According to Gregory Bateson,
What we mean by information — the elementary unit of information — is a difference which makes a difference, and it is able to make a difference because the neural pathways along which it travels and is continually transformed are themselves provided with energy. The pathways are ready to be triggered. We may even say that the question is already implicit in them.
In other words, we always need to know some second order logic, and presuppose a second order of “order” (cybernetics) usually shared within a distinct community, to realize what a certain claim, hypothesis or theory means. In Koichiro Matsuno’s opinion Bateson’s phrase
must be a prototypical example of second-order logic in that the difference appearing both in the subject and predicate can accept quantification. Most statements framed in second-order logic are not decidable. In order to make them decidable or meaningful, some qualifier needs to be used. A popular example of such a qualifier is a subjective observer. However, the point is that the subjective observer is not limited to Alice or Bob in the QBist parlance.
This is what is necessitated in order understand the different viewpoints in logic of mathematicians, physicists and philosophers in the dispute about the existence of time. An essential aspect of David Bohm‘s “implicate order” can be seen in the grammatical formulation of theses such as the law of motion:
While it is legitimate in its own light, the physical law of motion alone framed in eternal time referable in the present tense, whether in classical or quantum mechanics, is not competent enough to address how the now could be experienced. … Measurement differs from the physical law of motion as much as the now in experience differs from the present tense in description. The watershed separating between measurement and the law of motion is in the distinction between the now and the present tense. Measurement is thus subjective and agential in making a punctuation at the moment of now. (Matsuno)
The distinction between experiencing and capturing experience of time in terms of language is made explicit in Heidegger’s Being and Time.
… by passing away constantly, time remains as time. To remain means: not to disappear, thus, to presence. Thus time is determined by a kind of Being. How, then, is Being supposed to be determined by time?
Koichiro Matsuno’s comment on this is:
Time passing away is an abstraction from accepting the distinction of the grammatical tenses, while time remaining as time refers to the temporality of the durable now prior to the abstraction of the tenses.
Therefore, when trying to understand the “local logics/phenomenologies” of the individual disciplines (mathematics physics, philosophy, etc., including their fields), one should be aware of the fact that the capabilities of our scientific language are not limitless:
…the now of the present moment is movable and dynamic in updating the present perfect tense in the present progressive tense. That is to say, the now is prior and all of the grammatical tenses including the ubiquitous present tense are the abstract derivatives from the durable now. (Matsuno)
This presupposes the adequacy of mathematical abstractions specifically invented or adopted and elaborated for the expression of more sophisticated modalities of time’s now than those currently used in such formalisms as temporal logic.