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Teaching experience

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Teaching statement

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Proposed courses 3.1 Early modern philosophy . . . . . . . . . . . . . . . . . 3.2 Metaphysics . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Philosophy of language . . . . . . . . . . . . . . . . . . . 3.4 Introduction to logic . . . . . . . . . . . . . . . . . . . . 3.5 Intermediate logic . . . . . . . . . . . . . . . . . . . . . . 3.6 Philosophy 420: Computability and incompleteness 3.7 Logic in action . . . . . . . . . . . . . . . . . . . . . . . .

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Sample materials

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Evaluations 5.1 Boston University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Boston College . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 University of British Columbia . . . . . . . . . . . . . . . . . . . . . .

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Teaching experience

As instructor, Boston University • Early modern philosophy (Spring 2015, Fall 2015, Spring 2016) • Critical thinking (Spring 2015, Fall 2015, Spring 2016) • Introduction to Philosophy (Fall 2014) • Puzzles and paradoxes (Fall 2014) As instructor, Boston College • Introduction to logic (Spring 2016) • Symbolic logic (Fall 2015) As instructor, University of British Columbia • Epistemology (Spring 2014) • Symbolic logic (Fall 2010, Fall 2011, Spring 2012) As teaching assistant, University of British Columbia • 17th century philosophy (three times) • 18th century philosophy (twice) • Intermediate logic (three times) • Introduction to philosophy (twice)

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Teaching statement

Teaching is an opportunity to make a real difference in students’ lives. Academic freedom also requires teachers to decide which effects to seek. As a philosophy teacher, I aim to transmit skilled practice of craft; I also hope that as they adjust their lives to the practice, students grow as people. Distinctively philosophical skills include intellectual patience and empathy, exact and serious self-expression, and the appreciation of moral and legal commitments. In developing these skills, different challenges arise in different kinds of course. Others are more general. History of philosophy. One challenge of teaching history of philosophy is to get students to engage with thinkers from alien cultural contexts. Students need to get some historical information to see what would have been at stake, what’s controversial, and what would have looked like progress. At the same time, my ultimate goal isn’t for students to learn history but for them to do philosophy. So I’ve organized my teaching of history of philosophy around the cultivation of intellectual empathy. Empathy involves appreciating another person’s predicament, and thereby anticipating their emotional or cognitive responses. For example, Descartes tried to show that scientific knowledge depends on knowledge of God. To 21st-century undergraduates, this looks like the project of a religious reactionary. I’ve found that Descartes’ character emerges more clearly against the background of two other figures, Aquinas the great theorist of tradition, and Galileo the anti-theoretical knowledge-maker. Descartes’ central aim is to show that knowledge of reality doesn’t depend on deference to any textual traditions; rather, the existence of the self, of God, and of the world, can be determined purely by the exercise of general intellectual capacities. In this way, Descartes becomes intelligible to students as consolidating the early modern shift in the source of epistemic authority, from traditional religious hierarchies to collegial scientific experimentalism. Logic. Courses in formal logic present a quite different range of challenges. As a graduate student, I begun teaching logic by emphasizing mastery of the formalism. For example, a natural deduction system is a formal model of the activity of deductive argumentation. I taught from my own lecture notes, since compiled into a free textbook, which presents natural deduction as a formal model of informal reasoning practice. I also wrote a free online tool for interactive proof 3

construction, which catches errors and returns instant feedback. But, this formalism can make logic look to students like a game, in which they just have to make the ‘right move’ while what’s ‘right’ may as well be arbitrary. Without exercises explicitly bridging the formal and informal realms, students become adept at manipulating the model without better understanding the unformalized activity which is what really matters. So in my last few rounds of teaching, I’ve begun courses with a couple of weeks on informal argumentation analysis. This topic proves challenging even for technically sophisticated students, while helping just about everyone. However, methods of “argument diagrams” in established informal logic textbooks rarely extend to standard deductive forms like proof by contradiction or proof by cases. Surprisingly, the earliest natural deduction system due to Gentzen actually constitutes such an extension already. I’ve begun working on a new approach to teaching natural deduction which exploits this link to deepen the coverage of application of logic in informal reasoning. Critical thinking. The first thing I learned from teaching critical thinking courses is that many students think of argument as an instrument of combat or coercion. I try to supplant these by illustrating the variety of epistemic contexts in which argumentative structures operate. For example, if an argument gives a reason to believe the conclusion, then the premises must be believed independently. So the effectiveness of an argument depends finding an audience which believes the premises but not the conclusion. This audience can be another person or it can be the speaker herself. Perhaps most typically, the authors of an argument are a group of people who combine their insights to expand their common knowledge. I’ve also found that while textbooks supply arguments already neatly potted and trimmed, students often struggle to recognize speech or thought as argumentative in their extracurricular experience. So last semester, I assigned students to contribute to the course website each week an example that they find in the course of their usual reading, and to evaluate arguments contributed by others. We chose particular posted topics to debate in small groups; the groups then each presented to the whole class their reasoned responses. In this way, the course encouraged students students to reinterpret aspects of their own lives. Classroom environment. Each course offering generates its own, semesterlong community, and the history of each of these communities makes an impact 4

on student lives. I try to promote a class environment which is inclusive, collegial and fair. A particular challenge in philosophy is its impoverishment as a discipline by its history of exclusion of women. Today, poor retention rates of female students through upper-division coursework are well-documented. The causes of this phenomenon are complex, but they probably include gender-specific or gender-troped content, classroom discussion dynamics, unconscious instructor bias, and preconception of philosophy as a ‘male’ discipline. In early modern philosophy, gendered oppositions like action versus passion or mind versus body can usefully be made explicit. Likewise, the traditional metaphor of argumentation as battlefield can be replaced by a model of reciprocal benefit through exchange of reasons. Personal characteristics. One particular challenge for me as a teacher is my own attitude to philosophy, which can be demanding: I don’t see philosophy as contest of wits but as a collective effort to understand. Pedagogically, I need to keep working to simplify, simplify, simplify. It’s best for a teacher to initiate a philosophical proposal, and leaving it open for students to find the objections. I’m also getting better at sticking with students who don’t arrive entirely serious about the subject. After all, my 19-year-old self became a serious philosopher only thanks to teachers’ patience. Finally, philosophy often appears in popular culture as entirely a matter of opinion: thanks partly to Hume, I’ve begun to find that this appearance can be countered not by dogmatism but by humility. Conclusion. So to summarize, my pedagogical principles are tempered by pragmatic willingness to improve through creative engagement with students and colleagues. Over a few years’ teaching experience, I’ve varied my approaches and tried new techniques in pursuit of various teaching objectives, and look for further steps to improve in the future.

