Exact(3)
There's a confused debate going on about private boarding schools, with arguments about class and unfair privilege mixed up with a bewildering range of notions about children's emotional health.
There is, of course, a wide range of notions of validity, but here we are particularly interested in logical validity.
In the burgeoning literature on transport and equity, a range of notions is used to refer to the nexus between (a lack of) transport and persons' life opportunities.
Similar(55)
The second related reply is to maintain that there is still objectivity in a wide range of surrounding notions.
We also study the computational complexity of the problem of finding the best and the worst alternative for a given set of weighted goals, and of finding an alternative that is optimal for a group of agents, for a range of different notions of collective optimality proposed in social choice theory and welfare economics.
Thus, ⊢ is being used here as a schematic placeholder for a range of different logical notions, each of which will provide some notion of valid inference in some logical theory.
But the idea of a private language is more usually hidden: the confusions supposed to belong to it allegedly underlie a range of articulated philosophical notions and theories, without themselves being so articulated.
As a result, not only did Principia introduce a wide range of philosophically rich notions (including propositional function, logical construction, and type theory), it also set the stage for the discovery of crucial metatheoretic results (including those of Kurt Gödel, Alonzo Church, Alan Turing and others).
Yet, it might be argued, ordinary language allows for a range of irreducible causal notions, such as "scrape," "push," "wet," "carry," "eat," etc. (Anscombe 1975, p. 68) Why not take ordinary language at its word, and adopt a form of causal pluralism on which 'cause' is viewed as providing a merely nominal grouping of metaphysically diverse relations?
Still further definitions are possible when we widen the range of relevant concepts, employing notions such as responsibility, being in the clear, and blameworthiness.
A true intellectual conveys to the public new ideas on a wide range of subjects, unearthing these notions long before most people do.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com