Steve Agnew,
"You mention objects and you mention activity and so you do seem to believe in objects and activity since you use those words. Since there is no meaning to the word activity without time, it is not clear to me why you keep repeating that there are no time-like measurements."
Physics empirical evidence consists of observing patterns in changes of velocities of objects. It is the case that time is passing during changes of velocities. It is also the case that space is traversed during changes of velocities. So, velocities change with respect to either time or space. However, neither time nor space are accessible to us so that we may make measurements upon them. They cannot serve as standards of measurement. So, we substitute measures of object activity in their places. That is our only choice because we only observe object activity. With regard to the property of time in particular, it is not what the 't' in physics equations represents. Nor do symbols for length or distance represent the property of space. The 't' represents cycles of a specific object activity. Clocks measure the number of those cycles, or cycles of their own, that have occurred during a measurement of object activity. Physicists choose to speak and write using the word 'time' for 't', and compound words that include 'time' such as space-time or time-like. Theoretical physics introduces substitutes (educated guesses) to fill in for that which is unknown. Even with these theoretical intrusions present, the equations remain useful because they are designed to accurately model the patterns in changes of velocities of objects. It is the patterns that usually provide useful extrapolations and interpolations. What the equations cannot do is fix the empirically unsound guesses that theorists have injected into physics equations. A major effect of such theoretical guessing is the introduction of fundamental disunity into physics equations. That problem began with the decision to make mass an indefinable property. Theoretical physics is stuck with disunity that cannot be undone by the introduction of additional invented, and empirically unverifiable, 'properties'.
James A Putnam replied on Apr. 9, 2016 @ 14:03 GMT as "...I repeat the point made similarly earlier: There is no empirical evidence for interpreting object activity as representing either time or space. We have no experimental data for effects upon either time or space. The only empirically justified conclusion about the nature of space is that it consists of room for objects to move about in. Both space and time are fundamental indefinable properties. In other words, they cannot be explained. Only in the empirically unsound interpretations of theorists do speculative imaginings become 'science-like'..."
Time is an unexplained given; 'time' measurements and 'time' delays are misnomers for duration measurements and duration delays. Duration being counts of cyclic activity of objects that are not time. Time is not like objects and objects are not like time.
"I do actually agree that time is an axiom and so time is like activity which is like time, which is an identity. ..."
We do not know what time is like. We do know it is not like activity. Activity is objects changing their velocities. There is no empirical evidence for time having a velocity let alone a change of velocity. What is a physics fact is that time is a fundamental indefinable property.
"However, a second way to define a fundamental axiom is with the other two axioms of matter and action. Since action (or activity in your words) is the integral of matter in time, time is the differential of action with matter. This is the trimal nature of a closed universe."
Matter is an imagined mechanical substrate credited with being the source of observed properties. Those properties being defined by and represented by their units in physics equations. Matter has no units and is not represented in physics equations. There is no empirical evidence for the existence of matter. The choice of the idea of the existence of matter is a philosophical preference. Empirical evidence consists of effects. We do not know what cause is.
The mathematical term for 'action' does not include measured time. Time is not measurable. Measurements take time to occur but the unit of second is not a measurement of time. A measurement of time would involve the differences between two points of time. We have no way of accessing points of time. With regard to action being the product of either energy and 'time' or momentum and length: What is the physical meaning of 'action'? Its usefulness is not in question. Specifically: Why are its units Newtonsxmetersxseconds? Those units convey all of its meaning, and its purpose in physics equations.
"Color is a measurable property of an object. Color change is a measurable property of an object that is time like. Change is what happens to objects with different time delays. These are very common measurements of objects no matter what kind of stuff you use to make those objects."
It is not the measurements that are in question. The measurements give us the empirical information that we need in order to know what effects have occurred. It is the non-empirically supported practice of assigning, by means of employing inaccurate wording, additional effects that did not occur. For example, there is no evidence that time gets delayed. There is evidence that object activity gets delayed.
James Putnam