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3 3.1

Proposed courses Early modern philosophy

We’ll investigate the origins, the successes and the failures of the modern conception of human beings. This conception originated with a revolt against the medieval scholastic fusion of Aristotelian metaphysics and Christian theology. In the medieval tradition, religious authorities provided a systematic account of the nature and purpose of human life at the center of an intelligibly ordered cosmos. But the moderns discovered things aren’t always what they seem: the earth isn’t the center of the universe, and objects don’t fall just because they’re supposed to. Maybe human beings are not essentially different from other living organisms, and maybe organisms are just complicated machines. Who’s to say what we really know? What kind of things are we, that we can discover the nature of things for ourselves? Modern philosophy begins with the rise of modern science and with Descartes’ application of scientific methods to the study of his own self. We’ll see that this drove him to great natural scientific achievements. But the deep conflicts in Descartes’ resultant self-understanding defined a set of problems for his modern successors. We’ll then turn to Spinoza, who on the one hand worked out an even more austerely naturalistic conception of the world, yet who on the other hand sought an explanation of naturalism itself, as the only means to blessedness. Both Descartes and Spinoza as well as Leibniz, however, maintained that through its innate knowledge or power of understanding, the mind is on its own a source of insight into the nature of reality. The empiricists worked to undermine this doctrine. For Locke, the mind is at its origin a tabula rasa; and for Berkeley, it is inconceivable that something exist unperceived. In Hume, the apparent rational structure of the world, and even the very existence of the human self—altogether dissolves into the patterns of habitual association in the play of ideas. In this course, our aim will be to engage in philosophical conversation with people like Descartes, Elisabeth of Bohemia, John Locke, etc. Biologically speaking, none of these people are alive anymore. So, their part in the conversation must be represented by our knowledge of their thought. We’ll need to develop that knowledge through study of their texts. This will be the starting point from which we can work toward insight into fundamental philosophical questions. Outline of readings.

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• Aquinas: Summa Theologica (excerpts on the human mind) • Galileo: “Letter to Christina” • Descartes: Discourse on Method; Optics; Meditations • Spinoza: Ethics (on God, humanity, and freedom) • Locke: Essay (on nativism, substance, and personal identity) • Berkeley: Dialogues (on reality and perception) • Hume: Enquiry (causality, laws of nature, and miracles); Treatise (on the self)

3.2

Metaphysics

The branch of philosophy known as metaphysics is an attempt to investigate fundamental features of reality, or features of reality which are of fundamental concern to human beings. After briefly surveying various conceptions of metaphysics over the course of human history, we’ll turn to particular metaphysical problems. First, What makes something a person? If a person has changed unrecognizably— even to themselves—then what makes them the same person? Is a person a physical object? Second, what is the nature of physical objects? Is an object determined by the identity of its parts? Is a statue the same as the lump of clay which composes it? Does anything have a cause? Does a causal relationship between two things imply that if one occurs then the other must occur too? What do causal relationships stand between, anway? Objects? events? facts? Finally, what do we mean by saying that something must happen, or that it might’ve happened? Is it merely a matter of definition, or is there something “out there” in the world which explains the difference? Do things have natures, or features which make them the things they are? And is anything ultimately more fundamental than anything else, after all? • What is metaphysics? – Aristotle, Metaphysics A1; Kant, Groundwork to any Future Metaphysics 7

– Carnap, “The elimination of metaphysics”; Fine “What is metaphysics?” • Persons – Sydney Shoemaker, “Personal Identity: A Materialist Account”, – Parfit, “Personal Identity” • Objects – Aristotle, Categories (excerpts) – Locke, Essay (excerpts) – Lewis, The Plurality of Worlds (excerpts); “The paradoxes of time travel” • Causation – Descartes, Principles of Philosophy (excerpts), Hobbes, De Corpore – Hume, Treatise (excerpts); Mill A System of Logic (excerpts); Mackie (excerpts) – Lewis “Causation”; “Postscripts to ‘Causation’ ”; Counterfactuals (handout) – Salmon Causality and Explanation (excerpts); Hitchcock “Salmon on Explanatory Relevance” – Hitchcock “The intransitivity of causation revealed in equations and graphs” – Cartwright “Causality: one word, many things”; Woodward “Causation with a Human Face” • Modality and grounding – Leibniz: Discourse on Metaphysics; Wittgenstein: Tractatus (excerpts) – Carnap: Meaning and Necessity (excerpts); Lewis The plurality of worlds (excerpts) – Kripke: “Identity and necessity”; Kripke, Naming and Necessity (excerpts); – Fine: “Essence and modality” – Fine: “The Question of Realism” 8

3.3

Philosophy of language

• Foundations – Frege: “On Sense and reference”; – Frege: “The Thought” – Moore: “The nature of judgment”; Russell, Principles of Mathematics, Chs. 4-5; – Russell: “On Denoting” • What is language about, and how? – Strawson: “On referring” – Donnellan: “Reference and definite descriptions”; – Putnam: “The meaning of meaning” (excerpts) – Kripke: Naming and Necessity, Lectures 1 and 2; • Is language a system? – Tarski: “On the semantic conception of truth and the foundations of semantics”; handout on Tarski’s theory of truth – Carnap: “The concept of intension for a robot”; handout on intensional semantics – Austin: “A plea for excuses”; Grice “Meaning” – Quine: “Two dogmas of empiricism”; Word and Object (excerpts); Chomsky: “Quine’s empirical assumptions” – Kripke On Rules and Private Language (excerpts)

