Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...

This is a reply to Timothy Williamson ’s paper ‘Tennant’s Troubles’. It defends against Williamson ’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson ’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson ’s attempt to cause problems for the anti-realist by means of a supposed rigid designator generates a contradiction (...) with arithmetic right away, upon instantiating the obviously relevant theorem that every natural number is provably odd or provably even. The paper also explains and formulates a globally restricted knowability principle, which likewise blocks the attempted reductio. (shrink)

What psychological and philosophical significance should we attach to recent efforts at computer simulations of human cognitive capacities? In answering this question, I find it useful to distinguish what I will call "strong" AI from "weak" or "cautious" AI. According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion. (...) But according to strong AI, the computer is not merely a tool in the study of the mind; rather, the appropriately programmed computer really is a mind, in the sense that computers given the right programs can be literally said to. (shrink)

This article offers an analysis of ignorance. After a couple of preliminary remarks, I endeavor to show that, contrary to what one might expect and to what nearly all philosophers assume, being ignorant is not equivalent to failing to know, at least not on one of the stronger senses of knowledge. Subsequently, I offer two definitions of ignorance and argue that one’s definition of ignorance crucially depends on one’s account of belief. Finally, I illustrate the relevance of my analysis by (...) paying attention to four philosophical problems in which ignorance plays a crucial role. (shrink)

In this paper, I provide a defence of the New View, on which ignorance is lack of true belief rather than lack of knowledge. Pierre Le Morvan has argued that the New View is untenable, partly because it fails to take into account the distinction between propositional and factive ignorance. I argue that propositional ignorance is just a subspecies of factive ignorance and that all the work that needs to be done can be done by using the concept of factive (...) ignorance. I also defend two arguments of mine in favour of the New View against Le Morvan’s criticisms. As to the Linguistic Argument, I point out that the intuitions of the adherent of the New View about cases of true belief that fall short of knowledge are really intuitions about factive rather than propositional ignorance. As to the Excuse Argument, I argue that true belief is exculpatorily relevant: a true belief in a proposition p , where disbelief that p or suspension on p would provide at least a partial excuse, is relevant in that it renders one blameworthy for one’s action, unless further excuses hold. Finally, I reply to two closely related objections that might be levelled against the New View, namely that it seems false that one can reduce one’s ignorance by arbitrarily believing as many propositions as possible and that it seems false that an intellectually conscientious and critical person is more ignorant than an intellectually sloppy and credulous person just because the latter has more true beliefs. (shrink)

In this article, Lucas maintains the falseness of Mechanism - the attempt to explain minds as machines - by means of Incompleteness Theorem of Gödel. Gödel’s theorem shows that in any system consistent and adequate for simple arithmetic there are formulae which cannot be proved in the system but that human minds can recognize as true; Lucas points out in his turn that Gödel’s theorem applies to machines because a machine is the concrete instantiation of a formal system: therefore, for (...) every machine consistent and able of doing simple arithmetic, there is a formula that it can’t produce as true but that we can see to be true, and so human minds and machines have to be different. Lucas considers as well in this article some possible objections to his argument: for any Gödelian formula we could, for instance, construct a machine able to produce it or we could put the Gödelian formulae that we had proved as axioms of a further machine. However - as Lucas underlines - for every of such machines we could again formulate another Gödelian formula, the Gödelian formula of these machines, that they are not able to proof but that we can recognize as true. More general arguments, such as the possibility to escape Gödelian argument by suggesting that Gödel’s theorem applies to consistent systems while we could be inconsistent ones, are moreover refuted by Lucas by maintaining that our inconsistency corresponds to occasional malfunctioning of a machine and not to his normal inconsistency; indeed, a inconsistent machine is characterized by producing any statement, on the contrary human being are selective and not disposed to assert anything. (shrink)

Gödei's Theorem seems to me to prove that Mechanism is false, that is, that minds cannot be explained as machines. So also has it seemed to many other people: almost every mathematical logician I have put the matter to has confessed to similar thoughts, but has felt reluctant to commit himself definitely until he could see the whole argument set out, with all objections fully stated and properly met. This I attempt to do.

