Roy Sorensen

This enjoyable book presents a potpourri of paradoxes with the purpose of showing how they connect to serious philosophical issues. The main paradoxes are Zeno's, the sorites, Newcomb's problem, the paradoxes of confirmation, the surprise examination, and the paradoxes of self-reference. A final chapter defends the assumption that contradictions are unacceptable and an appendix throws in sixteen minor paradoxes. Along the way, R. M. Sainsbury peppers the reader with helpful queries and provocative asides.

"Logic and ethics are fundamentally the same, they are not more than duty to oneself"(Otto Weininger). So goes the head quotation of Ray Monk's biography Ludwig Wittgenstein: The Duty of Genius. Monk thereby introduces Wittgenstein's peculiar admiration for the crackpot author of Sex and Character along with Wittgenstein's moralistic dedication to logic. Monk elaborates with anecdotes. For instance, Wittgenstein would pace Bertrand Russell's room mixing logic with selfcriticism. Russell asked Wittgenstein whether he was thinking about logic or his sins. "Both!" barked Wittgenstein.

A para-reflection is a privational phenomenon that is often mistaken for a reflection. You have seen them as the ‘reflection’ of your pupil in the mirror. Your iris reflects light in the standard way but your pupil absorbs all but a negligible amount of light (as do other dark things such as coal and black velvet). Para-reflections work by contrast. Since they are parasitic on their host reflections, para-reflections are relational and dependent in a way that reflections are not. Nevertheless, para-reflections obey nearly all the laws of reflection with exquisite fidelity. Para-refractions display parallel obedience to the laws governing refraction. Physicists and psychologists who study optics have neglected these everyday phenomena. Happily, physicists have been attentive and insightful about other privational phenomena such as vacuums and cold spots. I conclude that this kind of subtle treatment of negative things needs to be extended to optics. 1 The invisible red herring 2 Mind-independent privations 3 Para-reflections are mind-independent 4 Parasitical entities 5 Para-refractions and shadows 6 How science has coped with privations.

A para‐reflection is a privational phenomenon that is often mistaken for a reflection. You have seen them as the ‘reflection’ of your pupil in the mirror. Your iris reflects light in the standard way but your pupil absorbs all but a negligible amount of light (as do other dark things such as coal and black velvet). Para‐reflections work by contrast. Since they are parasitic on their host reflections, para‐reflections are relational and dependent in a way that reflections are not. Nevertheless, para‐reflections obey nearly all the laws of reflection with exquisite fidelity. Para‐refractions display parallel obedience to the laws governing refraction. Physicists and psychologists who study optics have neglected these everyday phenomena. Happily, physicists have been attentive and insightful about other privational phenomena such as vacuums and cold spots. I conclude that this kind of subtle treatment of negative things needs to be extended to optics.1 The invisible red herring2 Mind‐independent privations3 Para‐reflections are mind‐independent4 Parasitical entities5 Para‐refractions and shadows6 How science has coped with privations.

Ockham's razor is popularly phrased as a prohibition against multiplying entities beyond necessity. This prohibition should extend to the receptacle for these entities. To state my thesis more positively and precisely, both qualitative and quantitative parsimony apply to space, time, and possibility. All other things equal, we ought to prefer a hypothesis that postulates less space. Smaller is better. Admittedly, scientists are ambivalent about economizing on the void. They praise simplicity. Yet astronomers have a history of helping themselves to as much empty space as they wish—staggering common sense with the vastness of the universe. This largesse is abetted by an aesthetic bias for sublime hypotheses. Whereas abductions based on beauty converge with parsimony, abductions based on the sublime diverge from parsimony. Awe stifles our inner accountant. Both types of abduction are popular. Both are dubious because we lack independent assurance that the universe is beautiful or sublime. The analogy between space and time supports an extension of parsimony to time. Uniformitarian geologists regarded time as a free resource. However, geologists and cosmologists must justify their postulation of an immense past. Possibility follows suit. Contrary to David Lewis, possible worlds should be minimized. Parsimony about possibilities provides a rationale for parsimony about absences. Absences are possibilities that are not actual. So proliferation of absences entails proliferation of possibilities. We should admit only those absences which do explanatory work.

My thesis is that you can lie with ‘ P therefore Q ’ without P or Q being lies. For you can lie by virtue of not believing that P supports Q. My thesis is reconciled with the principle that all lies are assertions through H. P. Grice’s account of conventional implicatures. These semantic cousins of conversational implicatures are secondary assertions that clarify the speaker’s attitude toward his primary assertions. The meaning of ‘therefore’ commits the speaker to an entailment thesis even though the speaker does not enter that commitment into the text. Insincere conventional implicatures are akin to insincerely asserted footnotes. An absence of lies in the text is compatible with the presence of lies in the meta-text.

If you read this abstract, then you will understand what my essay is about. Under what conditions would the preceding assertion be a lie? Traditional definitions of lying are always applied to straight declaratives such as ‘The dog ate my homework’. This one sided diet of examples leaves us unprepared for sentences in which conditional probability governs assertibility. The truth-value of conditionals does not play a significant role in the sincere assertion of conditionals. Lying is insincere assertion. So the connection between lying and falsehood is broken when lying with conditionals. Drawing on Frank Jackson's account of indicative conditionals. I argue that it is possible to lie with true conditionals by virtue of their false conventional implicatures. False conversational implicatures only guarantee misleading assertions, not lies. Lying remains a semantic rather than a pragmatic affair.

