Monday, 28 September 2015

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

By Catarina Dutilh Novaes
(Cross-posted at NewAPPS)

“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:

Monday, 7 September 2015

Cambridge Companion to Medieval Logic - Table of Contents

By Catarina Dutilh Novaes

(This post can be safely classified as an instance of shameless self-promotion, but here we go anyway...) Last week Stephen Read and I delivered the full manuscript of the forthcoming Cambridge Companion to Medieval Logic to Cambridge University Press. We still need to go through the whole production process (including indexing), but at this point it is safe to assume the volume will appear somewhere in 2016. We've been working on this volume for nearly 3 years, and so we are suitably thrilled to be nearing completion!

Many people asked me about the Table of Contents for the volume, and so I figured I might as well make it public -- now that we know there will not be any changes to chapters and/or contributors. Here it is:

0   Introduction – Catarina Dutilh Novaes and Stephen Read      

PART I: Periods and traditions

1   The Legacy of Ancient Logic in the Middle Ages – Julie Brumberg-Chaumont         
2   Arabic Logic up to Avicenna – Ahmad Hasnawi and Wilfrid Hodges  
3   Arabic Logic after Avicenna – Khaled El-Rouayheb      
4   Latin Logic up to 1200 – Ian Wilks          
5   Logic in the Latin Thirteenth Century – Sara L. Uckelman and Henrik Lagerlund   
6   Logic in the Latin West in the Fourteenth Century – Stephen Read  
7   The Post-Medieval Period – E. Jennifer Ashworth   

PART II: Themes
8   Logica Vetus – Margaret Cameron           
9   Supposition and properties of terms – Christoph Kann          
10 Propositions: Their meaning and truth – Laurent Cesalli        
11 Sophisms and Insolubles – Mikko Yrjönsuuri and Elizabeth Coppock           
12 The Syllogism and its Transformations – Paul Thom    
13 Consequence – Gyula Klima          
14 The Logic of Modality – Riccardo Strobino and Paul Thom      
15 Obligationes – Catarina Dutilh Novaes and Sara L. Uckelman 

Bridges 2 – Workshop at Rutgers

The Rutgers Philosophy Department and the Rutgers Center for Cognitive Science will be hosting a workshop (on Logic, Language, Epistemology, and Philosophy of Science) September 18-20. The workshop will bring together scholars from the NYC area, Amsterdam (the Institute for Logic, Language, and Computation), and Munich (the Munich Center for Mathematical Philosophy). The schedule for the workshop is posted on the Bridges 2 webpage:

The event is open to the public.