Miguel de Unamuno and Heraclitus: from ‘The Eternal Elegy’ (‘La elegía eterna’) to ‘The Cut Flower’(‘La flor tronchada’)

The aim of this brief article is to demonstrate and analyze the influence of Heraclitus’s thought on some of the poems written by Miguel de Unamuno, in particular ‘La elegía eterna’ and ‘La flor tronchada’. At times –as in ‘La elegía eterna’– Heraclitus merely serves as a sort of a walking stick, an aid to his efforts to poetically reveal his anxieties. On other occasions –as in ‘La flor tronchada’– he genuinely needs Heraclitus’s philosophy to illustrate his view of human life and its relation to God as unending warfare.

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.