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Working in philosophical logic, I love the opportunity to learn from so many people through history, and not only to learn, but to pass on a tradition, and to have the opportunity to extend the tradition, and to refine it a little, in passing it on. It’s been a delight to learn from some great figures, the historical figures through their writing, and my contemporaries in person, both as face-to-face teachers (while a student, I learned logic from Sheila Oates-Williams, Neil Williams, Rod Girle, Ian Hinckfuss, and Graham Priest), but the learning doesn’t stop when you finish your degree.

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In the previous entry I explored the connection between proofs and necessity. Here, I want to spend a little time exploring the other side of the logical street, the connection between models and possibility. As I have already explained, one core insight from 20th Century work in logic is the fundamental duality between proof theory and model theory. You can define logical notions like validity by way of proofs (a valid argument is certified by the existence of some proof) or by way of models (an argument is shown to be invalid by the existence of some model which serves as a counterexample).

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The next two thoughts are motivated by the two complementary aspects of contemporary research in logic, proof theory and model theory. As I try to emphasise to my students, there are two broad ways you can define logical concepts like validity. Following the way of proofs, an argument is valid if there is some proof leading from the premises to the conclusion. Following the way of models, an argument is valid if there is no model in which the premises are true and the conclusion is not.

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I’m not totally happy with the word for he next item on the list of twelve things I love about philosophical logic. The word on the list is attention, and it gets at something that I have learned, and which seems to me to be an important distinctive about working in philosophical logic, but I’m not altogether sure that “attention” is the best word for it. Maybe after I’ve explained what I mean, you could suggest a better short label for the phenomenon I’m gesturing towards.

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Some of my phrasing in the last two posts about what I love about philosophical logic have emphasised capacities, or abilities. I’ve described the pleasure of the “aha!” moment in terms of the kinds of mastery you acquire in handling the concepts you have, and I described the joys of conceptual expansion in terms of abilities gained. This is to take a pragmatic perspective on logic, to consider the connection to practices and actions.

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I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.

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