In ‘Epistemic Modals’ (2007), Seth Yalcin proposes Stalnaker-style semantics for epistemic possibility. He is inspired by John MacFarlane’s ingenious defence of relativism, in which claims of epistemic possibility are made rigidly from the perspective of the assessor’s actual stock of information (rather than from the speaker’s knowledge base or that of his audience or community). The innovations of MacFarlane and Yalcin independently reinforce the modal collapse espoused by Jaakko Hintikka in his 1962 epistemic logic (which relied on the implausible KK principle and heavy idealizations). I respond to this new challenge with fresh objections to the underlying S4 equivalence: p p . I also propose counter-analyses of the intriguing data which Yalcin cites in support of his new semantics. A key collateral motivation for this defence of irredundant iterations is to ward off a threat to higher order vagueness

In ”Formal Problems about Knowledge,” Roy Sorensen examines epistemological issues that have logical aspects. He uses Fitch's proof for unknowables and the surprise test paradox to illustrate the hopes of the modal logicians who developed epistemic logic, and he considers the epistemology of proof with the help of the knower paradox. One solution to this paradox is that knowledge is not closed under deduction. Sorensen reviews the broader history of this maneuver along with the relevant alternatives model of knowledge which assumes that ”know” is an absolute term like ”flat.” Sorensen argues that the difference between epistemic absolute terms and extensional absolute terms gives rise to an asymmetry that undermines recent claims that there is a structural parallel between the supervaluational and epistemicist theories of vagueness, and he suggests that we have overestimated the ability of logical demonstration to produce knowledge.

Creationists believe that C. K. Chesterton created Father Brown in his detective stories. Since creating implies a creation, Father Brown exists. Atheists object that the same reasoning could prove the existence of God. But creationists such as Jonathan Schaffer insist atheists do believe that God exists. Serious metaphysics rarely concerns existence. The disagreement between the theist and the atheist is about the nature of God, not His existence. Schaffer underestimates the religious imagination. There could be a religion that explicitly regarded God as a fictional character. The tenets of this, presently hypothetical, religion are developed in a dialogue.

In “The Reappearing Act” István Aranyosi postulates a new way of seeing to solve a puzzle posed in “The Disappearing Act;” an object that is exactly shaded can be seen simply by virtue of its contrast with its environment – just like a shadow. This object need not reflect, refract, absorb or block light. To undermine the motive for this heretical innovation, I generalize the puzzle to situations involving inexact shading. Aranyosi cannot extend his solution to these variations because he needs to conserve principles of camouflage. On the bright side, the solution to the puzzle that I propose in my book Seeing Dark Things does extend to these variations.

The poster boy for my paper is the King's Messenger in Lewis Carroll's Through the Looking Glass. Recall that since the White Queen lives backwards, her memory works forwards. She pities Alice who can only remember things after they happen. Alice asks which things the Queen remembers best: `Oh, things that happened the week after next,' the Queen replied in a careless tone. `For instance, . . . there's the King's Messenger. He's in prison now, being punished: and the trial doesn't even begin till next Wednesday: and of course the crime comes last of all.' (Chapter V) Is the King's Messenger being treated unjustly? Why not prepunish people for their future crimes? True, it is generally easier to have knowledge about past crimes than future crimes. But is unpredictability the only problem with prepunishment?

What do you get when you cross a fallacy with a good argument? A fugu, that is, a valid argument that tempts you to reach its conclusion invalidly. You have yielded to the temptation more than you realize. If you are a teacher, you may have served many fugus. They arise systematically through several mechanisms. Fugus are interesting intermediate cases that shed light on the following issues: bare evidentialism, false pleasure, philosophy of education, and the ethics of argument. Normally, a fugu will not yield knowledge from known premises. But if the reasoning is only slightly fallacious, they do yield knowledge. These mild fugus show that we can gain knowledge by invalid reasoning. This is a conservative resource for historians. They want to credit discoveries to Euclid rather than those who made minor corrections to his proofs, such as David Hilbert. We also benefit from this practice of grandfathering in old standards of knowledge attribution. For we can compete spiritedly for priority. We do not need to worry that credit will instead go to future scholars who will make the minor amendments needed to raise present proofs to a future standard of demonstration

The principle of charity says that all agents are rational. The principle of meta‐charity says that all agents believe all agents are rational. My thesis is that the arguments which are used to support charity also support meta‐charity. Meta‐charity implies meta‐meta‐charity. By recursion, the principle of charity implies that it is common knowledge. But there appears to be intelligent, well‐informed disagreement with the principle of charity. So if the entailment thesis holds, opponents of the principle of charity have a new objection to the principle. Defenders of the principle of charity must either refute the entailment thesis or accept much stronger consequences than they expected.“As I am, so I see.”—Ralph Waldo Emerson.

If a spinning sphere casts a shadow, does the shadow also spin? This riddle is the point of departure for an investigation into the nature of shadow movement. A general theory of motion will encompass all moving things, not just physical objects. Ultimately, I argue that round shadows do indeed spin. Shadows are followers of the objects that cast them. Parts of the shadow correspond to parts of the leader, so motion of the caster's parts accounts for motions of the shadow's parts. I conclude with a discussion of how the dynamic aspects of shadows impose subtle constraints on other puzzles about shadows

A Brief History of the Paradox is the first narrative history of paradoxes. Sorenson draws us deep inside the tangles of riddles, paradoxes and conundrums by answering the questions which are seemingly unanswerable. Can God create a stone too heavy for him to lift? Can time have a beginning? Which came first, the chicken or the egg? Filled with illuminating anecdotes, A Brief History of the Paradox is vividly written and will appeal to anyone who finds trying to answer unanswerable questions a paradoxically pleasant endeavour.