The boundary between physical causality and logical or mathematical implication doesn’t always seem to be clearcut. Take two examples.
(1) The product of two and an integer is an even integer. So if I double an integer I will find that the result is even. The first statement is clearly a timeless mathematical implication. But by recasting the equation as a procedure I introduce both an implied separation in time between action and outcome, and an implied physical embodiment that could be subject to error or interruption. Thus the truth of the second formulation strictly depends on both a mathematical fact and physical facts.
(2) The endpoint of a physical process is causally related to the initial conditions by the physical laws governing the process. The sensitivity of the endpoint to the initial conditions is a quite separate physical fact, but requires no new physical laws: it is a mathematical implication of the physical laws already noted. Again, the relationship depends on both physical and mathematical truths.
Is there a recognized name for such hybrid cases? They could perhaps be described as “quasi-causal” relationships.
The boundary between physical causality and logical or mathematical implication doesn’t always seem to be clearcut. Take two examples.
(1) The product of two and an integer is an even integer. So if I double an integer I will find that the result is even. The first statement is clearly a timeless mathematical implication. But by recasting the equation as a procedure I introduce both an implied separation in time between action and outcome, and an implied physical embodiment that could be subject to error or interruption. Thus the truth of the second formulation strictly depends on both a mathematical fact and physical facts.
(2) The endpoint of a physical process is causally related to the initial conditions by the physical laws governing the process. The sensitivity of the endpoint to the initial conditions is a quite separate physical fact, but requires no new physical laws: it is a mathematical implication of the physical laws already noted. Again, the relationship depends on both physical and mathematical truths.
Is there a recognized name for such hybrid cases? They could perhaps be described as “quasi-causal” relationships.