Stronger Objectivity for Sciences From Below

Wilhelm Dilthey on the Objectivity of Knowledge in Human Sciences

Wilhelm Dilthey was one of the first thinkers whose philosophy centred on the reflection of the nature of human sciences. These sciences had evolved into academic disciplines already within the context of the concept of scientificalness (Wissenschaftlichkeit) of German Idealism. They underwent a certain crisis of foundations in the nineteenth century in connection with the general rise of empir...

Priority Setting on the Path to UHC: Time for Stronger Institutions and Stronger Health Systems: Response to Recent Commentaries

Stronger Cuts from Weaker Disjunctions

We discuss an enhancement of the Balas-Jeroslow procedure for strengthening disjunctive cuts for mixed 0-1 programs. It is based on the paradox that sometimes weakening a disjunction helps the strengthening procedure and results in sharper cuts. When applied to a split cut derived from a source row of the simplex tableau, the enhanced procedure yields, besides the Gomory Mixed Integer cut (GMI)...

Constructing Cardinals from Below

If the initial segment Σ of Ω is a set, then it has a least strict upper bound S(Σ) ∈ Ω. Thus, for numbers α = S(Σ) and β = S(Σ′), α < β iff α ∈ Σ′; α = β iff Σ = Σ′; S(∅) is the least number 0 (although Cantor himself took the least number to be 1); if Σ has a greatest element γ, then α is its successor γ + 1; and if Σ is non-null and has no greatest element, then α is the least upper bound of...

Kuratowski Theorem from below

Proof. Let us assume that G is planar but not free planar. Then there exists an edge xy not belonging to the graph whom adding to the graph it becomes non-planar. Then in G for an arbitrary cycle C through x, y there exists a pair of screening bridges Bx and By x from y with respect to C, i. e. either Bx and By are not placeable on one side against C or they are connected [i.e. not placeable to...