3.4

Introduction to logic

The aim of this course is to promote student facility in the construction and evaluation of deductive arguments. The course falls into three units, representing successively finer analyses of the subject-matter. The course begins with an examination of informal argumentation practice. We’ll take the perspective that the primary function of argument is the extension of knowledge. More precisely, a good argument is one whose premises are 9

known, and which establishes further knowledge on their basis. We introduce the familiar method of argument diagramming to show that arguments are constructed by successive acts of inference. The second segment of the course introduces students to family of patterns of reasoning which depend only truth-functionality. A formal language is introduced and given a semantics via the usual truth-tables. We then elaborate the method of argument diagramming into the full-fledged natural deduction system. The segment concludes with applications of the logic of truth-functionality to the evaluation of natural language arguments. We then turn to predicate logic. After noting that not every logical consequence originates in truth-functionality, we enrich the formal language to represent the concepts of predication, equality, and generality. We then present a semantics and the resulting notions of truth, satisfaction, validity, and definability. After suitably elaborating the method of natural deduction, the course concludes with further construction and evaluation of deductive arguments in informal contexts. Outline • Informal logic – The function of arguments – The method of argument diagrams • Truth-functional logic – The language of truth-functional logic – Semantics: truth-tables, truth-values, and validity – Natural deduction • Quantificational logic – Predication, equality and generality in natural language – Semantics: structures, truth, validity and definability – Natural deduction extended • Dessert – Russell, “On denoting” 10

3.5

Intermediate logic

Reasoning practice depends on the fact that arguments fall into stepwise patterns of inference, with each step primitively recognizable as correct. This already suggests that reasoning itself can become the object of mathematical inquiry. This course is an introduction to the resulting field of study, mathematical logic. The goal of the course is to train students to think rigorously and precisely about abstractions. The first segment of the course presents some basic mathematical tools: first the method of proof by induction as applied to numbers, strings, and wellfounded trees, and second some naive set theory, concluding with a proof of Cantor’s theorem. A “diagnostic” homework assignment early in this segment will communicate, in both directions, a sense of the appropriate level of mathematical sophistication. The second segment introduces students to the metalogical perspective in the manageable special case of truth-functional logic. After presenting a system of natural deduction, we’ll identify some of its fundamental symmetries by investigating the class of admissible rules of inference. We show that the natural deduction system is equivalent to a Hilbert-style system, by proving that every Hilbert-style rule is admissible, and conversely that the Hilbert system satisfies the deduction theorem. We then turn to semantics. After showing that the notion of truth-functional derivability requires that if truth-functional logic has a truth-functional semantics, then the connectives must have their usual truthtables, we present a constructive and a Henkin-style proof of the completeness theorem, deducing the compactness, Post-completeness, and interpolation theorems as corollaries. The third and most substantial segment of the course investigates first-order logic as a purportedly exhaustive analysis of mathematically definite reasoning. After extending the notions of syntax and proof already developed, we establish the admissibility of a handful of convenient rules of inference, and introduce the notions of definitional extension and of interpretability between theories. We then turn to basic model theory. After defining and playing around with the concepts of truth, satisfaction and definability over a structure, we prove the completeness, compactness, Lowenheim-Skolem, interpolation and definability theorems. We then identify some expressive limitations of first-order logic, namely the existence of nonstandard models of arithmetic, and the nonabsoluteness of countability. After considering some extensions of first-order logic which purport to resolve these defects, the course concludes with a proof of Lindstrom’s 11

theorem and some reflections on its attendant analysis of the very concept of a logic. Outline • Truth-functional logic – Syntax and semantics; induction on wellfounded trees – Natural deduction and sequent calculus – Admissibility of inference rules – A constructive completeness proof • Predicate logic – Natural deduction extended – Interpretability and relative consistency – truth, satisfaction and definability – Definability, isomorphism, and elementary equivalence – The completeness theorem – Lowenheim-Skolem and compactness theorems – The definability and interpolation theorems

3.6

Logic in action

In recent decades logic has spread from the foundations of mathematics to find applications in a broad range of subjects. In this course, we’ll consider three families of application, following the presentation of van Benthem et al, Logic in Action. We’ll begin with a review of classical propositional logic. We’ll then introduce the classical modal operators, discuss their various interpretations, and develop the Kripke semantics. Then we’ll investigate the application of logic to knowledge. Classical logic regards propositions as either true or false; but we can also ask about a proposition whether or not it is known, and by whom. This motivates the introduction of modal operators representing state of knowledge of individual agents, and the 12

development of a system of epistemic logic. We’ll then use the logic of public announcements to move from representing information states to representing information change, and conclude with some applications to information security. We’ll then consider a logic of actions. The system begins from the insight that actions are logically structured as relations between states. Relational algebraic operations of union, composition, inverse then give a natural semantics for a purely imperative logic of action. We complete the construction of propositional dynamic logic by introducing query formulas to represent conditional actions as well. Outline • Classical background – Logic and life – Propositional logic • Modality – Interpretations of modality – Kripke frames • Knowledge – Logic and knowledge – Modelling knowledge change – Epistemic logic – Update – The logic of public announcements • Action – Actions as relations – Operating on relations – Propositional dynamic logic

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Sample materials

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http://www.whythis.net/teaching/f15bu/emo/about

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Early Modern Philosophy

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Philosophy 310, Fall 2015

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Boston University

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Course resources, including announcements, handouts, etc., will be posted here. Similarly the website contains a discussion forum. To access these you'll need to sign up at the site. It's pretty straightforward, but the routine goes like this: 1. from the course homepage, click signup 2. at the /signup page, enter a username, your email address and a password 3. at the next page, /affiliate, enter the code [[redacted for public circulation]] plus your name 4. check your email, and click on the link in the message you'll shortly receive 5. reload the course website.

Texts

Instructor: Max Weiss Office: 745 Commonwealth, Room 504 Office hours: Wednesday, 2:00-4:00 Email: [email protected] Meetings: 11-12:30 TTh, KCB 102

The following will be available in the campus bookstore: Descartes, Selected Philosophical Writings. Cambridge, 1988. Spinoza, The Essential Spinoza. Hackett, 2006. Hume, An Enquiry Concerning Human Understanding. Hackett, 1993. Kant, Prolegomena to any Future Metaphysics. Hackett, 2001.

