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Easy as 1, 2, 3 ? -- Wittgenstein on counting

By Catarina Dutilh Novaes

(Cross-posted at M-Phi)

 

“A B C

It's easy as, 1 2 3

As simple as, do re mi

A B C, 1 2 3

Baby, you and me girl”

45 years ago, Michael Jackson and his troupe of brothers famously claimed that counting is easy peasy. But how easy is it really? (We’ll leave aside the matter of the simplicity of A B C and do re mi for present purposes!)

Counting and basic arithmetic operations are often viewed as paradigmatic cases of ‘easy’ mental operations. It might seem that we are all ‘born’ with the innate ability for basic arithmetic, given that we all seem to engage in the practice of counting effortlessly. However, as anyone who has cared for very young children knows, teaching a child how to count is typically a process requiring relentless training. The child may well know how to recite the order of numbers (‘one, two, three…’), but from that to associating each of them to specific quantities is a big step. Even when they start getting the hang of it, they typically do well with small quantities (say, up to 3), but things get mixed up when it comes to counting more items. For example, they need to resist the urge to point at the same item more than once in the counting process, something that is in no way straightforward! 

The later Wittgenstein was acutely aware of how much training is involved in mastering the practice of counting and basic arithmetic operations. (Recall that he was a schoolteacher for many years in the 1920s!) Indeed, counting and adding objects can be described as a specific and rather peculiar language game which must be learned by training, and which raises all kinds of philosophical questions pertaining to what it is exactly that we are doing when we count things. Perhaps my favorite passage in the whole of the Remarks on the Foundations of Mathematics is #37 in part I: 

Formal Methods in Philosophy: a Brief Introduction (Part I)

By Catarina Dutilh Novaes

(Cross-posted in M-Phi)

There is a Bloomsbury Philosophical Methodology Reader in the making, being edited by Joachim Horvath (Cologne). Joachim asked me to edit the section on formal methods, which will contain four papers: Tarski's 'On the concept of following logically', excerpts from Carnap's Logical Foundations of Probability, Hansson's 2000 'Formalization in philosophy', and a commissioned new piece by Michael Titelbaum focusing in particular (though not exclusively) on Bayesian epistemology. It will also contain a brief introduction to the topic by me, which I will post in two installments. Here is part I: comments welcome!

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Since the inception of (Western) philosophy in ancient Greece, methods of regimentation and formalization, broadly understood, have been important items in the philosopher’s toolkit (Hodges 2009). The development of syllogistic logic by Aristotle and its extensive use in centuries of philosophical tradition as a formal tool for the analysis of arguments may be viewed as the first systematic application of formal methods to philosophical questions. In medieval times, philosophers and logicians relied extensively on logical tools other than syllogistic (which remained pervasive though) in their philosophical analyses (e.g. medieval theories of supposition, which come quite close to what is now known as formal semantics). But the level of sophistication and pervasiveness of formal tools in philosophy has increased significantly since the second half of the 19^th century. (Frege is probably the first name that comes to mind in this context.)

It is commonly held that reliance on formal methods is one of the hallmarks of analytic philosophy, in contrast with other philosophical traditions. Indeed, the birth of analytic philosophy at the turn of the 20^th century was marked in particular by Russell’s methodological decision to treat philosophical questions with the then-novel formal, logical tools developed for axiomatizations of mathematics (by Frege, Peano, Dedekind etc. – see (Awodey & Reck 2002) for an overview of these developments), for example in his influential ‘On denoting’ (1905). (Notice though that, from the start, there is an equally influential strand within analytic philosophy focusing on common sense and conceptual analysis, represented by Moore – see (Dutilh Novaes & Geerdink forthcoming).) This tradition was then continued by, among others, the philosophers of the Vienna Circle, who conceived of philosophical inquiry as closely related to the natural and exact sciences in terms of methods. Tarski, Carnap, Quine, Barcan Marcus, Kripke, and Putnam are some of those who have applied formal techniques to philosophical questions. Recently, there has been renewed interest in the use of formal, mathematical tools to treat philosophical questions, in particular with the use of probabilistic, Bayesian methods (e.g. formal epistemology). (See (Papineau 2012) for an overview of the main formal frameworks used for philosophical inquiry.)

Facing the facts - Wittgenstein as a Kantian? (guest post)

For my MA course on Wittgenstein earlier this year, students had to write a short essay, blog post-style, on the Tractatus. One of them, Joseph Wilcox, took up the challenge of asking what exactly it means to say that Wittgenstein's project in the Tractatus is essentially a Kantian project -- something I kept hammering on them relentlessly. (To me at least this seems like the best and perhaps the only way I can make sense of the Tractatus!) The result is the insightful post below. (Proud teacher here!)

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By Joseph Wilcox

Wittgenstein [in the Tractatus] is a Kantian philosopher. Or so I'm told.

What exactly does it mean to say that someone is a Kantian philosopher? I always find it hard to grasp what is meant by such comparisons. Is it some fundamental belief that they share? Is it a field of thought that they both enter into? Is it a common goal that guides their thinking?

