Recent content by cianfa72

Yes sorry, only later I realized the point was about isotropy of light intensity and not light propagation process (speed).

Why assume the isotropy of light in this frame (i.e. in the frame where the horizontal blue plane has equation t= const). The light cone (yellow) is invariant and in that frame is isotropic, isn't it ?

As far as I can tell, the parallel transport on the round sphere, when considering it embedded in 3D ambient euclidean space, works as follows. Take a curve C on the sphere starting from point p and a vector v in the tangent space at p. Move v along C pointing in the same direction within the...

Ah ok. So suppose to start with the turret's gun pointing in one given direction. Then, along the path being taken from the tunk hull on Earth's surface, the turret's gun is parallel transported (according to the Levi-Civita connection). Suppose now the gun initially points along the direction...

Yes, as @Orodruin said in #27, we can assume a sort of 2D gyroscope (i.e. free to rotate only around one axis).

As far as I understand this, using a gyroscope internal to the tank's hull and programming the turret to counter-rotate at the same tank's rotation rate w.r.t. it, one basically "implements" the parallel transport of the turret's attached gun along the path being taken from the tank. Only when...

Ok, a well-formed formula (wff) is (syntactically) provable if and only if it is valid since we're assuming a sound and (semantically) complete logic system (like FOL or Sentential (or propositional) logic are). What does it mean that in Sentential logic there are contingent wffs ?

Sorry, let me try to show my understanding: classic FOL is sound and complete (by Godel completeness theorem) hence a FOL wff is syntactically provable (i.e. a theorem) iff it is valid (i.e. True in every model/interpretation). Decidability is another matter. FOL is semi-decidable in the sense...

Sorry, could you be more explicit? Thanks.

As far as I can tell, ##|\mathbb N|## and ##|\mathbb R|## denote the cardinality of sets ##\mathbb N## and ##\mathbb R## respectively. Ok, you mean within ZFC formal theory (i.e. no from the "outside") the proposition/statement ##\varphi## "there is a cardinal number strictly between ##|\mathbb...

Yes, valid is understood as semantically valid.

Ok, you mean that a proposition is True on the elements of the topological model assigned open subset. Then if such a set is the entire space we can just say it is True, contrasts with the case of empty set when it is False. Better, I'd say it is valid when it is True (in the above sense)...

In any topological model for IPL, propositions are assigned open subsets of an underlying topological space by induction starting assigning open subsets to propositional variables (i.e. to atomic propositions). This semantics do not assign any binary truth-value to propositions, i.e. one can't...

Ah yes, indeed thinking about it ¬P is defined as ¬P := P → ⊥ and any topological model/interpretation maps ⊥ to the empy set. Then, by using the definition of → logic connective in any topological model, one gets the result.

Ah ok, so basically in logic semantic as noun doesn't exist/apply at all. Ah, so is ##\lnot P## assigned the interior of the complement of the open subset assigned to P ?