Overview We will examine the origins, the successes and the failures of the modern conception of human beings, with special emphasis on the nature of human knowledge. This conception originated with a revolt against scholastic fusion of Aristotelian philosophy and Christian theology. began with the rise of modern science and with Descartes' application of scientific method to the study of his own self. But it drove him to a self-understanding as of a ghost in a machine. So we'll turn to Spinoza, who on the one hand worked out an even more austerely naturalistic conception of the world, yet who on the other hand sought an explanation of naturalism itself, as the only means to blessedness. Both Descartes and Spinoza as well as Leibniz, however, maintained that through its innate knowledge or power of understanding, the mind is on its own a source of insight into the nature of reality. But the empiricists worked to undermine this doctrine. For Locke, the mind is at its origin a tabula rasa; and in Hume, the faculty of reason altogether dissolves into the patterns of habitual association in the play of ideas. Finally, we'll consider Kant's attempt to overcome the empiricist challenge. For Kant, some knowledge does not depend on experience, namely knowledge of space and time; but this can be only because, for Kant, space and time do not pertain to things in themselves. So even though nature is governed by universal laws, those laws do not constrain the source of human action.

Readings not drawn from these texts will be circulated in class, and posted on the course website.

Coursework For the sake of evaluation, coursework will be divided into equally weighted units as follows: two papers (a unit each) four quizzes (two units total) final exam (two units) in-class and online participation (a unit each)

Papers Due dates for the two papers are as follows: Thursday, 29 October Thursday, 10 December

Website

The aim of each paper should be to complete an interesting philosophical task, by addressing an issue which arises from previous lectures and reading. Each paper has a strict maximum length of 1000 words.

The course website is at http://whythis.net/emo

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Quizzes and final exam

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The quizzes will be brief exercises designed to see that you've been reading the assigned texts and trying to make sense of them. Final exam questions will in general resemble quiz questions, perhaps with a couple of slightly longer-format exercises as well.

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The final exam will be given on 17 December 2015, 12:30-2:30pm in the same classroom as the usual class meetings.

Participation

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Thu, 03 Sep

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Tue, 08 Sep

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This divides into two equally-weighted components: in-class and online.

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The in-class component depends partly on attendance and partly on contributing to class discussion. A signin sheet will be passed around at each class meeting, and if you miss at most two classes, then your mark on this component is guaranteed to be at least a B.

Aquinas 1274: Excerpts on the Eucharist aquinas and aristotle [html] [pdf]

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The other component depends on participation in the forum. You should aim to compose a short post about once every other week. This post might either...

Descartes, *Discourse on Method* parts 1-3 Descartes,*Optics*

1. begin a new forum thread by presenting a question about, or objection to, the assigned reading 2. respond to another student's post.

Tue, 22 Sep Descartes, *Meditation 2* notes on meditation 2 [html] [pdf]

These should be about a pargraph long, though brief clarifying questions or comments might often be in order too. Note that posts which spark productive discussion, or even inspire your colleagues' papers, will be especially helpful to your online participation mark!

Tue, 29 Sep

Thu, 10 Sep Galileo 1615: Letter to Grand Duchess Christina Galileo 1632: *Dialogue on two world-systems* I (excerpts) from ptolemy to galileo [html] [pdf]

Thu, 17 Sep Descartes, *Meditation 1* notes on meditation 1 [html] [pdf]

Thu, 24 Sep Descartes, *Meditation 3*

Thu, 01 Oct quiz 1 notes on meditation 3 [html] [pdf]

Road map

Tue, 06 Oct Descartes, *Meditation 6* notes on meditations 4-6 [html] [pdf]

Here's the plan: Introduction (week 1) Aquinas and Galileo (week 2) Descartes (weeks 3-5) Spinoza (weeks 6-7) Locke (week 8) Berkeley (week 9) Hume (weeks 10-11) Kant (weeks 12-13) Legacies (week 14)

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Thu, 08 Oct Descartes, *Passions of the Soul*

Thu, 15 Oct Spinoza, *Ethics:* Book I diagram for ethics book i [pdf] notes on book i of spinoza's ethics [html] [pdf]

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Tue, 20 Oct notes on book ii of spinoza's ethics [html] [pdf]

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Tue, 27 Oct Locke 1690: Enquiry I Chs 1-3 (pages 1-12) notes on locke [html] [pdf]

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Tue, 03 Nov reading: berkeley, dialogue i [html] [pdf] notes on berkeley, dialogue i [html] [pdf]

Tue, 10 Nov Hume, *Enquiry*, sections 1-3 notes on hume's enquiry, sections i-iii [html] [pdf]

Tue, 17 Nov Hume, *Enquiry* sections 5-7 notes on hume's enquiry, sections v and vii [html] [pdf]

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Thu, 22 Oct quiz 2 notes on books iii-v of spinoza's ethics [html] [pdf]

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Locke 1690: Enquiry II Chs 1-2, 12, and 23 (pages 18-23, 43-45, and 97-100) paper #1

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Thu, 05 Nov

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Thu, 12 Nov Hume, *Enquiry* section 4 quiz 3 notes on hume's enquiry, section iv [html] [pdf]

Thu, 19 Nov Hume, *Enquiry* section 10

Tue, 24 Nov Tue, 01 Dec Hume 1739: Treatise, i pages 132-140 notes on hume on the self [html] [pdf]

Tue, 08 Dec Kant, *Prolegomena* notes on kant's prolegomena, ii [html] [pdf]

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notes notes on kant, iii (10 Dec) [html] [pdf] notes on kant's prolegomena, ii (08 Dec) [html] [pdf] notes on kant's prolegomena, i (03 Dec) [html] [pdf] quiz 4 (03 Dec) [pdf] notes on hume on the self (01 Dec) [html] [pdf] notes on hume's enquiry, section x (26 Nov) [html] [pdf] notes on hume's enquiry, sections v and vii (17 Nov) [html] [pdf] notes on hume's enquiry, section iv (12 Nov) [html] [pdf] bonus reading: hume's autobiography (11 Nov) [html] [pdf] notes on hume's enquiry, sections i-iii (10 Nov) [html] [pdf] notes berkeley, dialogue i cont'd (05 Nov) [html] [pdf] reading: berkeley, dialogue i (03 Nov) [html] [pdf] notes on berkeley, dialogue i (03 Nov) [html] [pdf] notes on locke (27 Oct) [html] [pdf] notes on books iii-v of spinoza's ethics (22 Oct) [html] [pdf] notes on book ii of spinoza's ethics (20 Oct) [html] [pdf] diagram for ethics book i (15 Oct) [pdf] notes on book i of spinoza's ethics (15 Oct) [html] [pdf] notes on meditations 4-6 (06 Oct) [html] [pdf] notes on meditation 3 (01 Oct) [html] [pdf] notes on meditation 2 (22 Sep) [html] [pdf] notes on meditation 1 (17 Sep) [html] [pdf] from ptolemy to galileo (10 Sep) [html] [pdf] aquinas and aristotle (08 Sep) [html] [pdf]

