For example:
Technology will keep advancing in terms of innovation purely because it has not stopped advancing.
Is there a fallacy for this?
This can also be described as the "problem of induction," not that this is an outright fallacy. The most famous example is Hume's observation that just because the sun has risen every day for thousands of years provides us with no deductive proof or certainty that it will rise tomorrow.
The example you give is also doubtful in many other ways, since "advancement" is a value judgment many would criticize, especially in regard to technology. So we might also describe this as a "Panglossian" view of technology, from Voltaire's Doctor Pangloss, who was in turn based on a misrepresentation of Leibniz's proof that we live in the "best of all possible worlds."
One could also call it a species of "Whig history," in the sense that history is viewed as inevitable progress towards the present, assumed circularly as the best outcome of that history. Or it can just be deemed "techno-optimism," which acts as a term of ironic reprobation in the mouths of many critics, from Ned Ludd to Heidegger.
The specific (informal) fallacy you're talking about (the one in the question title) is called "hasty generalization". In technical terms, it is inductive reasoning with insufficient evidence. To know whether you are reasoning inductively correctly or falling into the pit of the above mentioned fallacy, inductive logic is helpful.
People cite Moore's law as if it's an absolute law of nature, but there is some evidence that it's tailing off.
“The last two technology transitions have signaled that our cadence today is closer to two and a half years than two,” Intel CEO Brian Krzanich said during a conference call with analysts
https://www.wsj.com/articles/BL-DGB-42647
Then there's the story of the farmers who fed the turkeys every day - until Christmas.
While this is not a direct answer it may broaden the scope of the discussion and put the "fallacy" you mention in context.
As Nelson has said, predicting future events on the basis of regularities observed in the past — induction — is not wrong; it is merely a statement of expectations, not of certainties.
One could argue that induction is a special case of the Lindy Effect. The wikipedia article describes it as "a theory that the future life expectancy of some non-perishable things like a technology or an idea is proportional to their current age".
Interestingly, the principle has much broader applications than that; specifically (if that's the right word here) it is applicable to everything. The reason is that things, circumstances, nations, theories etc. all have their respective life span. For elementary particles it may be nanoseconds, for stars it may be billions of years, for humans 50 or 100. Now when we behold something — a particle, a human, a star, the universe — it is statistically unlikely that we are very close to either end of its existence. It is no coincidence that the universe, the sun as well as you and me are somewhere in the broad middle of their existence, most likely. For purely statistical reasons we can assume that the two of us will still be there next year, the sun will not explode in the next billion years, and the universe will not change significantly in the next 2 billion years or so.
What makes this rule powerful is that it can be applied without any knowledge whatsoever about its subject. The Egyptians didn't know anything about the nature of the sun or the moon but it was unlikely that the regularity of their interactions would change soon after it had been consistent for many hundred years of observation. Without having inspected my car I can safely assume that it takes me to work tomorrow — I'm confident that it will run another couple of years.
What we call "induction" is another way of saying that circumstances we have observed for a while are unlikely to change within a time which is significantly shorter than the past observation time.
Summing up, even if we know nothing about the sun and the Earth we can safely assume that their interaction will not change during our life time after it has been consistently following the same rules for thousands of years, for purely statistical reasons: It is unlikely that we are close to a spectacular event which will alter this long-term relationship.
Thomas Paine referred to something similar to this as "governing beyond the grave". Just b/c we've done something a certain way in the past doesn't necessarily mean we should do it that way in the future.
The key word here is "unlikely." I have awakened every morning since I was born. Inductively, I should be immortal.
Blue Sun "2 + 2 = 5 for all moderately large values of 2"
S(n) -> S(n+1)
to prove lots ofS(k)
. This takes a bunch of true propositions and tries to infer that their truth comes from aS(n) -> S(n+1)
rule.