It is quite remarkable that the problem of encoding as treated here admits a rather simple mathematical formulation: it is the study of embeddings of one free monoid into another. We may consider this to be a basic problem of alge- bra. There are related problems in other algebraic structures. For instance, if we replace free monoids by free groups, the study of codes reduces to that of subgroups of a free group. However, the situation is quite different at the very beginning. In fact, according to the Nielsen-Schreier theorem, any subgroup of a free group is itself free, whereas the corresponding statement is false for free monoids. Nevertheless the relationship between codes and groups is more than an analogy, and we shall see in this book how the study of a group associated with a code can reveal some of its properties. It was M.P. Schutzenberger’s discovery that coding theory is closely related to classical algebra. He has been the main architect of this theory. The main basic results are due to him and most further developments were stimulated by his conjectures.
в четверг на кафедре матлогики МГУ будет доклад «Введение в гомотопическую теорию типов»
“The noscript of this book may sound to some readers like Good as Evil, or perhaps Cabbages as Kings. If logic and metaphysics appear disjoint, the reason is not just the lingering spell of a logical positivist conception of metaphysics as cognitively meaningless and logic as cognitively meaningful but analytic.”
Williamson, Modal logic as Metaphysics
Williamson, Modal logic as Metaphysics
Consider the contrast between a newtonian conception of absolute space and a Galilean conception of relative space. The relativist claims that there is no fact of the matter about absolute motion, no difference between an inertial frame moving at constant velocity through space and the frame at rest. The newtonian acknowledges that according to the physical theory they both accept, there is no difference in the way bodies behave in an inertial frame at rest and the way they behave in one moving at constant velocity. The issue between the absolut- ist and the relativist is whether there is a metaphysical difference.
Step 1: I love my merely possible coin
Step 2: Read Williamson
Step 3: Where is my merely possible coin…
Step 4: Nowhere.
Step 2: Read Williamson
Step 3: Where is my merely possible coin…
Step 4: Nowhere.
только сейчас до меня дошло что Сталнакер имеет в виду под инвариантными классами преобразований над шкалами
(день инсайтов)
(день инсайтов)
буквально сегодня видел на ютубе короткое видео про cycle notation of permutations, а тут в статье это используется
The upshot is that in a coherent equivalence system, worlds indistinguishable at a given world must in particular be indistinguishable in terms of indistinguishability.