Is the concept of spacetime logical?

[Specforces]

Now I know science claims that time can speed up, and can produce mathematical equations to support this.

However, being more interested in in the subject from a philosophical stand point than science or maths, I have great trouble with the logic of 'time' speeding up. If it is proved philosophically illogical, does this then nullify scientific and mathematical proof? After all philosophy has pointed out how both science and mathematics rely on certain assumptions.

Anyway - here are some of my thoughts on the subject of time:

Time is a measurement system. It deals with short durations and long durations. A short duration is fast and long duration is slow. THe longer the duration of the measure the slower the measure. So surely it is the 'duration of the measure' that can be speedier or not, not 'time' itself as a measurement system.

Lets compare this with the measurement system of tempurature. You can have degrees of hot or cold within the tempurature system. But the Temperature 'system' itself cannot get hotter or colder. That is talking nonsense.

If I fly to another part of space where I age more quickly and the plants grow faster, and then fly back to earth and I look much older than you who have stayed on this planet, does that mean time went faster on the foreign planet. Or does it just mean the physical laws of nature move at a faster rate. After all, we all know there is a medical condition on earth where some people age very quickly. Was time faster on the other planet? Again. How could it have been; time itself can't speed up. Even if I perceived that time was going at a slow rate on the foreign planet doesn't necessarily mean it actually was. After all, we all know that time can appear to go fast when we're having fun and slowly when we're bored.