The relational states of the given object: intensionality and extensionality. Some examples from physics, mathematics and everyday life

The author examines the reality of an object in a situation. Such a given is due to the corresponding actual (intentional) property that forms the situation with the studied object in the act of attention. In a situation, an object has its own way of being – a mode. Modes are conditionally divided into strong and weak. In epistemological terms, the reality of an object in a situation has two states relative to each other, depending on the position of the cognizing subject in relation to this object. In accordance with this, the object is known either intensionally or extensionally. A phenomenological approach is used. The difference between internal and external observers in the constituted situation is shown. Such a distinction does not occur at all, but depends on the actual property in the situation. The act of cognition introduces asymmetry into the reality of its relational states: one of them will be relevant (with a strong mode), the other – only possible (with a weak mode) in the same situation. This asymmetry, in particular, manifests itself in wave-particle dualism and is expressed through the principles of complementarity and uncertainty. In particular, it is shown that the complementarity principle indicates the duality of the given object, expressed through its relational states, and the uncertainty principle indicates the difference of modes (strong and weak) of these states in the same situation. In support of what has been said, some other examples from physics, as well as from mathematics and everyday life are given.

uncertainty principle, potential infinity, the complementarity principle, object modus, cardinal numbers, wave-particle dualism, experiment in physics, internal observer, principle of relativity, canonically conjugate quantities