Is a dog from the present considered to be the same thing as the same dog 1 sec in the future? What are the distinctions philosophers tend to make when we refer to the same thing at a different time. What are the various views on this and has there been a consensus on how we should treat them? How do we assess a truth position when the elements being judged exist in different times?
tl;dr- Whether or not something is the same from one moment to the next depends on the model framework; either model is valid. As for the continuity of one's identity, that's an emotional concern not determinable by logic alone.
To quote this answer:
Summary: Equality is context-subjective, sameness isn't so much.
Things are equal in some sense when they're interchangeable in that sense.
Things are the same when they're equal in all ways that we care to identify.
So, something is the same from-moment-to-moment if we don't care to identify the moment in which it exists as a meaningful distinction. I'm trying to stress that "in all ways we care to identify" part, as the choice of ways that we care to identify is subjective.
I mean, we can take two views here:
Things exist at a moment in time, such that things that exist at different moments in time are distinguishable.
Things can exist across moments in time, such that when we point to a thing at different moments in time, we're merely pointing at the same thing in different ways.
Both are consistent and therefore valid.
Say that someone asks if
1+1=2in decimal (Base-10); or
1+1=10in binary (Base-2).
What'd be the answer to that question?
They're both valid! We can say that
1+1 is either
10, depending on that frame; so long as we're consistent, it's all good.
Likewise, if we ask if a dog is
the same in a second from now; or
different in a second from now;
both'd be valid. We can say that it's either, depending on our frame, as long as we're consistent.
Of course, we can force errors. For example:
It'd be wrong to say that
It'd be wrong to say that a dog is the same in a second from now in a frame in which we say that things exist at precise points in time.
Those would be examples of consistency errors.
Related: Do people die every moment?
I think people sometimes wonder about the continuity of their personal identity; are people the same consciousness from-moment-to-moment?
From a scientific perspective, it's equally valid to say that you are or aren't, so long as the meaning of those descriptions is understood consistently. This is, there's no scientific reason that you have to see it either way.
The big question is how someone self-identifies. This is, do you care to perceive yourself as the same thing from-moment-to-moment; or, do you care to distinguish your identity across time in some way? Unfortunately, logic isn't going to tell you how you should feel; that's up to you.
That said, you can appreciate both models. This is, you can see your[-temporal-]self as dying at each moment while seeing your[-timeless-]self as existing across time. Then you can be upset about one while happy about the other. I mean, there's no reason that your emotions have to be rooted in a single perspective.