Thu, 03 Dec quiz 4 notes on kant's prolegomena, i [html] [pdf] quiz 4 [pdf]

Thu, 10 Dec paper #2 notes on kant, iii [html] [pdf]

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notes / Oct. 20, 2015 / notes on book ii of spinoza's ethics

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Review of Ethics I

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Monism: There is only one substance all "individual things" are modes of it the attributes of the substance are what the intellect perceives of it attributes include Thought and Extension, but there are infinitely many Whatever happens, happens of necessity Since Nature is infinite, whatever could happen does happen This implies that whatever happens, must happen1

Spinoza includes Thought and Extension among the attributes Since God is infinite, God has all attributes So God is a thinking thing and God is an extended thing

Attributes are explanatorily isolated (2p6) Each attribute must be conceived through itself (1p10) Cf. Descartes: M has a complete conception of I-as-a-thinkingthing, and a complete conception of a body-as-extended-thing So the modes of an attribute are to be explained only by other modes of that attribute, plus the general nature of that attribute itself Hence the motion and rest of bodies can be explained, an can only be explained, by the motion and rest of other bodies there cannot be any causal dependence of the body on the mind Likewise, the ideas of a mind cannot causally depend on states of the body.

Recall that in the Meditations, Descartes implicitly distinguishes between the order of knowledge and the order of nature For example, In the order of knowledge, your own existence is primary But in the order of nature, the existence of God is primary The Meditations follows the order of knowledge So in the Meditations, the sign of a starting point is certainty Starting points must be immune to the skeptical hypothesis The propositions of the Ethics do not follow the order of knowledge but the order of nature Thus, the starting points of the Ethics need not be intrinsically certain They become certain only after their role in constituting the order of nature is understood

Attributes are structurally parallel (2p7) In Part I Spinoza introduced as an axiom "The knowledge of an effect depends on, and involves, knowledge of its cause" (1a4). Now Spinoza claims that 1a4 implies "the order and connection of ideas is the order and connection of things" (2p7). So there is only one genuine order of ideas The ordering of ideas is the order of explanation It corresponds to the order of causality in their objects Note that causality includes relations between infinite modes dependence of one law on another relations between finite modes

Plan for Part II What is a human being? The order of ideas is the same as the order of things The mind, in the order of ideas, is the counterpart of the body in the order of things So the human mind and human body are one and the same thing, just conceived in different ways.

2015-12-29, 3:57 PM

Recall from Part I: An attribute is an explanatorily complete presentation of the nature of God Within each attribute you can distinguish the whole attribute itself infinite modes, which follow from the nature of the whole attribute i.e., eternal general structural properties of the attribute e.g., for extension, laws of physics finite modes, which follow from other finite modes i.e., temporary, particular features e.g., for extension, ordinary bodies

God is both thinking and extended (2p1-2)

Notes on epistemology

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dependence of one finite thing on another Recall that Descartes distinguished, in the realm of ideas, between order of justification and order of explanation Spinoza rejects this distinction For Spinoza there simply is no autonomous "order of knowledge"

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Finite things

notes

A thing is finite if it can be limited by another thing and finite "of its kind" if it can be limited by another thing of the same kind (1d2) Any finite thing is to be understood, in its existence and its activity, as the effect of other finite things as required by general laws (1p28) The causal history of finite things extends infinitely far both forward and backward God is the cause of a finite thing only insofar as some other finite things are considered to be part of God The existence of no finite thing follows from God's absolute nature immediately (2p9) Thus, to explain why any finite thing exists or acts in a certain way, you can only point to other finite things, and show how it follows from them according to more general (infinite) modes

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A mode of extension is really any portion of matter-in-space e.g., a dog, a dog and its owner, the top half of a dog and the bottom half of its owner, etc., are all more or less real modes of extension A bunch of stuff constitutes an individual to the extent that the stuff works together to produce an effect (cf. 2d7) Many things are caused by the parts of the dog working together to constitute a dog E.g., that we are out of kibbles A few things are caused by the dog-and-owner together e.g., walks and their consequences Hardly anything is caused by the top half of the dog and the bottom half of the owner Thus being an individual is a matter of degree Ultimately, individuality is itself to be explained in physical terms The dog is causally powerful because it consists of stuff which preserves a fixed ratio of motion and rest... E.g., nose and tail are at different ends of the body Hence Spinoza like Descartes rejects the Aristotelian appeal to form in explanation of (organic) unities

The mind is the idea of the body (2p13) The mind is an idea of something... but what? For each person there is an individual thing, a human body, such that when that body is affected, the person feels it (2a4) Thus, the affections of the human mind correspond to the affections of the human body So, it is reasonable to conclude that the object of the idea which constitutes the human mind is the human body

"all individuals, albeit in different degrees, are nevertheless animate" (2p13s) For every extended thing, there is in Thought an idea of it The idea of that thing stands to the thing just as the mind stands to the human body So, we might just as well say that not only human beings have minds but that all individuals do Isn't that nuts? Is the table sitting there wondering when this class is over?

Spinoza's human being No mention of a (human) person appears until Part 2: "The essence of man does not involve necessary existence; that 2015-12-29, 3:57 PM

The mind is an idea (2p11) For Spinoza, there is an idea, or mode of thought, which basically constitutes the human mind It is axiomatic that man thinks (2a2) Among the most fundamental thoughts of man are the desire to exist and the love of oneself But, Spinoza assumes, the idea of something desired or loved precedes the desire or love The idea of what is desired in the desire to exist is the same as the idea of what is loved in the love of oneself This idea is then the most fundamental manifestation of man under the attribute of thought But the most fundamental manifestation of man under the attribute of thought is the human mind So the idea of what is desired in the desire to exist, and the idea of what is loved in the love of oneself, is the human mind

Individuals

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is, from the order of Nature it is equally possible that a certain man exists or does not exist" (2a2) Thus, in the order of the Ethics, a person appears only after the structure of Nature-as-a-whole has been fixed Moreover, the appearance of persons is the appearance of the general kind human beings whereas in Descartes what appears first is the "first person", the I And the claim is precisely that the existence of any particular person is a metaphysical accident whereas in Descartes, the claim is that the existence of a human is an epistemic necessity

