A Dialogue on Time: Two Logics of Time and Physics

This master thesis examines the distinction between tense logic
and first order logic concerning time. In particular it studies
whether this distinction exists in physics or not.
Firstly a general test is made: translating sentences concern-
ing time from physics into the two logics. The results here are
inconclusive, as it is possible for both logics to represent the sen-
tences, so this experiment does not reveal a similar distinction
in physics. However this test also reveals some properties of the
logics: tense logic holds a local view on time while first order logic
holds a global view, and it is possible to translate tense logical
formulas into first order logic with the standard translation.
Secondly it is examined whether properties of reversibility in
physics can be compared with properties of the two logics; this
is done under the conjecture that there is a correspondence be-
tween first order logic and reversibility in physics and tense logic
and irreversibility in physics. Through this study it is concluded
that it is not possible to see this correspondence with the tested
property; time symmetry, since symmetry seems to concern the
underlying structures, not the logic itself. It is, on the other hand,
possible to see the correspondence while looking at the property
of being fundamental. Through a presentation of Onsager's re-
ciprocal relation, reversibility is shown to be fundamental. In
logic, fundamentality of first order logic is argued for through the
standard translation.
Finally it is noted that the finite model property and the decid-
ability of tense logic gives useful properties that the more funda-
mental first order logic has not.
It is concluded that it is unclear whether the distinction of time
between the two logics exists in physics.