In epistemology, the traditional definition of knowledge is :
True, Justified, Belief
https://plato.stanford.edu/entries/knowledge-analysis/
As per your reasoning, you said :
Therefore it seems reasonable to me to claim that the only "truth"
people are capable of knowing is the "truth" that they assume to be
true in their reasoning. Also all the deduced "truths" from such true
assumptions would be counted as such truths.
According to the definition of knowledge, people sure are capable of knowing X as long as X is a bold truth (not only "truth" with double quotes), and there is a justification for X .. And they believe that X is true.
These conditions, of which truth and justification are out of one's control (you cannot control what is true, and you cannot provide a good justification or evidence if it is not available .. all you can do is believe it).
But hold on .. I find a problem with the word "assume"
An assumption cannot be "known", because you only assume what is unknown, what has no justification or truth.
So, according to your question, there is a problem with this part :
Therefore it seems reasonable to me to claim that the only "truth"
people are capable of knowing is the "truth" that they assume to be
true in their reasoning. Also all the deduced "truths" from such true
assumptions would be counted as such truths.
Assumption and Knowledge cannot possibly coexist. Either you know X or you assume X and not both.
Let's consider an example :
- Premise 1 : If Unicorns exist then they are beautiful
- Premise 2 : Unicorns exist
- Conclusion : Unicorns are beautiful.
Premise 1 is true because I know what a Unicorn is supposed to look like and I see it as a beautiful creature if it existed (my conditional is true, because I know the definition of a Unicorn, and it is true that if Unicorns existed, they they would be beautiful , this is justified because I saw paintings and cartoon of Unicorns).
Premise 2, this cannot be knowledge (it is not only a conditional, but an assertion) :
- If Unicorns do not exist, then I cannot absolutely know Premise 2 .. I cannot know what is false.
- I have no good evidence for the existence of Unicorns, Premise 2 is not justified, therefore : I cannot know it.
- I do not believe that Unicorns exist, so I cannot know this assumption.
I can assume it, and because I can assume they exist (to build on that premise) , it is impossible to know it at the same time.
Hope this helps.