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Some bodies are more complicated and powerful than others Human bodies can move around, process stimuli from the environment, build hydrogen bombs, etc. It's these capacities that make humans intelligent Chairs don't have them, so chairs aren't intelligent Similarly: compare a living human body and a corpse

The human mind is composite (2p15) Recall that for Descartes, the human mind is simple and indivisible Spinoza strongly rejects this Being an individual is a matter of degree Minds are the ideas of individuals So being a mind is a matter of degree too Example: consider a person Tony i. just as he is ii. with a notebook iii. after three beers These three different ways of considering Tony pick out different individuals each individual has different set of cognitive capacities and so has a different "mind"

Perception (2p16) The human body contains various "soft" or "fluid" parts, which receive impressions from the external bodies which strike them (2post5) Since these impressions are caused by external bodies, an idea of such an impression depends on the idea of the external body The idea of this impression is what we call perception of the external body (2p16c1) This indicates that the nature of perception thus depends more on the nature and condition of your own body than it does on that of the body outside of it (2p16c2) The nature of your body determines what features of the external body can induce an impression on you at all () The condition of your nervous system, etc., determines how the impression propagates into you (e.g., as in the body of waking or sleeping person, etc.) 1. Proof. Suppose that P happens. And let W be an arbitrary possible world. Since P actually happens, this constitutes, at W , the possibility of the happening of P. But, since the infinitude of nature is necessary, therefore whatever might happen at W does happen at W . Hence, P happens at W . But W was arbitrary. Hence, if P actually happens, then P happens at every possible world. I.e., P happens necessarily if at all.↩

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Contents

Preface

Contents Preface

iii

1 Introduction

E. W. Beth

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2 Truth-functional logic 2.1 Assumptions . . . . . . . . 2.2 Conditional and negation . 2.3 Conjunction and disjunction 2.4 Absurdity . . . . . . . . . .

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3 Metatheory of truth-functional logic 3.1 Syntax of truth-functional logic . . . . 3.2 Proof theory for truth-functional logic 3.3 Semantics . . . . . . . . . . . . . . . . 3.4 Metatheorems . . . . . . . . . . . . . .

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monadic predicates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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80 . 80 . 97 . 99 . 104 . 109 . 112

4 Quantificational logic 4.1 Quantification with 4.2 Formalities . . . . 4.3 Semantics . . . . . 4.4 Polyadic predicates 4.5 Identity . . . . . . 4.6 Exercises . . . . .

Perhaps this study can be helpful in overcoming the obstacles created by undue moral rectitude.

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Index

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This is the second of an anticipated five drafts of an introductory logic textbook. This draft and its predecessor formed the bases of two oﬀerings of an introductory course at the University of British Columbia. The course was aimed primarily toward majors in philosophy and cognitive science. The book is intended to fill a seeming gap in the panoply of introductory logic material that is today available. The point of the book is to respect methodologically the viewpoint that logic is the study of the relationship of logical consequence. The notion of logical truth becomes a limiting special case. There are several courses of revision that future drafts should incorporate. In particular, future drafts should pursue systematically the analysis of informal deductive argumentation. Furthermore, Chapter 4 should split along the model of Chapters 2 and 3. And there can always be more exercises. I am indebted to the authors of three other introductions, each in its own way masterful: Beginning Logic by E. J. Lemmon, Logic: Techniques of Formal Reasoning by Kalish, Montague and Marr, and Deductive Logic by W. Goldfarb. I am indebted profoundly to the student participants in those two oﬀerings of Philosophy 220 for their generosity and resourcefulness. I’m also grateful to Paul Bartha, Roger Clarke, Yannig Luthra, and Ori Simchen for discussion and encouragement, and to Sanford Shieh, who taught me logic unbeknownst to himself. Suggestions for improvement of the book will almost certainly be justified. I’d be grateful to receive them. Max Weiss [email protected] December 1, 2011

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a statement and replace in it all its atomic statements with propositional variables, then the result is called a formula.

2.1

Chapter 2

Truth-functional logic A proposition is a truth-function of elementary propositions. Ludwig Wittgenstein

Our plan is now to agree on a system of rules of inference. The system will form a kind of workspace within which we can construct the derivations of sequents. By constructing a derivation of a sequent we will confirm that the sequent is logically valid. The correctness of an inference generally depends on the structure of the statements involved. Thus, a system of rules of inference reflects an analysis of the structure of statements. In this chapter we’ll develop the logic of those statements which are built up out of statements by means of truth-functions. In ordinary language, a truth-function is expressed by words like “not,” “and,” “or,” “if. . . then.” Such words, or their symbolic counterparts “¬,” “∧,” “∨,” “→” we will call truth-functional connectives. So the plan for this chapter is to study the logical relationships that hold between statements insofar as they are built up out of other statements using truth-functional connectives. By stating some rules of inference of truth-functional logic, we will exhaustively characterize those logical relationships that hold between statements in virtue of their truth-functional structure. Not every statement is built up out of others: for example, the statement “Socrates jumps” must, from the present perspective, be regarded as simple, as atomic. Although this statement does have parts, truth-functional logic has nothing to say about them. For this reason, in truth-functional logic it is convenient to represent atomic statements using the propositional variables “p,” “q,” “r,” and “s.”1 Then, instead of writing “we brought our umbrellas and the sun came out,” we might simply write instead “p and q,” or more elegantly “p ∧ q.” The essential point is that in any given context, diﬀerent atomic statements should be represented by diﬀerent variables. If, in this way, we take 1 If a hideously complicated problem requires more variables, then we introduce nonnegative integral subscripts, as in p0 , q0 , r0 , s0 , p1 , . . . .

