But once we introduce new sentences joining the terms we have so far with logical connectives we are likely to need to postulate yet further attitude types and to need further principles to capture their logical properties.
Not just any partial ordering qualifies as a part-whole relation, though, and establishing what further principles should be added to (P.1)–(P.3) is precisely the question a good mereological theory is meant to answer.
In addition to Transitivity and Completeness, vNM introduce further principles governing rational preferences over lotteries, and show that an agent's preferences can be represented as maximising expected utility whenever her preferences satisfy these principles.
Rott (2001) discusses many further principles and variants of the above.
If the order-inversion expressed by contraposition is seen as a fundamental property of negation, a hierarchy of stronger negations can be obtained syntactically by postulating further principles and semantically by characterizing these principles by means of conditions on compatibility frames $(W, C, \leq)$.
The answer would depend on some further principles that explained why and how past decisions as a kind are relevant, if they are, to instant cases.
No further principles are required to understand the principal aspects of rocketry and space flight (although, of course, a formidable technology is needed to carry them out).
Although the principles of rationality governing individual choice still apply, arguably there are further principles of rationality governing expectations of the actions of others (and of their expectations concerning your actions and expectations, and so forth).
We have also been guided by two further principles: that, when it comes to remuneration, MPs should be treated as professionals; and that any new package of remuneration should be modern in outlook and application.
