Science & Logic

What is mathematics about?

I commend to you James Franklin’s latest article “Mathematics as a Science of Non‑abstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics.)  ¶ Franklin approaches the dispute between these three views, and between alternative ways of spelling out the Aristotelian view, by way of the question: What is mathematics about?  The Platonist says that it is about a realm of abstract objects distinct from both the world of concrete material things and the human mind.  The nominalist says that it is not really about anything, since mathematical entities are in no way real.  The Aristotelian approach rejects nominalism and agrees with Platonism that mathematical entities are real.  But it disagrees with the Platonist about the location of these entities.  They are, for the Aristotelian, properties of concrete particular things themselves, rather than denizens of a Platonic “third realm.” But exactly what sort of properties of concrete particular things?  Franklin suggests that different views which can plausibly all be characterized as broadly “Aristotelian” have proposed different properties as the ones mathematics is paradigmatically concerned about.  Some say that mathematics is fundamentally about the study of quantity; some say it is fundamentally about relations; some say it is about structure; and some say it is about patterns.  Franklin discusses all of these possibilities and notes... -

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Duchamp on ‘Alien Thought’

In 1976, AI pioneer Joseph Weizenbaum described machinic reasoning as ‘alien thought.’ Weizenbaum reasoned that, since the domain of thinking was “determined by man’s humanity,” “every other intelligence, however great, must necessarily be alien.”’[i] Several decades later, the expression is used to mark the difference between algorithmic determinism of the ‘if you don’t pay your car insurance you’ll be automatically locked out of your car’ kind and the more mysterious machinic operations like incomputability. First discovered by mathematician Gregory Chaitin, incomputability arises from algorithmic indeterminacy.[ii] Both are notoriously difficult to understand in a qualitative, non-formulaic way; however they are similar to indeterminate artistic procedures, such as those pioneered by the ‘father of conceptual art’ Marcel Duchamp. ¶ Much of Duchamp’s early work, like his... -

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THE FATE OF ANALYSIS, #43–Is the Later Wittgenstein a Behaviorist? No.

TABLE OF CONTENTS I. Introduction                                                                                                 II. Classical Analytic Philosophy                                                                II.1 What Classical Analytic Philosophy Is: Two Basic Theses                                           II.2 What Classical Analytic Philosophy Officially Isn’t: Its Conflicted Anti-Kantianism              II.3 Classical Analytic Philosophy Characterized in Simple, Subtler, and Subtlest Ways II.4 Three Kinds of Analysis: Decompositional, Transformative, and... -

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Cameron Buckner will livestream “Understanding Adversarial Examples Requires A Theory Of Artifacts For Deep Learning” on April 16

We are excited about the next Neural Mechanisms webinar this Friday. As always, it is free. You can find information about how and when to join the webinar below or at the Neural Mechanisms website—where you can also join sign up for the mailing list that notifies people about... -

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Cameron Buckner will livestream “Understanding Adversarial Examples Requires A Theory Of Artifacts For Deep Learning” on April 16 We are excited about the next Neural Mechanisms webinar this Friday. As always, it is free. You can find information about how and when to join the webinar below or at the Neural Mechanisms website—where you can also join sign up for the mailing list that notifies people about upcoming webinars, webconferences, and more! Understanding Adversarial Examples Requires A Theory Of Artifacts For Deep Learning Cameron Buckner (University of Houston) 16 April 2021h14-16 Greenwhich Mean... Brains Blog -


THE FATE OF ANALYSIS, #43–Is the Later Wittgenstein a Behaviorist? No. TABLE OF CONTENTS I. Introduction                                                                                                 II. Classical Analytic Philosophy                                                                II.1 What Classical Analytic Philosophy Is: Two Basic Theses                                           II.2 What Classical Analytic Philosophy Officially Isn’t: Its Conflicted Anti-Kantianism              II.3 Classical Analytic Philosophy Characterized in Simple, Subtler, and Subtlest Ways II.4 Three Kinds of Analysis: Decompositional, Transformative, and Conceptual                 II.5 Frege, The First … [continue reading] Against Professional Philosophy -


Time Time Time is what a clock is used to measure. Information about time tells the durations of events, when they occur, and which events happen before which others. So, time plays a very significant role in the universe’s structure. Nevertheless, despite 2,500 years of investigation into the nature of time, there are many unresolved issues, … Continue reading Time → Internet Encyclopedia of Philosophy -


Hadrian the Seventh: extracts (16) baron corvoCatholicismFrederick Rolfehadrian the seventh Man Without Qualities -


What is mathematics about? I commend to you James Franklin’s latest article “Mathematics as a Science of Non‑abstract Reality: Aristotelian Realist Philosophies of Mathematics.”  It’s a helpful brief survey of different ways that an Aristotelian alternative to Platonist and nominalist approaches to mathematics might be developed.  (Franklin explores these issues in greater depth in his book An Aristotelian Realist Philosophy of Mathematics.)  Franklin approaches the dispute between these three views, and between alternative ways of spelling out the Aristotelian... Edward Feser -


Theory Change As we have seen in the previous article, Chapter 6 of Modal Empiricism presents various criticisms of the realist arguments. However, one of the most influential reason to doubt scientific realism is the so-called pessimistic induction (Laudan 1981). It rests on the observation that many theories of the past, even successful ones, are now replaced by better ones that posit a completely different ontology, and so, we have good reasons to think that the same... Modal Empiricism -


