"Steve3007 wrote: ↑May 7th, 2014, 3:58 am Of course, the way that we come to the conclusion that those other bodies are engaged in predictable repetitive motion is by comparing them with other instances of predictability. Why, for example, do we consider the Earth to orbit the Sun in a predictable, regular fashion? How would we predict it? By comparing to other things that we regard as predictable.
If we say that we measure time by comparison with objects that undergo regular repetition then we have to define the term "regular repetition". It means: "doing the same thing at regular intervals in time". But how do we measure whether they're doing that? We're still trying to establish how we measure time.
I think, however we word it, our definitions always have a tendency to be circular. When Einstein defined time as: "what we measure with a clock", he invited the question: "What is a clock?". I don't know of any verbal answer to that question that doesn't involve using the word "time", or another word whose definition, in turn, uses the word time. (e.g: "an object that performs a repeated activity at regular intervals of time, like ticking").
Of course, we could point to a whole load of "clocks" and say: "whatever it is that those things have in common, that's a clock (The form of the clock, as Plato might put it)". Ultimately, I think, that is how we define our abstractions, whether they be "time" or any other generalized concepts. We create them by inducing from individual observations.
I think, however we word it, our definitions always have a tendency to be circular. When Einstein defined time as: "what we measure with a clock", he invited the question: "What is a clock?". I don't know of any verbal answer to that question that doesn't involve using the word "time", or another word whose definition, in turn, uses the word time. (e.g: "an object that performs a repeated activity at regular intervals of time, like ticking")."
A clock is a perfectly periodic process, which is a process of which the period time is constant. "Hey, period time! Circular?" No. Lemme explain.
A pendulum, for example, is not an ideal clock, as there is friction which diminishes the amplitude and the period time depends on the amplitude. If there would be no friction, no gravitational waves, no EM radiation, a constant gravitational field, a constant pendulum length, etc., then the pendulum could maybe be perfect, and that pendulum could be used like a perfect clock. Modern clocks give or take a second in a billion years or so! But a truly perfect periodic clock doesn't exist. It's an ideal.