The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportunity to revisit some of the issues examined in (...) the earlier book, in light of the evolving debate over realism and anti-realism. (shrink)

I discuss the question of when knowledge of higher order ignorance is possible and show in particular that, under quite plausible assumptions, knowledge of second order ignorance is impossible.

Fitch’s argument purports to show that for any unknown truth, p , there is an unknowable truth, namely, that p is true and unknown; for a contradiction follows from the assumption that it is possible to know that p is true and unknown. In earlier work I argued that there is a sense in which it is possible to know that p is true and unknown, from a counterfactual perspective; that is, there can be possible, non-actual knowledge, of the actual (...) situation, that in that situation, p is true and unknown. Here I further elaborate that claim and respond to objections by Williamson, who argued that there cannot be non-trivial knowledge of this kind. I give conditions which suffice for such non-trivial counterfactual knowledge. (shrink)

Historically, there has been great deliberation about the limits of human knowledge. Isaac Newton, recognizing his own shortcomings, once described himself as “a boy standing on the seashore... whilst the great ocean of truth lay all underscored before me.” In _Ignorance,_ Nicholas Rescher presents a broad-ranging study that examines the manifestations, consequences, and occasional benefits of ignorance in areas of philosophy, scientific endeavor, and ordinary life. Citing philosophers, theologians, and scientists from Socrates to Steven Hawking, Rescher seeks to uncover the (...) factors that hinder our cognition. Rescher categorizes ignorance as ontologically grounded, or epistemically grounded. He then defines the basis of ignorance: inaccessible data; statistical fogs; secreted information; past data that have left no trace; future discoveries; future contingencies; vagrant predicates; and superior intelligences. Such impediments set limits to inquiry and mean that while we can always extend our existing knowledge-variability here is infinite-there are things that we will never know. Cognitive finitude also hinders our ability to assimilate more than a certain number of facts. We may acquire additional information, but lack the facility to interpret it. More information does not always increase knowledge; it may point us further down the path toward an erroneous conclusion. In light of these deficiencies, Rescher looks to the role of computers in solving problems and expanding our knowledge base, but finds limits to their reasoning capacity. As Rescher's comprehensive study concludes, ignorance itself is a fertile topic for knowledge, and recognizing the boundaries of our comprehension is where wisdom begins. (shrink)

Epistemic logic is the branch of philosophical thought that seeks to formalize the discourse about knowledge. Its object is to articulate and clarify the general principles of reasoning about claims to and attributions of knowledge. This comprehensive survey of the topic offers the first systematic account of the subject as it has developed in the journal literature over recent decades. Rescher gives an overview of the discipline by setting out the general principles for reasoning about such matters as propositional knowledge (...) and interrogative knowledge. Aimed at graduate students and specialists, Epistemic Logic elucidates both Rescher's pragmatic view of knowledge and the field in general. (shrink)

This philosophically rich volume examines the limits of human knowledge and considers their implications.

On an initially plausible view of ignorance, ignorance is equivalent to the lack or absence of knowledge-that. I argue that this view is incorrect, as lack of sufficient justification for one's true belief or lack of belief doesn't necessarily amount to ignorance. My argument rests on linguistic considerations of common uses of 'ignorant' and its cognates. The phrase 'is ignorant of', I argue, functions differently grammatically and semantically from the phrase 'does not know', when the latter is used propositionally. 'Is (...) ignorant of' does not have a genuine propositional use but is best understood as equivalent to 'is not knowledgeable of'. I further argue that 'knowledgeable' and 'ignorant' are relative gradable expressions. Relative gradables typically are associated with an implicit or explicit standard of comparison, give rise to borderline cases and trigger the Sorites Paradox in their unmarked form. From these linguistic considerations, it follows that being ignorant admits of degree, and that one can fail to be ignorant despite lacking true beliefs concerning the propositions constituting a particular subject matter. The proposed treatment of knowledgeability and ignorance of facts and subject matters lends itself to an alternative reply to the problem of skepticism, which I will call the ‘simple response’. In the final section of the paper I argue that ignorance can also reflect incompetence with respect to a particular activity. The latter, I argue, is a case of lacking a particular kind of ability-involving knowledge-how, viz. practical knowledge of how to perform the activity in question. (shrink)

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)