From a
deducibility point of view it is better and easier to work with a refined system than with a rough system.
Tax
deducibility simply means that a $1000 donation to
Lapointe nicely brings out how Bolzano's broader perspective on which elements in propositions can be viewed as significantly variable leads him to equally broader notions of quantification (universal validity (Gultigkeit)) and
deducibility. She also shows how Bolzano is then able to extend both notions (validity and
deducibility) to forms besides those of the then--traditional logic (e.g., involving relations; cf.
Meillassoux interprets this supposed
deducibility of the categories as 'an unconditional necessity that abolishes the possibility of there being an in-itself that could differ from them'.
The turnstile [??] stands for "logico-mathematical
deducibility." The absurdum [perpendicular to] applies to three cases: those K[phi] where [phi] is itself inconsistent, cases in which inconsistency results from iterations of K operators (e.g.
a defined sentence in an S-denied theory can be partially deducible and partially undeducible (we talk about degrees of
deducibility of a sentence in an S-denied theory).
However, rejection of some of our efforts to formulate logic does not amount to a rejection of logic itself, that is, the concept of
deducibility. For,
deducibility is presupposed by the very possibility of improvement through criticism, which depends on deductively valid arguments which transmit truth from premises to conclusion (are truth-preserving) and retransmit falsity from the conclusion to the conjunction of the premises.
With the current maximum
deducibility limit at 100%, it impossible to create sufficient savings to protect plans in the event of a downturn in the market.
To benefit from the tax
deducibility of interest payments on debt raised to repurchase shares.
One of the contributions of this article is to show how the recursive processes of inquiry maintain objective rationality even in the absence of analytic
deducibility.
So, in order to find out what he means, you normally have to assume that he is not committing any logical errors [...] But what is impossible, in regard to logical
deducibility, is to achieve some firm determination of how a person understands occurrences of logical particles that is quite independent of determining what his singular intuitions are about logical contradiction and
deducibility."
But the identities are so deducible all the same, and their
deducibility is what makes the phenomena in question reductively explainable.
We recall that there are completeness theorems for ordinary propositional logic (PC) and intuitionistic logic (IL) which assert connections between the analogous forms of
deducibility in these logics and the behavior of morphisms, or valuations, of formulas into certain classes of lattices: Boolean algebras in the case of PC and Heyting algebras in the case of IL.
1959: "Entailment and
Deducibility", in Proceedings of the Aristotelian Society, 59, pp.