9

Assumptions

As was noted at the conclusion of Chapter 0, the rules of inference are really actions on sequents. In general, an inference rule lets us construct a derivation of some new sequent given that we’ve constructed derivations of some other sequents already. But of course we have got to have some way to get oﬀ the ground in the first place. We need some initial rule to let us write down a sequent, and consider it thereby to be derived. However, we are insisting that the derivation of a sequent should make the validity of the sequent evident. So, since the initial rule will allow us to derive some sequents without any further evidence, the sequents it lets us derive must be valid self-evidently. Now, there is one very simple kind of sequent whose validity is indisputable, namely a sequent whose conclusion is the same as its hypothesis. Such a sequent had better be valid. A statement cannot go from true to false if we do not change the statement in any way. Thus, as initial rule we adopt the rule of assumptions, or asm. Now for an oﬃcial statement of the rule asm: For any formula A, for any step (k) of a derivation we can put (k) A asm [k] The main formula of step (k) is the formula A. In the citation the asm[k] following the formula, asm indicates the rule asm justifying this step. A line like (k) that is justified by the rule asm we will refer to as an assumption of the formula A. This rule is intended to model the practice with which often an argument begins, as in: “Suppose that Merkel and Berlusconi have a love child.” “Suppose that cats are cleverly disguised robots.” “Suppose that there is a largest prime number.” As these examples should indicate, we can assume absolutely anything we want, provided that it is an actual statement—i.e., something that is either true or false. Now, by applying the rule asm to a crazy statement like one just listed, we obtain a new line that has this statement as its conclusion. So it looks like we are actually aﬃrming such a crazy statement. The saving grace is that when applying the rule of assumptions, we assert the assumed statement under the hypothesis of that very statement, or assert the statement on the logical basis of that very statement. Logically speaking, when we assume a statement, our only commitment is to the fact that it is a logical consequence of itself. The rule of assumptions codifies our recognition of the validity of sequents of the form A ⊢ A. There are a couple of philosophical points to note about the rule of assumptions. You might wonder whether one can always be sure that whenever we utter a sentence twice, the second utterance must be true provided that the first utterance is true. Couldn’t a sentence become false over time? This is correct. For example, somebody might say to himself “she loves me” and then six months later again say to himself “she loves me;” and maybe it was true only once. But this is not really a counterexample, for 10

! " ! " ! " B B are derivations. Since (A → C) B P is the formula A P → C P , it follows by the mp clause that

and

is a derivation too. Hence

.. .. . ! " ! " ! " . ! " B B X B YB P ⊢ (A → C) P P ⊢AP ! " ! " B X,Y B P ⊢C P .. ... . X ⊢ (A → C) Y⊢A X,Y ⊢ C

! " is safe. The remaining clauses are similar: following the definition, push the B P through the main connective onto the immediate subformulas, and verify that the result is still an instance of the inference rule in question. The set S is thereby seen to satisfy property (II) as well. This means that every derivation belongs to S, hence that ! " every derivation is safe for the arbitrary substitution B P . Hence substitution preserves derivability.

4. Suppose that A, B ⊢ C is derivable but A ⊢ C is not derivable. Show that A ⊢ B is not derivable. 5. Suppose that B ′ ⊣⊢ B ′′ and C ′ ⊣⊢ C ′′ are derivable. Show that the following are also derivable: a) B ′ → C ′ ⊢ B ′′ → C ′′ ;

b) B ′ ∧ C ′ ⊢ B ′′ ∧ C ′′ ; c) B ′ ∨ C ′ ⊢ B ′′ ∨ C ′′ .

6. Show that the following rules are admissible in TF:

a) b) ‘Hypothetical syllogism’:

.. .. . . X ⊢A→B Y⊢B→C hs X,Y ⊢ A → C

Exercises

.. .. . . X ⊢A Y, A ⊢ B X,Y ⊢ B

c)

1. Construct a derivation of the following sequents in the style of Unit 1. To the right of each line of the derivation, write out the sequent whose derivation the line completes. Then, construct a tree proof of the same sequent. At every node of the tree proof, write out the number of the line in the first derivation that corresponds to this node.

d)

a) ¬(p ∨ q) ⊢ ¬p ∧ ¬q;

b) p ∨ q, ¬q ⊢ p;

.. . X,A → B ⊢ C X,B ⊢ C

f)

.. . X,A → B ⊢ A X ⊢A

2. Justify the following claims by constructing appropriate proof trees. a) If the sequent X ⊢ A ∨ (B → C) is derivable, then so is the sequent X ⊢ (A ∨ B) → (A ∨ C).

b) The sequent X ⊢ (A ∧ (B ∨ C)) is derivable if and only if the sequent X ⊢ (A ∧ B) ∨ (A ∧ C) is derivable.

g)

c) If X ⊢ ⊥ is derivable, then X ⊢ A is derivable for any formula A.

3. Suppose that either X ⊢ A is derivable or Y ⊢ B is derivable. Further suppose that Z ⊢ ¬(A ∨ B) is derivable. Show that X , Y, Z ⊢ ⊥ is derivable. 59

.. . X , ¬A ⊢ A X ⊢A

e)

c) p ∨ q, ¬q ∨ r ⊢ p ∨ r.

d) If A → B ⊢ C is derivable, then so is B ⊢ C.

... X ⊢A→C X,A ⊢ C

.. . X,A ∧ B ⊢ C X,B ∧ A ⊢ C

7. Show that the following rules are admissible in TF: a) ∧-i in the hypotheses: 60

• M |= ∃xA if and only if M |= A[no /x] for some object o in |M|; and • M |= ∀xA if and only if M |= A[no /x] for every object o in |M|. Say now for example that |M| is the set of all living people, and that F M is the set of people born in Hawaii. Let’s check whether M |= ∀x∃y(¬F x ↔ F y). Well, consider an arbitrary object o in |M|. Suppose on the one hand that o was born in Hawaii. Since Hillary Clinton was not born in Hawaii, therefore there is an o′ , namely Hillary, such that M |= ¬F no ↔ F no′ . On the other hand, suppose that o was not born in Hawaii. Since Obama was born in Hawaii, still there’s an o′ such that M |= ¬F no ↔ F no′ . Thus in either case there’s an o′ such that M |= ¬F no ↔ F no′ . So, by the definition of |= for existentially quantified formulas we have M |= ∃y(¬F no ↔ F y) for any object o. Hence it follows that M |= ∀x∃y(¬F x ↔ F y) by the definition of |= for universally quantified formulas.

