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
Knowledge of first-order classical logic is an essential prerequisite. Cursory knowledge of set theory is recommended. For those who need to brush up on these topics, the following texts are recommended.
Logic:
Enderton, H. B. (1972). A mathematical introduction to logic. Academic Press.
Ch. 0-2.
Set theory:
Enderton, H. B. (1977). Elements of set theory. Academic press.
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 (ms1).
MOTIVATING HIGHER-ORDER METAPHYSICS.
Readings: Rayo & Yablo (2001), Bacon (2024).
SEMANTICS
Readings: Krämer (2014)
PROPERTIES
Readings: Jones (2018)
METHODOLOGY
Readings: Sider (ms2)
Bibliography
MANDATORY READINGS
Bacon, Andrew (2024). A Case For Higher-Order Metaphysics. In Peter Fritz & Nicholas K. Jones (eds.), Higher-order Metaphysics.
Jones, Nicholas K. (2018). Nominalist Realism. Noûs 52 (4):808-835.
Krämer, Stephan (2014). Semantic values in higher-order semantics. Philosophical Studies 168 (3):709-724.
Rayo, Agustin & Yablo, Stephen (2001). Nominalism through de-nominalization. Noûs 35 (1):74–92.
Sider, T. (ms1). Crash course on higher-order logic <https://tedsider.org/teaching/higher_order_20/higher_order_crash_cours e.pdf>
Sider, Ted (ms2). Higher order metametaphysics. <https://tedsider.org/papers/higher_order_metametaphysics.pdf>
OPTIONAL READINGS
Goodman, Jeremy (2016). An Argument For Necessitism. Philosophical Perspectives 30 (1):160-182.
Goodman, Jeremy (2024). Higher-order logic as metaphysics. In Peter Fritz & Jones Nicholas (eds.), Higher-Order Metaphysics. Oxford University Press.
Hofweber, Thomas (2022). The case against higher-order metaphysics. Metaphysics 1 (5):29-50.
Liggins, David (2021). Should a higher-order metaphysician believe in properties? Synthese 199 (3-4):10017-10037.
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.
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.
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
Oral examination.
Other information
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