As often seems to be the case when it comes to philosophy, I am inclined to say that all the options must have some truth to them. In the case of Wittgenstein, however, I've been led to believe that it is the goal he sets out to achieve that forms the main connection between him and the lifework of his Prussian predecessor. What is it then, that both of these thinkers desire above everything else? The answer is to limit. To designate a point or level beyond which something does not or may not extend or pass. To place a restriction on the size or amount of something permissible or possible. On first looking, this doesn't seem like a very encouraging, confident or even useful objective. Why in the world would we bother to spend our precious time thinking about that which we can't reach? Isn't it far more interesting to seek to pass over such borders? Isn't it more inspiring to think that the impossible can serve as a beacon to aspire to? Isn't the thought of placing limits a token of the kind of pessimism that might cause one to give up hope?

Foucault And Kripke On Names And Rigid Designators

By: Samir Chopra

In 'What is An Author', Michel Foucault writes:

Conceptual genealogy for analytic philosophy - Part III.1: Genealogy as vindicatory or as subversive

This is the sixth installment of the series of posts on my conceptual genealogy project.  Part I is here; Part II.1 is here; Part II.2 is here; Part II.3 is here; Part II.4 is here; a tentative abstract of 2 years ago, detailing the motivation for the project, is here. 

In this post, I discuss in more detail the two main categories of genealogy that were mentioned in previous posts: vindicatory and subversive genealogies.

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III. Applications of genealogy

In the spirit of the functionalist, goal-oriented approach adopted here, a pressing question now becomes: what’s the point of a genealogy? What kind of results do we obtain from performing a genealogical analysis of philosophical concepts? I’ve already mentioned vindication and subversion/debunking en passant along the way, but now it is time to discuss applications of genealogy in a more systematic way.[1]

III.1 Genealogy as vindicatory or as subversive

By now, it should be clear that genealogy is a rather plastic concept, one which can be (and has been) instantiated in a number of different ways. Craig offers a helpful description of a range of options:

[Genealogies] can be subversive, or vindicatory, of the doctrines or practices whose origins (factual, imaginary, and conjectural) they claim to describe. They may at the same time be explanatory, accounting for the existence of whatever it is that they vindicate or subvert. In theory, at least, they may be merely explanatory, evaluatively neutral (although as I shall shortly argue it is no accident that convincing examples are hard to find). They can remind us of the contingency of our institutions and standards, communicating a sense of how easily they might have been different, and of how different they might have been. Or they can have the opposite tendency, implying a kind of necessity: given a few basic facts about human nature and our conditions of life, this was the only way things could have turned out. (Craig 2007, 182)

Conceptual genealogy for analytic philosophy - Part II.1: Nietzschean Genealogy

By Catarina Dutilh Novaes

This is the second installment of my series of posts with different sections of the paper on conceptual genealogy that I am working on. Part I is here; a tentative abstract of 2 years ago, detailing the motivation for the project, is here. 

I now present some of the basics of Nietzschean genealogy which will then be central for my general project. The goal here is thus not to offer a thorough account of Nietzsche's thought on the matter, obviously (a lifelong project!), but it should still be an accurate presentation of some aspects of it. If that is not the case, please do let me know! (I rely mostly on Geuss' and Leiter's interpretations.) Feedback in general is more than welcome.

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The mundane, commonsensical sense of genealogy is typically related to the idea of vindication, i.e. of validation of one’s authority through the narrative of one’s origins. This is particularly conspicuous in historical disputes for political power within the traditional monarchic model: a contestant has a claim to the throne if she can prove to be a descendent of the right people, namely previous monarchical power-holders. In such cases, a genealogy is what Geuss (1994, 274) describes as ‘tracing a pedigree’, a practice as old as (Western?) civilization itself. The key idea is the idea of transmission of value: a person with noble ancestry inherits this status from her ancestors.

Conceptual genealogy for analytic philosophy - Part I: Analytic philosophy and the a-historical conception of philosophy

By Catarina Dutilh Novaes

As some readers may recall (see this blog post with a tentative abstract -- almost 2 years ago!), I am working on a paper on the methodology of conceptual genealogy, which is the methodology that has thus far informed much of my work on the history and philosophy of logic. Since many people have expressed interest in this project, in the next couple of days I will post the sections of the paper that I've already written. Feedback is most welcome!

Today I post Part I, on the traditionally a-historical conception of philosophy of analytic philosophers. Tomorrow I will post Part II.1, on Nietzschean genealogy; on Thursday and Friday I will post Part II.2, on the historicity of philosophical concepts, in two installments.

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Wiliams (2002) and Craig (2007) fittingly draw a distinction between genealogies that seek to expose the reprehensible origins of something and thereby decrease its value, and genealogies that seek to glorify their objects by exposing their ‘noble’ origins. The former are described as ‘subversive’, ‘shameful’ or ‘debunking’, while the latter may be dubbed ‘vindicatory’. (I will have much more to say on this distinction later on.) Nietzsche’s famous genealogical analysis of morality is the archetypal subversive genealogy, and has given rise to a formidable tradition of deconstruction of concepts, values, views, beliefs etc. by the exposure of their pudenda origo, their shameful origins. As described by Srinivasan (2011, 1),

Nietzsche’s innovation prompted a huge cultural shift towards subversive genealogical thinking – what might be called the ‘Genealogical Turn’ – including Freudian analysis, 20th-century Marxism, Foucault’s historical epistemology, certain strands of postcolonial and feminist theory, and much of what goes by the label ‘postmodernism’. These ideological programmes operate by purporting to unmask the shameful origins – in violence, sexual repression, gender or racial hegemony and economic and social oppression – of our concepts, beliefs and political structures.