4.4

Polyadic predicates

In this chapter we’ve begun to break down atomic formulas into predicates and terms. We’ve so far considered atomic formulas to have a structure like F t where F is a predicate and t is a term. That is, we’ve considered only predicates that produce a formula when combined with a single term. But consider the following example: (1) Mother Teresa loves everybody. [1]

sentence should be understood to contain two terms, say t for Mother Teresa and o for Obama. Suppose we introduce a new, dyadic predicate L, and write Lxy to say that x loves y. Then we can use Lto to say that Mother Teresa loves Obama. And the argument as a whole can be reconstructed as follows: (1) (2) (3)

∀yLty Lto ∃xLxo

asm [1] 1 ∀e [1] 2 ∃i [1]

Thus we’ve demonstrated the validity of the sequent ∀yLty ⊢ ∃xLxo. The demonstration requires that we introduce a new kind of predicate that is said to be dyadic because it produces a formula from not just one but two terms. The full development of quantificational logic requires not only predicates that are monadic but also predicates that are polyadic, combining together more than one term to produce an atomic formula. Happily, the introduction of polyadic predicates requires no new inference rules. Consider a slightly more complicate example. (1) All yoga teachers are narcissists. (2) So all children of yoga teachers are children of narcissists.

(2) So somebody loves Obama. [1] Using the technology developed so far, then the sentence assumed on step (1) could at best be understood to say that everybody has the property F , where to have the property F is to be loved by Mother Teresa. On the other hand, the conclusion drawn on step (2) would be understood to say that somebody has some other property G, namely the property of loving Obama. Thus, on the best analysis so far available, the sequent corresponding to step (2) would be represented ∀yF y ⊢ ∃xGx. And such a sequent had better not be derivable. Nonetheless, the validity of the argument just given is clear. We might spell it out in more detail: (1) Mother Teresa loves everybody. [1] (2) So Mother Teresa loves Obama. [1] (3) So somebody loves Obama. [1]

Write Y x to mean that x is a yoga teacher, N x to mean that x is a narcissist, and Cxy to mean that x is a child of y. Then the sequent corresponding to (2) can be represented like this: ∀x(Y x → N x) ⊢ ∀x(∃y(Y y ∧ Cxy) → ∃y(N y ∧ Cxy)). And a derivation is readily available: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

∀x(Y x → N x) ∃y(Y y ∧ Cay) Y b ∧ Cab Yb Y b → Nb Nb N b ∧ Cab ∃y(N y ∧ Cay) ∃y(N y ∧ Cay) ∃y(Y y ∧ Ca) → ∃y(N y ∧ Cay) ∀x(∃y(Y y ∧ Cxy) → ∃y(N y ∧ Cxy))

asm [1] asm [2] asm [3] 3 ∧e [3] 1 ∀e [1] 4, 5 mp [1, 3] 3, 6 tf [1, 3] 7 ∃i [1, 3] 2, 3, 8 ∃e [1, 2] 2, 9 cp [1] 10 ∀i [1]

It appears that (2) follows from (1) by ∀e, and that (3) follows from (2) by ∃i. In other words, first we instantiate the universal generalization in (1) to Obama; and then we existentially generalize from Mother Teresa in (2) to somebody in (3). The middle

Although the introduction of polyadic predicates does not call for any new rules of inference, the resulting language is incomparably more expressive. There are actually

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5

Evaluations

5.1

Boston University

1. Relevance of assigned readings 2. Difficulty of course (1=easy,5=difficult) 3. Workload (1=light,5=heavy) 4. Overall rating of discussion instructor 5. Overall rating of lab instructor 6. Usefulness of assignments and papers 7. Overall course rating 8. Effectiveness in explaining concepts 9. Ability to stimulate interest 10. Encouragement of class participation 11. Fairness in grading 12. Promptness in returning assignments 13. Quality of feedback to students 14. Availability of outside of class 15. Rating of instructor

100f14 3.7 3.9 3.5 3.3 NA 3.4 3.5 3.3 3.5 3.1 3.4 3.1 3.2 3.5 3.5

• 100f14 is Introduction to Philosophy, Fall 2014 • 261f14 is Puzzles and Paradoxes, Fall 2014 • 160s15 is Critical Thinking, Spring 2015 • 310s15 is Early Modern Philosophy, Fall 2015

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261f14 4.6 3.1 3.1 NA NA 3.8 3.7 3.4 3.5 3.8 4.1 4.0 3.6 4.2 3.7

160s15 3.7 3.3 3.3 4.2 4.1 3.9 3.7 3.4 3.5 3.5 4.0 3.8 3.7 3.9 3.7

310s15 4.5 3.2 3.1 NA NA 4.1 4.3 4.2 4.1 3.7 4.0 3.9 4.0 4.3 4.3

5.2

Boston College

1. The course was well organized. 2. The course generally followed the syllabus. 3. Class attendance was necessary for learning course material. 4. The course was intellectually challenging. 5. Compared to similar courses, the workload was heavy: 6. How would you rate this course overall? 7. The instructor was prepared. 8. The instructor was available for help outside of class. 9. The instructor returned assignments/tests conscientiously. 10. The instructor showed enthusiasm about the subject matter. 11. The instructor stimulated interest in the subject matter. 12. The instructor’s explanations were clear. 13. The instructor treated students with respect. 14. How would you rate this instructor overall as a teacher? • 5577f15 is Symbolic Logic, Fall 2015

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5577f15 4.5 4.6 4.8 4.8 4.3 4.0 4.8 4.5 4.8 4.8 4.0 4.3 4.3 4.0

5.3

University of British Columbia

1. The instructor made it clear what students were expected to learn. 2. The instructor communicated the subject matter effectively. 3. The instructor helped inspire interest in learning the subject matter. 4. Overall, evaluation of student learning was fair. 5. The instructor showed concern for student learning. 6. Overall, the instructor was an effective teacher. 7. student participation in class was encouraged by the instructor. 8. High standards of achievement were set. 9. The instructor was generally well prepared for class. 10. The instructor was readily available to students outside of class. 11. The instructor treated students with respect. 12. Considering everything how would you rate this course? 13. Considering everything, how would you rate this instructor? 14. Were the textbooks and/or readings used in this course appropriate for this course? • 220f10 is Symbolic Logic, Fall 2010 • 220f11 is Symbolic Logic, Fall 2011

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220f10 4.1

220f11 3.9

3.7

3.9

4.1

4.2

4.2 4.4 4.0 4.4

4.1 4.3 4.1 4.0

4.1 4.1 4.5

4.0 4.1 4.5

4.6 4.0

4.8 3.9

4.1

4.0

3.7

4.1