On Traversing the Excluded Middle

Andrew Weir: Excluded Middle (2019)

Acrylic paint on paper, 36 x 48 cm
saatchiart.com

 

Logicians to the left of me, Derrideans to the right, 

here I am, stuck in the excluded middle with you ... [1]

 

 

I. 

 

In classical logic, the law of the excluded middle (p ∨ ¬ p) states that either a proposition or its negation has to be true.

 

It is the third of the three great laws of thought upon which rational discourse is based; the other two being the law of identity - each thing is identical with itself - and the law of non-contradiction - propositions cannot both be true and false at the same time.

 

But such axiomatic rules don't really mean a great deal to me as someone who is happy to do their thinking in the moral no-go zone that is the excluded middle; i.e., the evil realm of fuzzy logic, dark limpidity, and what Nietzsche terms dangerous knowledge.

 

 

II. 

 

Similarly, as someone who privileges difference over identity and refuses to be haunted by the spectre of logical contradiction, I'm prepared also to cheerfully transgress the other two laws. For as I wrote in a post from a few years ago:

 

'Whether our analytic philosophers like to admit it or not, some forms of thinking rely upon daimonic inspiration and so are not regulated by reason alone. Our very greatest poets, for example, creatively affirm paradox and ambiguity; they are unafraid of appearing inconsistent or irrational and are proud to proclaim that if, like Whitman, they contradict themselves, that's because they contain multitudes.' [2]

  

One suspects that a good deal of the continued hostility aimed towards those who take a more continental approach to philosophy is that we see the latter as more of an art than a science (unless it be a gay science). Nothing enrages the Anglo-American mindset more than logical inconsistency and the idea that some feel free in the excluded middle to affirm the neither/nor and defy the spirit of gravity so that thinking becomes pleasurable.      

 

 

III. 

 

In sum: without wishing to explicity reject the law of the excluded middle, I don't support its rigid enforcement and, like Deleuze, see le milieu exclu as a zone in which becoming is stamped with the character of being and where not only do new possibilities emerge, but it is reasonable to demand the impossible.

 

 

Notes

 

[1] I'm paraphrasing a lyric from the well-known song by the Scottish folk rock band Stealers Wheel entitled. 'Stuck in the Middle With You', written by Gerry Rafferty and Joe Egan. It can be found on their eponymous debut album Stealers Wheel (A&M Records, 1972) - or played by clicking here. 

 

[2] See the post entitled 'Hello Darkness My Old Friend ...' (1 Oct 2021): click here. 

 

This post is for Bryan Kam who probably cares more - and certainly knows more - about this topic (and many others) than I do. London-based for the last 20 years, Kam studied English and Russian literature at Princeton and Cambridge, but is also widely read in both Western and Eastern philosophy. He regularly publishes work on Substack: click here. 

      According to Kam, the law of the excluded middle, born in Athens c. 350 BC, died in Amsterdam in 1908 at the hands of L. E. J. Brouwer. That might be true, but, unfortunately, even dead concepts can still retain an icy grip on our thinking.  

 

 

Hello Darkness My Old Friend ...

Hello darkness, my old friend - by Niranjan Morkar

dribble.com

 

 

I. 

 

The three fundamental laws of logic - (i) the law of non-contradiction; (ii) the law of the excluded middle; and (iii) the principle of identity - are all well and good, but cannot be thought valid for all forms of thinking. 

 

Why? Because - whether our logicians like to admit it or not - some forms of thinking rely upon creative madness and daimonic inspiration and so are not regulated by reason alone. 

 

Our very greatest poets, for example, playfully affirm paradox, ambiguity, and what Barthes terms the pleasure of the text; they are unafraid of appearing inconsistent or irrational and are proud to proclaim that if, like Whitman, they contradict themselves that's fine with them (for they contain multitudes) [1].        

 

II. 

 

Similarly, our great poet-philosophers, like Heidegger, argue that even the most enlightened thinking requires darkness: 

 

"This darkness is perhaps in play for all thinking at all times. Humans cannot set it aside. Rather they must learn to acknowledge the dark as something unavoidable and to keep at bay those prejudices that would destroy the lofty reign of the dark. Thus the dark remains distinct from the pitch black as the mere and utter absence of light. The dark however is the secret of the light. The dark keeps the light to itself. The latter belongs to the former. Thus the dark has its own limpidity." [2] 

 

This dark limpidity of thinking, is something that must always be protected. However, it's hard to do so when everything is now lit up with electric lights and we aspire to an ideal of excessive brightness that is brighter than a thousand suns.

 

As Heidegger says:   

 

"The light is no longer an illuminated clearing, when the light diffuses into a mere brightness [...] It remains difficult [...] to keep at bay the admixture of the brightness that does not belong and to find the brightness that is alone fitting to the dark. [...] Mortal thinking must let itself down into the dark depths of the well if it is to see the stars by day. It remains more difficult to guard the limpidity of the dark than to procure a brightness that only wants to shine as such. What only wants to shine, does not illuminate. [3]

 

In sum: whenever you start to think about thinking, you are instantly transported into darkness ...

 

 

Notes

 

[1] See Walt Whitman, Song of Myself, 51: click here to read on poets.org.  

 

[2] Martin Heidegger, Basic Principles of Thinking (Freiburg Lectures, 1957), in Bremen and Freiburg Lectures, trans. Andrew J. Mitchell, (Indiana University Press, 2012), p. 88.

 

[3] Ibid., pp. 88-89. 

 

 

This post (as promised) is for Jenina Bas Pendry. 

 

For a sister post to this one, click here.