What is the (recent) history of the term ‘intuitions’ in philosophy?

By Catarina Dutilh Novaes

As reported a few weeks ago, I’ve been working on a paper with my student Leon Geerdink (for a volume on the history of early analytic philosophy being edited by Chris Pincock and Sandra Lapointe) where we elaborate on a hypothesis that I first presented in a blog post more than 3 years ago: that the history of analytic philosophy can to a large extent be understood as the often uneasy interplay between Russellianism and Mooreanism, in particular with respect to their respective stances on the role of common sense for philosophical inquiry. In the first part of the paper, we present an (admittedly superficial and selective) overview of some recent debates on the role of intuitions and common sense in philosophical methodology; in the second part we discuss Moore and Russell specifically; and in the third part we discuss what we take to be another prominent instantiation of the opposition between Russellianism and Mooreanism: the debate between Carnap and Strawson on the notion of explication.

The paper is now almost ready (and we’d be happy to share the draft if anyone is interested), but one puzzle remains: when and how did the term ‘intuitions’ begin to be used in the philosophical literature in its current sense(s)? (As argued by C.S.I Jenkins, the term seems to be used in different senses in the current debates.) As established by Leon, Russell and Moore do not use the term ‘intuitions’ in any of these senses (and in particular, not in the sense of common sense and folk beliefs); instead, they use the term in the technical, largely Kantian, sense of immediate knowledge. We have not found occurrences of the term in the Carnap/Strawson debate either.

Does anyone know the answer to this pressing question? The SEP entry on intuitions is silent on the history of the terminology, and I haven’t found any discussions of this issue in the recent papers I’ve been reading for this project (maybe I’m missing something?). Not much hinges on this matter for the purposes of my paper with Leon, but it did make us curious. Perhaps our knowledgeable readers know the answer? We hope so!

 

Intuitions and common sense in recent debates on philosophical methodology

By Catarina Dutilh Novaes

I am working on a paper now (together with my student Leon Geerdink, for a volume on the history of early analytic philosophy being edited by Chris Pincock and Sandra Lapointe) where I elaborate on a hypothesis first presented at a blog post more than 3 years ago: that the history of analytic philosophy can to a large extent be understood as the often uneasy interplay between Russellianism and Mooreanism, in particular with respect to their respective stances on the role of common sense for philosophical inquiry. In the first part of the paper, we present an (admittedly superficial and selective) overview of some recent debates on the role of intuitions and common sense in philosophical methodology; in the second part we discuss Moore and Russell specifically, and in the third part we discuss what I take to be another prominent instantiation of the opposition between Russellianism and Mooreanism: the debate between Carnap and Strawson on the notion of explication.

I am posting here a draft of the first part, i.e. the overview of recent debates. I would be very interested to hear what readers think of it: is it at least roughly correct, even if certainly partial and incomplete? Are the categories I carved up to make sense of these debates helpful? Can they be improved? Feedback would be most welcome!

UPDATE: I forgot to mention that a paper that has been extremely useful for me to organize my thoughts on this topic is Michael Della Rocca's 'The taming of philosophy', which gets quite extensively discussed in other sections of my paper with Leon. It is an excellent paper. However, there is still a substantive disagreement between Della Rocca and us, namely that we think there is a lot more tension between Russell and Moore on the question of common sense's role for philosophy than Della Rocca recognizes (he describes both Moore and Russell as fans of common sense).

Firing the Canon?

With Robert Brandom (and for recognizably Hegelian reasons) I think that Whig histories are necessary. I also agree with conservative critics that American English departments damaged their own enrollments when the 1980s attacks on the canon led to too sweeping curricular changes. In every field, it's very important for students to master a Whig history that allows them to critically engage with contemporary work and that gives them an analogical jumping off point to apply their knowledge elsewhere. And students know this.

I also agree about 90% with Brandom on how this Whig history should be put together for philosophy. A philosopher must understand Kant, how Kant led to Hegel, how (and hopefully why with respect to the 19th century) Hegel was finally suppressed in the "back to Kant" movement, how phenomenology and logical positivism pushed the neo-Kantian moment to its breaking point, and how contemporary philosophy is a reaction to the agonies and ecstasies of positivism and phenomenology.

But as helpful commentators (Peter Gratton, Robin James, Ed Kazarian, Carl Sachs, James K. Stanescu (AKA Scu), and various anonymous people) pointed out in this thread's discussion, the Brandomian Whig history is populated exclusively by white males, which is extraordinarily problematic for reasons adumbrated there. What to do about this?

Schliesser on Geach and Anscombe

Eric has some very interesting things to say here, about giving credit where credit is due, and about boundary-enforcing in philosophy.