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Thus the purely qualitative descriptivist theory seems to avoid the above problems for direct reference theories.
For direct reference theorists, to say that Hesperus = Phosphorus is to say no more and no less than to say that Hesperus = Hesperus.
Genuine, familiar ambiguity poses no trouble for direct reference theorists: for them, the semantic value of 'Phosphorus', when that term is used for the planet, is just Venus.
But Chalmers' epistemic and subjunctive intensions do spell trouble for direct reference theorists (and are accordingly rejected: see, e.g., Soames 2005.
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The effective piezoelectric, piezomagnetic, thermoelectric and magnetoelectric moduli can be expressed in compact explicit formulae for direct references and applications.
Much of the impetus for the theory of direct reference came from the implications of the semantics of modal logic for the intentionality of singular thoughts and beliefs.
For contexts in which the theory of direct reference is taken for granted, rigidity and its consequences at least for names might be helpfully explained in terms of how they follow from direct reference: direct reference can take center stage.
The theory of direct reference for names is so intimately associated with the theory that names are rigid de jure that some philosophers have supposed that names cannot be rigid in this way, because names are not directly referential (see Fitch's 2004 discussion, p. 54).
The fate of rigidity's significance is distinct from the fate of direct reference's significance.[8] Finally, even if direct reference is to be taken for granted and rigidity for names does follow from direct reference, one might not draw the conclusion that rigidity loses interest.
So, while opponents of the theory of direct reference are free to deny that names are rigid or rigid de jure (as, e.g., Rosenberg does: 1994), it is hardly clear that this is a general requirement for accounts opposed to direct reference.
But don't look for a direct reference to the cuttlefish -- it doesn't have quite the cultural resonance it did back in Lincoln's day.
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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