic advantage its defenders claim it has. (shrink)

In a letter of 1932, Karl Popper described Die beiden Grundprobleme der Erkenntnistheorie – _The Two Fundamental Problems of the Theory of Knowledge_ – as ‘…a child of crises, above all of …the crisis of physics.’ Finally available in English, it is a major contribution to the philosophy of science, epistemology and twentieth century philosophy generally. The two fundamental problems of knowledge that lie at the centre of the book are the problem of induction, that although we are able (...) to observe only a limited number of particular events, science nevertheless advances unrestricted universal statements; and the problem of demarcation, which asks for a separating line between empirical science and non-science. Popper seeks to solve these two basic problems with his celebrated theory of falsifiability, arguing that the inferences made in science are not inductive but deductive; science does not start with observations and proceed to generalise them but with problems, which it attacks with bold conjectures. _The Two Fundamental Problems of the Theory of Knowledge_ is essential reading for anyone interested in Karl Popper, in the history and philosophy of science, and in the methods and theories of science itself. (shrink)

In a letter of 1932, Karl Popper described Die beiden Grundprobleme der Erkenntnistheorie – _The Two Fundamental Problems of the Theory of Knowledge_ – as ‘…a child of crises, above all of …the crisis of physics.’ Finally available in English, it is a major contribution to the philosophy of science, epistemology and twentieth century philosophy generally. The two fundamental problems of knowledge that lie at the centre of the book are the problem of induction, that although we are able (...) to observe only a limited number of particular events, science nevertheless advances unrestricted universal statements; and the problem of demarcation, which asks for a separating line between empirical science and non-science. Popper seeks to solve these two basic problems with his celebrated theory of falsifiability, arguing that the inferences made in science are not inductive but deductive; science does not start with observations and proceed to generalise them but with problems, which it attacks with bold conjectures. _The Two Fundamental Problems of the Theory of Knowledge_ is essential reading for anyone interested in Karl Popper, in the history and philosophy of science, and in the methods and theories of science itself. (shrink)

In a letter of 1932, Karl Popper described _Die beiden Grundprobleme der Erkenntnistheorie – The Two Fundamental Problems of the Theory of Knowledge_ – as ‘…a child of crises, above all of …the crisis of physics.’ Finally available in English, it is a major contribution to the philosophy of science, epistemology and twentieth century philosophy generally. The two fundamental problems of knowledge that lie at the centre of the book are the problem of induction, that although we are able (...) to observe only a limited number of particular events, science nevertheless advances unrestricted universal statements; and the problem of demarcation, which asks for a separating line between empirical science and non-science. Popper seeks to solve these two basic problems with his celebrated theory of falsifiability, arguing that the inferences made in science are not inductive but deductive; science does not start with observations and proceed to generalise them but with problems, which it attacks with bold conjectures. _The Two Fundamental Problems of the Theory of Knowledge_ is essential reading for anyone interested in Karl Popper, in the history and philosophy of science, and in the methods and theories of science itself. (shrink)

Logic, in one of the many sense of that term, is a theory about what follows from what and why. Arguably, the correct theory has to be determined by abduction. Over recent years, so called logical anti-exceptionalists have investigated this matter. Current discussions have been restricted to deductive logic. However, there are also, of course, various forms of non-deductive reasoning. Indeed, abduction itself is one of these. What is to be said about the way of choosing the best (...) theory of non-deductive inferences? It would seem clear that an anti-exceptionalist should hold that essentially the same method of choice should apply to non-deductive logic. A number of issues need to be faced in the process, not the least of which is the circularity involved in an abductive justification for a theory of abduction. This paper discusses matters. (shrink)

The paper is an investigation into the prospects of an epistemology of non-conceptual knowledge. According to the orthodox view, knowledge requires concepts and belief. I present several arguments to the effect that there is non-conceptual, non-doxastic knowledge, the obvious candidate for such knowledge being non-conceptual perception. Non-conceptual perception seems to be allowed for by cognitive scientists and it exhibits the central role features of knowledge—it plays the knowledge role: it respects an anti-luck condition, it (...) is an achievement, it enables one to act for a reason, and it provides justification. Furthermore, it makes a straightforward and elegant explanation of perceptual knowledge possible: doxastic perceptual knowledge builds on non-conceptual perception as non-conceptual knowledge. Three objections that might naturally arise will be discussed and answered. Thus, the prospects of an epistemology without belief seem to be much better than the orthodoxy wants to have it. We can extend knowledge into the non-conceptual realm. (shrink)