Logic for the Blind as a Stimulus for the Design of Innovative Teaching Materials

Laurence Goldstein

Department of Philosophy
University of Kent, Canterbury - UK


I. The value of logic. Learning logic via the extended mind. The relevance of Howard Gardner’s theory of multiple intelligences.

W.V. Quine famously said “Logic is an old subject, and since 1879 it has been a great one” (p.vii of the preface to the first two editions of Methods of Logic). Quine was wrong and, to his credit, withdrew that remark from subsequent editions of that text. Not only (as Putnam pointed out) is the remark a slight to Boole; it also betrays ignorance of a wonderful mediaeval tradition that included Bradwardine, Buridan and Ockham and, most importantly, ignores Aristotle, the father of logic, who had the sensational idea that, like plants and animals, the content of what comes out of people’s mouths when they are debating, or reasoning to a scientific conclusion, can be taxonomized. And, further, that bad arguments can, with mathematical precision, be objectively shown to be such, thereby decisively settling disputes. Aristotle, of course, discussed only a rather narrow range of arguments, but his work held sway and was rightly revered for over two thousand years. The subject that Aristotle inaugurated is among those like History, Literature and Physics, that are not only of deep interest, but are totally absorbing and can shape a person’s personality and outlook on the world.

Those of us who are practising logicians know the extent to which we are reliant on writing things down and on manipulating symbols. In the jargon of a now fashionable view, we extend our minds because such manipulation that occurs outside the cranium is indispensable to developing ideas and proving results. In this way, the discipline is different from music, where great composers like Mozart can create whole symphonies in their heads, and juggling notes on paper is not the typical method of composing. In logic, we devise notations that are concise, economical and not unwieldy. Frege defends his two-dimensional concept-script (Begriffsschrift) on the grounds of its perspicuity. He argues that ‘the separate contents are clearly separated from each other, and yet their logical relations are easily visible at a glance (CN: 97; Kanterian 51-3). He further argues that written signs last longer than sounds, have sharp boundaries and are thus excellent tools for precise inference. Sounds are temporal and so do not reflect logical relations which, according to Frege are best displayed pictorially, invoking spatial intuition (Kanterian: 53). All this, of course, is bad news for the blind logician. But, reverting to our comparison with music, Beethoven, when deaf, was able to hear the music in the written score. Conversely, one might hope that the blind logician may be able to utilize a modality other than sight for doing logic. In the terminology of Howard Gardner’s theory of multiple intelligences, this would be a matter of invoking another intelligence to reduce reliance on the spatial-visual intelligence.


II. An illustration: A device by means of which blind people learn syllogistic: rationale, design, testing for effectiveness. Capturing beauty.

I shall demonstrate a device of my own design, built in the Haking Wong Engineering workshop of the University of Hong Kong, that is a tactile counterpart of the Venn-diagrammatic method of testing syllogisms for validity. Because there is an effective method for determining the validity of an arbitrary syllogism, it is easy enough to devise a computer program such that the blind user could type in 3 sentences (the premises and conclusion), hit a button, and be supplied with the verdict ‘valid’ or ‘invalid’. The educational value of this to the user would be close to zero, because the user would learn nothing about associating such sentences to relations between classes, or of existential import, or of the notion of the containment of a conclusion within the premises etc.. In other words, the user would not come to understand what is fascinating and beautiful about syllogistic. Any device that one invents needs to inculcate deep (as opposed to superficial) learning, while also being easy to use. Almost inevitably, prototypes will turn out to be defective or non-optimal in certain respects, and there may be a lengthy process of refining the design through repeated testing. The same is true of the users’ manual.






III. Extension of the dog-legged approach to the design of innovatory teaching materials.

Having invested a lot of thought into the design of teaching some aspect of logic to the blind user, some obvious questions present themselves. Will the device be a suitable learning instrument for the sighted user; in other words, is it more effective than traditional methods for teaching this particular aspect of logic? Is there some way of incorporating what one has learned from designing for the blind into a new device to be used by the sighted? How far can this two-stage or dog-legged design methodology be extended – to different modalities or ‘intelligences’, to different areas of learning, to learners across the age spectrum? In summary, the dog-legged design process is this:

  1. Identify some part of the syllabus that is taught by some traditional means, e.g. by book learning, where you feel the traditional teaching methods to be stodgy or ineffective.
  2. Construct learning material X (it may be a piece of apparatus, a competitive or collaborative activity for two or more students, an interactive computer game, etc.) for a target group of students that suffers some real or imaginary cognitive deficit. The use of X will engage a range of intelligences different from that invoked by the traditional teaching method.
  3. Construct a new apparatus, son-of-X that preserves all the pedagogical advantages of X but which also features elements that enhance the learning experience of students who do not suffer the cognitive deficit mentioned in 2.
  4. Test the effectiveness of the new apparatus against traditional methods of teaching. Effectiveness is measured not just by the speed at which the student solves various problems, but by the depth of the knowledge imparted. (Testing for depth of learning is a by no means trivial task.)


Boolos, G. 1998 (Richard Jeffrey and John P. Burgess, eds.). Logic, Logic, and Logic. Cambridge MA: Harvard University Press.

Frege, G. 1879 Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle, 1879. Translated in J. van Heijenoort (ed) From Frege to Gödel: A Source Book in Mathematical Logic, 1879--1931.Cambridge MA: Harvard University Press, 1967.

Goldstein, L. 1994.  ‘An Integrated Approach to the Design of an Immersion Program' (with Liu Ngar Fun), TESOL Quarterly, 28/4: 705-725.

Goldstein, L. 1996.  ‘Teaching Syllogistic to the Blind', in Jacob Mey and Barbara Gorayska (eds), Cognitive Technology: in Search of a Humane Interface. Amsterdam: Elsevier: 243-255.

Goldstein, L. 1999.  ‘Making a Virtue of Necessity in the Teaching of the Blind', Journal of Teaching Academic Survival Skills 1: 28-39.

Goldstein, L. 2010. ‘Gardner-Inspired Design of Teaching Materials: A Logical Illustration’ (with Martin Gough) Discourse 10/1: 173-202.

Goldstein, L. 2011.  ‘Adding a Dimension to Logic Diagramming’, in Patrick Blackburn, Hans van Ditmarsch, María Manzano and Fernando Soler-Toscano (eds), Tools for Teaching Logic. Heidelberg: Springer: 101-108.

Kanterian, E. 2012. Frege: A Guide for the Perplexed. London: Continuum.

Quine, W.V.O. 1950.  Methods of Logic. New York: Holt.