Learning objectives
The course aims to provide students with an introduction to the practice of philosophy with the tools of higher-order logic, that is to say, logic that allows quantification into terms of any logical type (singular terms, predicates, sentences, sentential operators, etc).
The goal will be implemented by (i) giving students the tools for understanding the notions, strategies, and overall direction of the (very much alive and in flux) debate on higher-order metaphysics; (ii) showing by way of specific case studies how higher-order thinking may constitute a net improvement over standard first- order thinking in the resolution of metaphysical problems; (iii) assessing the viability of the higher-order metaphysics research program by way of a cost- benefit analysis.
Prerequisites
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Course unit content
In the second half of the 20th century, philosophy was largely informed by W. V. O. Quine’s twofold metaontological thesis that (i) the notion of existence should be regimented in terms of the existential quantifier, and that (ii) quantification should be first-order. (First-order quantification is quantification into singular term position.)
Condition i, even though occasionally challenged, has essentially survived unscathed. Condition ii, on the other hand, is being questioned in a recent and sophisticated methodological turn that is associated with so-called ‘higher-order metaphysics’. Simply put, higher-order metaphysics is metaphysics carried out with the tools of higher-order logic.
Higher-orderists think, contra Quine, that quantifying into predicate or sentence position is both legitimate and indispensable. It is legitimate insofar as it is conceptually no less problematic than quantifying into singular term position. It is indispensable because it allows us to clarify, solve, or deflate a number of classical puzzles in metaphysics, logic, and philosophy at large.
The present course will provide an introduction to both higher-order logic and higher-order metaphysics, by reading, analyzing, and discussing some of the most impactful work from the last twenty years on the topic, as well as work in progress by influential logicians and metaphysicians. The overall goal is to understand to what extent it is possible, as well as desirable, to recast much of analytic philosophy in higher-order language, and so to jettison a core tenet of the Quinean wisdom.
Full programme
INTRODUCTION TO HIGHER-ORDER LOGIC
Readings: Sider, T. (ms1).
MOTIVATIONS FOR HIGHER-ORDER METAPHYSICS
Readings: Goodman (forth), Bacon (forth).
PROPERTIES AND HIGHER-ORDER METAPHYSICS
Readings: Hale (2013), Jones (2018), Liggins (2021).
IDENTITY AND HIGHER-ORDER METAPHYSICS Readings: Urbaniak (2009).
QUANTIFICATION AND HIGHER-ORDER METAPHYSICS Readings: Williamson (2003), Skiba (forth).
MODALITY AND HIGHER-ORDER METAPHYSICS Readings: Goodman (2016).
METHODOLOGY OF HIGHER-ORDER METAPHYSICS Readings: Sider (ms2), Hofweber (2022).
Bibliography
ESSENTIAL READINGS
Bacon, Andrew (forth). A Case For Higher-Order Metaphysics. In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics.
Goodman, Jeremy (2016). An Argument For Necessitism. Philosophical Perspectives 30 (1):160-182.
Goodman, Jeremy (forthcoming). Higher-order logic as metaphysics. In Peter Fritz & Jones Nicholas (eds.), Higher-Order Metaphysics. Oxford University Press.
Hale, B. (2013). Properties and the Interpretation of Second-Order Logic. Philosophia Mathematica 21 (2):133-156.
Hofweber, Thomas (2022). The case against higher-order metaphysics. Metaphysics 1 (5):29-50.
Jones, Nicholas K. (2018). Nominalist Realism. Noûs 52 (4):808-835.
Liggins, David (2021). Should a higher-order metaphysician believe in properties? Synthese 199 (3-4):10017-10037.
Sider, T. (ms1). Crash course on higher-order logic <https://tedsider.org/teaching/higher_order_20/higher_order_crash_course.pdf>
Sider, Ted (ms2). Higher order metametaphysics. <https://tedsider.org/papers/higher_order_metametaphysics.pdf>
Skiba, Lukas (forthcoming). Engineering Existence? Inquiry: An Interdisciplinary Journal of Philosophy.
Urbaniak, Rafal (2009). A Note on Identity and Higher Order Quantification. Australasian Journal of Logic 7:48-55.
Williamson, Timothy (2003). Everything. Philosophical Perspectives 17 (1):415– 465.
FURTHER READINGS
Fritz, Peter & Jones, Nicholas K. (eds.) (forthcoming). Higher-order Metaphysics. Oxford University Press.
Krämer, Stephan (2014). Semantic values in higher-order semantics. Philosophical Studies 168 (3):709-724.
Skiba, Lukas (2021). Higher-order metaphysics. Philosophy Compass 16 (10):1-11.
Trueman, Robert (2020). Properties and Propositions: The Metaphysics of Higher- Order Logic. Cambridge: Cambridge University Press.
Teaching methods
The teaching method will abide by the standards of logically informed analytic philosophy, which involves the presentation of theories and models by means of clear and rigorous definitions, which are then discussed, challenged, and put to test against a range of data, as well as formal results. The method is designed to optimize the understanding of a major ongoing shift, namely the shift to a higher- order conception of metaphysics.
Assessment methods and criteria
Esame orale.
Other information
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