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Wittgenstein does not explicitly say, however, how mathematical equations, which are not genuine propositions, are used in inferences from genuine proposition(s) to genuine proposition(s) [(Floyd 2002, 309), (Kremer 2002, 293 94)].
Sinn Fein's Conor Murphy told the BBC: "We always were prepared to consider a genuine proposition and we have one on the table now".
In the Tractatus, Wittgenstein claims that a genuine proposition, which rests upon conventions, is used by us to assert that a state of affairs (i.e., an elementary or atomic fact; 'Sachverhalt') or fact (i.e., multiple states of affairs; 'Tatsache') obtain(s) in the one and only real world.
For a genuine proposition to arise, a sentence type's literal content (as determined by syntax and conventional word meaning) must be enriched or otherwise modified by primary pragmatic processes based on the speakers' background knowledge relative to each particular context of use of the sentence.
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Furthermore, "The propositions that occur in the story, then, are not genuine propositions saying something about some particular person; they are instead merely pretended propositions" (Ibid.).
Unlike genuine propositions, tautologies and contradictions "have no 'subject-matter'" (6.124), "lack sense," and "say nothing" about the world (4.461), and, analogously, mathematical equations are "pseudo-propositions" (6.2) which, when 'true'correctect'richtigtig' (6.2321)), "merely mark… [the] equivalence of meaning [of 'two expressions']" (6.2323).
Wittgenstein answers this question, in part, by asserting that the only genuine propositions that we can use to make assertions about reality are contingent ('empirical') propositions, which are true if they agree with reality and false otherwise (4.022, 4.25, 4.062, 2.222).
She added: "What would be a genuine value proposition for your charity?
The Iraq guarantees were too risky to be a genuine commercial proposition.
This doesn't mean that quantum computers are yet ready to take over the computer industry, but this will be the year that they start to become a genuine commercial proposition.
If, however, "∀nφ(n)" is not a meaningful (genuine) mathematical proposition, what are we to make of this proof?
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com