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Peter Godfrey-Smith's Theory and Reality: An Introduction to the Philosophy of Science has just been released in a secodn edition. As he is one of the leading Philscis out there, and writes very well (His Other Minds was a NYT bestseller) I can recommend it. I have taught from the first edition.
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An old classic is Karl Popper, The Logic of Scientific Discovery, which is highly influential, though in my view over-long and contains too much pointless formalism. It features Popper's presentation of the view that science is primarily about falsifying, not confirming, theories.
Another frequently referred to text is Thomas Kuhn's The Structure of ...
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I would get a general lay of the land first before jumping into reading sources, you will benefit more from them when you have at least a vague idea of how they fit into the big picture. Some textbook recommendations can be found on Leiter Reports. Also LMU and UC Berkeley have helpful orientation pages. SEP has a number of relevant articles with extensive ...
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The most commonly used model of belief revision is the AGM model, named after Alchourròn, Gärdenfors and Makinson. Gärdenfors in particular has spent much of his career studying systems that model the rational reasoning process, and he has written several books and papers on the subject. The SEP article on the logic of belief revision has an introduction.
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The etymological sense of dia-bolic (throwing apart, shattering) is largely overshadowed by the Biblical sense. Luhmann did attempt to rehabilitate it, but without much success. Baraldi et al. in Unlocking Luhmann, p. 232 relate the etymological use in systems theory to that of sym-bolic:
"The most important structural characteristic of symbolically ...
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The approach that (at least) some Gettier cases are the result of misdescribing beliefs due to disregarding linguistic conventions (such as Grice implicatures) is still actively pursued and even rediscovered. See for example Jose-Mabaquiao, Resolving the Gettier Problem in the Smith Case: The Donnellan Linguistic Approach (2018), Ludlow-Segal, On a unitary ...
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Philosophy is usually done informally, simply because the concepts involved do not tend to yield to simple formalizations. Philosophical terms are often derived from natural language terms, which by nature are ambiguous and vary in their intended meaning between different people.
However, this leads to no end of disputes. Philosophers often cannot agree on ...
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The book by Ian Stewart and David Tall, The Foundations of Mathematics. In this book, he constructs some fundamentals of Mathematics (Number, Set, Functions, etc). From ideas from our daily experiences, he takes us to semi-advance ideas (Groups, Groupoids, Rings, Axiomatic Systems).
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General philosophy of science I'll leave to others to answer, I studied this years ago and we used the Curd and Cover book which contains lots of classic papers and excerpts etc. No idea if this has been superseded but it certainly covers the ground.
Re the subsidiary question on philosophy of physics - as introductory texts I would recommend Dean Rickles's ...
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I would highly recommend Michael Polanyi's Personal Knowledge. Polanyi is not terribly well known, but he brings a very interesting perspective, inasmuch as he was a chemist before he moved to philosophy; so he knows science from the inside. I got into him after reading an excerpt in graduate school and thinking, “Yes, that's how science actually works.” (To ...
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Rigour: strictly according determined constraints.
In science, rigour is possible, being the scientific method the constraints according which the process can be considered to produce scientific knowledge. Notice that scientific truth scope is empirical (that is, physical).
in philosophy, there's no equivalent. Notice that philosophical truth is not only ...
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