Operators in the paradox of the knower

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.I am deeply indebted to Robert F. Barnes and Evan W. Conyers, without whom these ideas might not have germinated and certainly would not have grown. Many of the results offered here evolved in the course of mutual discussion and correspondence. I am also grateful to an anonymous reviewer forSynthese for many very helpful suggestions.The current paper contains the technical results promised in Footnote 25 of Grim (1988) and Footnote 26, Chapter 3, of Grim (1991).     

The knower,inside and out

Adherents of the epistemological position called internalism typically believe that the view they oppose, called externalism, is such a new and radical departure from the established way of seeing knowledge that its implications are uninteresting. Perhaps itis relatively novel, but the approach to knowledge with the greatest antiquity is the one that equates it withcertainty, and while this conception is amenable to the demands of the internalist, it is also a non-starter in the opinion of almost all contemporary epistemologists since obviously it directly implies that we know nothing about the world. Perhaps skepticism is correct, but there are conceptions of knowledge at least as plausible as the certainty equation that do not obviously land us there. It is its promise along these lines that makes the so-called traditional conception of knowledge initially interesting. But contrary to popular belief, the traditional conception cannot be claimed by internalists if it is to have any chance at all in avoiding skepticism; to avoid skepticism, I shall argue, it has to have an externalist element.Moreover, each of the departures from the traditional view that appears in the Gettier literature is externalist as well, or at least all of the ones of which I am aware. The only genuine forms of internalism are those held by philosophers who draw a fairly sharp line between knowledge and justified belief, ignore the former, then offer an internalist account of the latter. This approach is very common and very plausible. But it is not as useful as is often thought; in particular, I shall suggest, it must succumb to a form of skepticism.     

The knower and the known

This paper is a presentation and discussion of Spinoza's view on the knower, or the mind, as an agent. The knower is on his view to be regarded as an active or generative complex cognitive experience. Imagination, reason and intuition are the cognitive principles. On account of their intrinsic relation to “the first law of nature”, that of selfpreservation, together with the thesis of the mind as constituted by ideas or knowledge, these principles function at the same time as moral principles. Consequently, it makes sense to speak of an individual's moral attitude toward everything be knows. A discussion of imagination, reason and intuition mainly as cognitive principles is followed by some concluding remarks on the cognitive and moral relation between human beings: To know another human being is to know his knowledge. The moral attitude of individuals to each other is a function of their mutual knowledge of knowledge.     

The knower and the known

This paper is a presentation and discussion of Spinoza's view on the knower, or the mind, as an agent. The knower is on his view to be regarded as an active or generative complex cognitive experience. Imagination, reason and intuition are the cognitive principles. On account of their intrinsic relation to the first law of nature, that of selfpreservation, together with the thesis of the mind as constituted by ideas or knowledge, these principles function at the same time as moral principles. Consequently, it makes sense to speak of an individual's moral attitude toward everything be knows. A discussion of imagination, reason and intuition mainly as cognitive principles is followed by some concluding remarks on the cognitive and moral relation between human beings: To know another human being is to know his knowledge. The moral attitude of individuals to each other is a function of their mutual knowledge of knowledge.     

Continuum,name and paradox

The article deals with Cantor’s argument for the non-denumerability of reals somewhat in the spirit of Lakatos’ logic of mathematical discovery. At the outset Cantor’s proof is compared with some other famous proofs such as Dedekind’s recursion theorem, showing that rather than usual proofs they are resolutions to do things differently. Based on this I argue that there are “ontologically” safer ways of developing the diagonal argument into a full-fledged theory of continuum, concluding eventually that famous semantic paradoxes based on diagonal construction are caused by superficial understanding of what a name is.     

