"An object's property had a specific value. That value became different."
How is something that's different different from something that's changed? It sounds like it's one and the same to me.
Also, you used the word "became". That word has temporal connotations. So if you define change in terms of time, you can't then go on to define time in terms of change without it being another circular definition.
I was defining time as the measurement of change. Change does not depend on measurement therefore there is no circular definition.
For example, a star is different from star light. When I look at the sky through a telescope I don't see a star,I see star light. Same can be said for any object as well,we see light emanating from an object therefore vision is perception of an object as measured by our optics.
Time is how me perceptually measure change. This distinguishment can potentially prove valuable much like how distinguishing perception of star light and the star itself is important(not so important for close objects but important at a grand scale.)
Modification,change and other words used to describe when something becomes different do not imply human measurement.
We can for example talk about a tree that fell in a forest with no human to measure that change. Did it happen? Yes. We can only say it didn't happen if we exclude all events beyond our perceptive ability from reality. In the same way,change does not depend on time but time is a measuremet of change.
The problem is that if you take the time and carefully consider all of your statements, and carefully lay them all out in a row in the right way, you will find you've got circularity hiding in them. I am confident in this statement because you are walking very well-covered ground, and lots of smart people have examined it all very closely. For instance, "change" intrinsically has a before and after element in it; you can't use it to define time. You can use it to define a measure of time (which is pretty much exactly how we in fact do it), but it isn't useful for defining time. But I do not say that is the only place circular definitions lie in your various posts here; it is only an example. It is very hard to discuss exactly what time is because the very words of our thoughts and in some sense the very temporal nature of our thoughts themselves continuously betray us. Being embedded in time is the ground state of our being and virtually an unperceived constant in our thinking, slipping in to our every concept and thought. It is very hard to extricate ourselves from that, if it is really possible at all.
It is all too easy for us to bury ourselves in so many words that we push the circularity of the argument behind so much obfuscation that we can no longer perceive the circularity, but it is still there. To truly define time, one must fundamentally start from some sort of perspective in which it does not exist, then show how it arises. This is not something you're going to pull off in English. It is soaked in time. You're going to have to use math or you are almost certainly just moving the obfuscation around. (And also deal with the question of what it means to "arise", though to some extent that's an artifact of English popping up again. There are mathematical ways of dealing with that.)
The question isn't "is before different than after?", nor is it anything about how much difference there is, or how it may relate to other differences. The question is "how is it that there is a before and after at all?", to which merely pointing out that there is a before and after isn't very helpful.
I'm in agreement about the uselessness of words to define time, but I doubt that even using math will help understand time. I'd argue that both math and time arise with thoughts, i.e with the faculty of defining concepts and reasoning about them, but defining a concept is not the same as understanding the essence of the thing that is being defined. I see mathematics as the extent to which "thought muscles" can be flexed (which admittedly is very impressive), but to understand the nature of time, one would have to "step out of thought" as well, which if possible would be a rare capability and obviously not an insight that could be conveyed with explanations or definitions...
This sounds like a circular definition because "modification" is a synonym for "change".