This essay discusses a prominent definition of universal concomitance in the Nyäya School of Classical Indian Philosophy. This définition holds that universal concomitance is equivalent to the absence of undercutting conditions. It will be shown that though this definition seems to be inadequate, there is an auxiliary condition that may be added which makes the equivalence between universal concomitance and the absence of undercutting conditions deductively correct. It will then be shown that this auxiliary condition fits well into the Nyäya (...) foundations of logic and that furthermore this auxiliary condition does not unreasonably restrict the applicability of the definition of universal concomitance as the absence of undercutting conditions. Hence, the conclusion is that this interpretation is a good candidate for how the definition of universal concomitance as the absence of undercutting conditions should be understood. (shrink)
We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.
We initiate a geometric stability study of groups of the form G/G 00, where G is a 1-dimensional definably compact, definably connected, definable group in a real closed field M. We consider an enriched structure M′ with a predicate for G 00 and check 1-basedness or non-1-basedness for G/G 00, where G is an additive truncation of M, a multiplicative truncation of M, SO 2(M) or one of its truncations; such groups G/G 00 are now interpretable in M′. We prove (...) that the only 1-based groups are those where G is a sufficiently “big” multiplicative truncation, and we relate the results obtained to valuation theory. In the last section we extend our results to ind-hyperdefinable groups constructed from those above. (shrink)
I found Shpet's article "A Work on Philosophy" [Rabota po filosofii], which we present to the reader's attention, in the Shpet archives stored in the Lenin State Library and passed it on to the editorial board of the journal Logos, where it was published by I. Chubarov. The small circulation of that journal makes it appropriate to republish this text, which is of major importance for an understanding of Shpet's philosophical position and provides a good clarification of the subsequent logic (...) of development of his conception. Although the article is unfinished, there is no reason to lament this fact, since all of its basic ideas and their logical development were realized by Shpet in subsequent publications. A whole series of his works is devoted to grounding and affirming so-called positive philosophy, the basic features of which I would like to clarify. (shrink)