Perceptual switching,eye movements,and the bus paradox

According to a widely cited finding by Ellis and Stark (1978 Perception 7 575-581), the duration of eye fixations is longer at the instant of perceptual reversal of an ambiguous figure than before or after the reversal. However, long fixations are more likely to include samples of an independent random event than are short fixations. This sampling bias would produce the pattern of results also when no correlation exists between fixation duration and perceptual reversals. When an appropriate correction is applied to the measurement of fixation durations, the effect disappears. In fact, there are fewer actual button-presses during the long intervals than would be expected by chance. Moving-window analyses performed on eye-fixation data reveal that no unique eye event is associated with switching behaviour. However, several indicators, such as blink frequency, saccade frequency, and the direction of the saccade, are each differentially sensitive to perceptual and response-related aspects of the switching process. The time course of these indicators depicts switching behaviour as a process of cascaded stages.     

Subjective utility,anticipated utility,and the Allais paradox

One of the most notable counterexamples to expected utility theory is the “Allais paradox” (M. Allais, 1953, Econometrica, 31, 503–546). A number of alternative theories have been proposed in an attempt to resolve this paradox, notably including Karmarkar, 1978, Karmarkar, 1979, 24, 67–72). It is shown that SWU theory necessarily involves violations of dominance, but that the theory can be modified to avoid these violations. The result is a special case of J. Quiggin's anticipated utility theory (1982, Journal of Economic Behaviour and Organisation, 3, 323–343).     

Relativism, sceptical paradox, and semantic blindness

Relativism about knowledge attributions is the view that a single occurrence of ‘S knows [does not know] that p’ may be true as assessed in one context and false as assessed in another context. It has been argued that relativism is equipped to accommodate all the data from speakers’ use of ‘know’ without recourse to an error theory. This is supposed to be relativism’s main advantage over contextualist and invariantist views. This paper argues that relativism does require the attribution of semantic blindness to speakers, viz. to account for sceptical paradoxes and epistemic closure puzzles. To that end, the notion of semantic blindness is clarified by distinguishing between content-blindness and index-blindness, and it is argued that the attribution of index-blindness required by the relativist account is implausible. Along the way, it is shown that error-theoretic objections from speakers’ inter-contextual judgments fail against relativism.     

Moral pickles,moral dilemmas,and the obligation preface paradox

Philosophical Studies - This paper introduces and defends a new position regarding the question of whether it is possible to have conflicting moral obligations. In doing so, it focuses on what I...     

Avoiding certain frustration, reflection, and the cable guy paradox

We discuss the cable guy paradox, both as an object of interest in its own right and as something which can be used to illuminate certain issues in the theories of rational choice and belief. We argue that a crucial principle—The Avoid Certain Frustration (ACF) principle—which is used in stating the paradox is false, thus resolving the paradox. We also explain how the paradox gives us new insight into issues related to the Reflection principle. Our general thesis is that principles that base your current opinions on your current opinions about your future opinions need not make reference to the particular times in the future at which you believe you will have those opinions, but they do need to make reference to the particular degrees of belief you believe you will have in the future.

Controlled information processing,automaticity, and the burden of proof

Cognitive psychologists often distinguish between voluntary and involuntary/automatic processes in attention and cognitive control. Dedicated experimental paradigms have been developed to isolate involuntary information processing, but these paradigms tend to assume a rigid and inflexible process that is either stimulus-driven or built up through simple repetition. In contrast, voluntary information processing is often assumed when processing is in line with arbitrarily defined task-specific goals. Here I review evidence from multiple cases suggesting that ostensibly goal-directed cognitive processes may not be so voluntary and controlled. It is argued that automatic processes can be conditionalized to reflect the task relevance of the stimuli and selection history in a variety of ways, rapidly and flexibly adjusting in order to facilitate future goal-directed behavior. As a result, many studies assumed to have measured a voluntary cognitive process have likely measured an amalgam of voluntary and automatic processes, thus blurring the distinction between the two. Automaticity may be much broader and more sophisticated than has previously been thought, which has wide-reaching implications for our conception of human cognitive control.