The Seba library treats Odd in 8 passages, across 5 authors (including Plato, Liu I-ming, Thomas Cleary, Liu Yiming).
instead of saying that oddness is the cause of odd numbers, you will say that the monad is the cause of them: and so of things in general
Plato's Socrates reformulates causal explanation by replacing 'oddness' as the cause of odd numbers with 'the monad,' grounding numerical oddness in the indivisible unity of the soul's animating principle.
, Phaedo, -385thesis
instead of saying that oddness is the cause of odd numbers, you will say that the monad is the cause of them: and so of things in general
The parallel passage reinforces the substitution of 'the monad' for 'oddness' as the deeper causal ground, linking numerical structure to the metaphysics of soul and life.
, Phaedothesis
the number three excludes the number four, because three is an odd number and four is an even number, and the odd is opposed to the even
Plato deploys odd/even opposition as a paradigm case for the doctrine that opposites mutually exclude one another, extending the argument beyond abstract ideas to the concrete inseparability of number and quality.
, Phaedothesis
we may refer to the sequence beginning with heaven as the odd sequence, and the one beginning with earth as the even sequence, since heaven is all yang, and yang lines are odd
Liu I-ming maps the odd/even numerical distinction onto the cosmological yang/yin polarity, making odd numbers the formal signature of creative, heavenly, masculine energy in the I Ching system.
, The Taoist I Ching, 1986supporting
we may refer to the sequence beginning with heaven as the odd sequence, and the one beginning with earth as the even sequence, since heaven is all yang, and yang lines are odd
Cleary's parallel translation confirms the identification of odd numerality with yang force and heavenly creative energy within the Taoist I Ching commentarial tradition.
, The Taoist I Ching, 1986supporting
two objects were identical and one was different, or odd. The objects were laid in a row, and the odd object was always on the left or right, never in the middle.
The oddity problem in comparative psychology operationalizes 'odd' as the structurally non-identical member of a triad, measuring abstract relational cognition in primates across developmental stages.
, The Principles of Psychology, 1890supporting
neither in us nor in nature can ever be at variance with itself: then, my friend, we were speaking of things in which opposites are inherent and which are called after them
Socrates distinguishes concrete instances of opposition from the essential opposite as such, a distinction that undergirds the logical force of odd's exclusion of even in subsequent argument.
, Phaedo, -385supporting
a significant association between the DAT1 10 allele and ODD, CD, and hyperactivity-impulsivity
In the neuropsychiatric register, ODD (Oppositional Defiant Disorder) appears as a comorbid diagnostic category whose association with dopamine transporter genetics is mediated through hyperactivity-impulsivity.
, Attention-deficit-hyperactivity disorder and reward deficiency syndrome, 2008aside