Can an equation validate it's way out of the circular science loop I posted With specific regard to
equations per se, they are subject by definition to mathematical proof. Thus they cannot be subject to "reasonable" doubt. Yet Descartes, the father of modern scientific method, in his work "Meditations", worried that a demon might be tricking him into believing that his proofs were good, even though they were false. He bootstrapped this into his proof for the existence of God, to get out of this quagmire, declaring that "God is not a deceiver". Shocking, considering that God turns out to be Electricity.
Anyway, when we get to scientific Propositions, they are subject to the problems of induction mentioned above. There is no way out -- No Exit (Sartre). And it gets worse.
Building on the work of Godel, in the 1940's (I believe) Church, Gooding & Turing conclusively established that for any robust System (of science, thought or mathematics) it will eventually be found that within the System there is at least one proposition P, and its opposite -P, and which one is true cannot be established within the System. It may be possible to conceive of a more comprehensive System which resolves that issue; but the new System will have its own P vs -P issues. This discovery brought an end to the project of the Enlightenment (which began in the 1500's or 1600's) which assumed that mankind's knowledge could increase incrementally over time, guided by the scientific method. Unfortunately facts (knowledge) are meaningful only within the context of a System; but all Systems are imperfect, being plagued by the problems mentioned.
The collapse of the Enlightenment, the crown jewel of the Modern Period of history, gave full rise to post-Modernism which had been lurking in the Arts, since Cubism circa 1907.