Hello Vyd,

Please consider the following reasoning:

Premise 1: I missed the bus to school.
Premise 2: Whenever I have missed the bus, I have been late to school.
Conclusion: I will be late for school.

This is what your example would look like if it is presented in the form of an inductive argument.

Notice that premise 1 is supported by experience (which, here, is premise 2). This experience is seen as an apt justification for the conclusion. This can perhaps be understood through another inductive argument example:

Premise 1: I have, at times, missed the bus to school.
Premise 2: I have had to look for alternative means of transportation in such cases, which had taken some amount of time.
Conclusion: As I missed the bus to school today, I will be late.

Foundationalism cannot be a solution for any inductive argument as all its premises would be probable at best (and never certain), eliminating the probability for having a base belief. In the case of deductive arguments, it can be considered, but that would mean partially removing justification as a requirement as it would not apply for *knowing* a certain 'base' premise. This would call into question imposing it as a requirement for any other premise also. It would become a slippery slope situation.

As far as the certainty of 'seeing the bus leave with one's own eyes' is concerned, philosophers could even question the certainty of sense-data. But I think asking that question here is not as relevant, as even with the most certain beliefs, there can be a question as to what exactly it is that makes that belief so certain. It is the infinite whats and the whys that can be asked for anything that is the issue here.