Exophilosophy: Aliens, Evolution, and Ethics The ctenophore’s brain suggests that, if evolution began again, intelligence would re-emerge because nature repeats itself. See the article, "Aliens in our midst" HERE.  The discovery of independent life beyond Earth would have deep philosophical implications for us, and our ideas of morality. "The Ethics of ET" HERE. After Nature -


Talk at Bilkent, April 12: Michael Trestman on Bee Consciousnes (Online Event) Title: Flower communication in social bees: a case study inbiophenomenology Speaker: Michael Trestman Psychology department seminar. Date: Monday, 12 April 2021Time: 16:30Zoom Meeting Information:https://zoom.us/j/8760742468?pwd=Q201VENwY09aUS9mb3hEcFpHSHA2UT09Meeting ID: 876 074 2468Passcode: 362441 Abstract: In this talk, I argue that behavioral, developmental,ecological, and evolutionary evidence support attributions ofconsciousness to bees, and further, that understanding the ways beesexperience their worlds is essential to fully understanding theirbehavior and evolution. For a conscious animal, the world as experiencedis a critically important component... Hesperous is Bosperous -


Philosophy talk at Boğaziçi: Sasha Mudd (Southampton/Pontificia Universidad Católica de Chile): Sasha Mudd on “A positive, capabilities-based account of epistemic justice.” 23/04/2021 – Via Zoom Sasha Mudd (Southampton/Pontificia Universidad Católica de Chile)will give a talk at Boğaziçi on Friday, April 23rd, 2021, 5.15 – 7pm (Istanbul time). Everyone welcome. Link: https://boun-edu-tr.zoom.us/j/97817367347 “A positive, capabilities-based account of epistemic justice.” ABSTRACT: In this paper, we deliver a positive, distributive, capabilities-based conception of epistemic justice, which is intended to improve upon Fricker’s canonical, failure-first, ‘discriminatory’ conception. We follow Fricker in taking Nussbaum’s capabilities-based approach to social justice as a starting point, however we go further... Hesperous is Bosperous -


Random QuoteThe position which is in process of becoming superseded wastes its polemical energies on fighting already outmoded features in the opposed view, and tends to see what is retained in the emerging position as only a deformed shadow of its own self.Georg Henrik von Wright (1916-2003) Philosophy by the Way -


Non-propositional representations I used to think that it’s quite possible that all our mental representations of the world are propositional in nature. To do that, I had to have a broad notion of proposition, much broader than what we normally consider to be linguistically expressible. Thus, I was quite happy with saying that Picasso’s Guernica expresses a proposition about war, a proposition that cannot be stated in words. Similarly, I was quite fine—my Pittsburgh philosophical pedigree comes... Alexander Pruss -


Symposium on Scott Scheall’s F. A. Hayek and the Epistemology of Politics New issue of C+T classical liberalismcosmos+taxisFriedrich HayekPolitical philosophyscott scheallsocial epistemology Man Without Qualities -


Num Nums My paper 'Negative Utility Monsters' is now forthcoming in Utilitas.  It's a very short and simple paper (2500 words, expanding upon this old blog post), but kind of fun.  Here's the conclusion:Nozick’s utility monster should no longer be seen as a damning objection to utilitarianism. The intuitive force of the case is undermined by considering a variant with immensely negative wellbeing. Offering significant relief to such a “Negative Utility Monster” plausibly should outweigh smaller harms... Philosophy, et cetera -


A Theory of Everything? In this episode, Philip Ball, Vanessa Seifert, and Jessica Wilson assess the prospects for a general theory of everything The Forum -


Believing is said of groups in many ways In defence of pluralism Recently, after a couple of hours discussing a problem in the philosophy of mathematics, a colleague mentioned that he wanted to propose a sort of pluralism as a solution. We were debating the foundations of mathematics, and he wanted to consider the claim that there might be no single unique foundation, but rather many different foundations, no one of them better than the others. Before he did so, though, he wanted... M-Phi -


James Booker: Audio Documentary Allen ToussaintFats DominoJames Bookermac Rebennacknew orleanspianoray charlesScott Billington Man Without Qualities -


Scientific Success Scientific realists assume that theoretical terms refer to natural properties, and that theories correctly describe how these properties are dynamically related in the world. This view requires an account of representation that is stronger than the one presented in chapter 3 of Modal Empiricism. Instead of assuming that the symbols of models are mapped to a context specifying empirically accessible properties, we should assume that they directly refer to real objects and properties in the... Modal Empiricism -


Best estimates and credences Some people think that expected utilities determine credences and some thing that credences determine expected utilities. I think neither is the case, and want to sketch a bit of a third view. Let’s say that I observe people playing a slot machine. After each game, I make a tickmark on a piece of paper, and if they win, I add the amount of the win to a subtotal on a calculator. After a couple of... Alexander Pruss -


A Confederacy of Dunces: extracts (48) Ignatius looked sternly at the young boy who had placed himself in the wagon’s path. His valve protested against the pimples, the surly face that seemed to hang from the long well-luricated hair, the cigarette behind the ear, the aquamarine jacket, the delicate boots, the tight trousers that bulged offensively in the crotch in violation… Man Without Qualities -


Hadrian the Seventh: extracts (15) baron corvoCatholicismFrederick Rolfehadrian the seventh Man Without Qualities -