How should we understand these notions?
Although medieval semantic theory had used similar notions, the Port-Royal notions found their way into numerous 18th- and 19th-century discussions of the meanings and reference of terms; they appeared, for example, in John Stuart Mill’s influential text A System of Logic (1843).
In fact, much classic reasoning about games involves notions that are familiar from logic.
To be sure, some of these notions have received more attention in deontic logic than others.
Kant distinguishes two notions of the sublime: the mathematically sublime and the dynamically sublime.
In game theory, a harmony between these is often sought in notions of equilibrium for strategy profiles.
In the next two subsections, we will discuss the notions characterised by the other two characterisations.
Predicates representing these notions can be inserted into a formal structure that contains a preference relation.
None of these notions is original with Ockham, although he develops them with great sophistication and employs them with skill.
But for some it is puzzling that physicalism is stated using modal notions (i.e. notions such as possible worlds) and nonetheless is contingent.
Normative notions must combine with notions for agency and with temporal notions to be of maximal interest—which introduces considerable logical complexity.
A metaethical view might claim to provide an account of all evaluative notions, or of all normative notions, or of all moral notions, or or some set of moral notions.
Given we cannot give a satisfactory account of intrinsicality using only broadly logical notions, it is natural to investigate whether we can give a satisfactory account using a larger set of notions.
Primitive logical notions must be completely understood, and our understanding of them must be direct in the sense that it doesn’t depend on or involve an understanding of notions that must be classified as extra-logical.
Although his exposition of these notions is tailored to his proof theory, the notions are designed also to characterize the basic features of any scientific claim, where the principal examples come mostly from mathematics.
Some welfare consequentialist notions of the good incorporate a distributive element—e.g., welfare prioritarianism—and this feature may make it more plausible to see these notions as internal to the requirements of a relationship.
If Lewis’s three characterisations concerning intrinsicality characterise different notions, the three characterisations described in section 1.2 concerning having a property in an intrinsic fashion also characterise different notions.
Nevertheless, the notions of functionings and capabilities in themselves can be employed as elements in explanations of social phenomena, or one can use these notions in descriptions of poverty, inequality, quality of life, and social change.
Of course, these notions of definition, meaning and synonymy would themselves need to clarified, But they were thought to be sufficiently obvious notions, whose clarification didn’t seem particularly urgent until Quine raised serious questions about them much later (see §3.6ff below).
It would be good if we could analyse intrinsicality using only broadly logical notions, where broadly logical notions are exhausted by the narrowly logical notions of conjunction, negation and existential quantification, the modal notion of metaphysical possibility, the mereological notion of parthood, and the basic notions associated with property theory and set theory, such as the notions expressed by ‘state of affairs’, ‘property’, ‘relation’, ‘possible world’, ‘instantiates’, ‘is a member of’ and ‘set’.
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It would be good if we could analyse intrinsicality using only broadly logical notions where broadly logical notions are exhausted by the narrowly logical notions of conjunction negation and existential quantification the modal notion of metaphysical possibility the mereological notion of parthood and the basic notions associated with property theory and set theory such as the notions expressed by state of affairs property relation possible world instantiates is a member of and set