Can there be a priori truths for science, even if science is heavily based on the scientific method with empirical evidence? What if we're using examples like theoretical physics? Please explain.
See A Priori :
“A priori” and “a posteriori” refer primarily to how, or on what basis, a proposition might be known. In general terms, a proposition is knowable a priori if it is knowable independently of experience, while a proposition knowable a posteriori is knowable on the basis of experience.
A priori justification [of knowledge] has thus far been defined, negatively, as justification that is independent of experience and, positively, as justification that depends on pure thought or reason.
Having said that, if we consider the most abstract empirical sciences, like theoretical physics, whose axioms are very far from mere "generalizations from experience", it is hard to maintain that there is no some sort of empirical support for them.
Without the complex network of experiences, experiments and theoretical predictions built up by scientists during some centuries of inquiries, it is difficult to imagine that someone can "devise" in a purely a priori manner theories like Relativity or Quantum Mechanics.
We tend to label a priori truths in science as Mathematics, instead of being part of any given Science, even when the mathematics is evolved directly for a given scientific purpose, like calculus for Newtonian dynamics and the second generation of statistics for biological testing.
But most of the content of Mathematics is a priori. We can see this because when we find that it does not fit the outside world, it does not become false, just less-used. Any a posteriori argument simply has no force against its 'truth', only against its 'applicability'.
If mathematical constructs must be derived to make sense of a theory, that material is a priori. The scientific theory itself then is a posteriori, in that it will deploy the mathematical mechanics against actual observations. The theory might fail, end yet the math might live on and find a different application entirely.
I would suggest this is because the mathematics is dredged up out of human intuition through idealizations that are made about observations rather than observations themselves. The ideal forms simply are not true of the observations themselves. But they are the simplified forms that appeal to human psychology, which is "from before" the data.
From that point of view: Celestial mechanics is not a priori, but the Calculus is. Relativity may not be a priori, but tensor theory is. Quantum mechanics may not be a priori, but matrix mechanics is.
A priori truth is a knowledge obtained before and independent from experience.
The issue of a priori truth for any kind of science has first been investigated by Aristotle in Book 1 of his Metaphysics. From today's point of view the only a priori truths of science are the rules of logic and the syllogisms of logic: The law of non-contradiction has already been stated by Aristotle.
Kant - deeply impressed by Newtonian mechanics - claimed that natural science like Newtonian mechanics also disposes of a priori knowledge. See his work Metaphysical Foundations of Natural Science (1786).
Today his claim is rejected by the scientific community. Today's science is much more cautious. As you write, science always starts by observation and experiment. All general knowledge is considered hypothetical. It can be confirmed by observation but not proved. It can can always be refuted by new experiments. Then the underlying theory has to be improved or replaced by a new theory.
Hence the only a priori truths of science belong to the domain of logic.
The principle of inertia seems to be a good candidate for an "apriori truth": it is never verified and connot be verified positively, but explanations are adduced why a certain body does not continue its regular movement to infinity.
The conservation of energy was also considered a good candidate and different kinds of energies have been introduced in order to save it. (Feynman has memorably written on this topic.) Recently people have started to argue that it does not apply for the universe as a whole; however, appealing to symmetry and eventually explaining why it is not observed still seems to be a kind of aprioristic stance.
So, one might like to argue that principles are apriori ruths.
A useful contrast is a priori with a posteriorai; and to take each as a kind of ideal point.
Arguments in science can be closer to either in this continuum.
Consider what constitutes a definition of force in Aristotle - though he doesn't use the word:
it is that which has the capacity to cause change, and can actually cause change in another; and this by contact; and that another has the capacity to be changed, and can actually be changed.
This, though doubtlessly by A is based on experience; elsewhere for example, A says:
as for movement, it would be strange if we failed to notice the downward motion of a stone; nor do we fail to notice it is at rest on the Earth.
Which, does make A sound as though he was reacting, as a theorist of physics, here, to a critique of 'armchair' theorising by the wholly empirically minded; a critique that is just as much levelled today, as much as then.
It's also possible, I think, to discern here, the historical mythos of Newtons falling apple - which every schoolboy learns, and then has to unlearn - and which mythically prompted his thought towards gravity; though on the evidence above, it seems a well prompted and fruitful observation.
Beautiful question: yes, there's an a priori knowledge: causality. Everyone knows nature's mechanism of action and reaction, cause and consequence. Since we start existing inside the mother's belly, we make stimulus and get reactions. We know that. Nature works with that. Math describes that perfectly, because causality has been perfect (until quantum mechanics found some incoherences). We speak and interact following the causality mechanism.
The mechanisms of causality are related to systems -all things-. There is no cause if there is no system over which to apply it. So, knowledge is built over this a priori base: actions and reactions we clearly identify over things we are familiar with.
This is a topic of the systems theory, and I'm an author, so please consider this as an opinion. I write about this because the systems theory requires this kind of adjustments, in the meantime, it's heavily incomplete.
Every empirical science has an a priori foundation.
If a proposition is a priori, it means it's not justified by experiments.
Any proposition is supported by one or more principles.
Principles are foundational truths which are not deduced from any other (that's why we call them Principles).
If every proposition had to be deduced from another, that would create a problem of infinite regression and no proposition would ever be justified.
Principles are a priori in the same say Logic is.
The Principle of Non-contradiction described by Aristotle in his Metaphysics is assumed to be valid in every empirical science. Thus, every empirical science has an a priori foundation.
Therefore, in answer to your question: there can be no science without a priori truths!