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Practical inference: practical conclusions go from an idea, a wish, or a statement, and lead to an intention of action. Practical conclusions lead to a weaker justification than extended normative conclusions. (See C. Beisbart, “Handeln Begründen, Motivation, Rationalität, Normativität“, Münster, 2007, p. 223).

Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

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Anthony Kenny on Practical Inference - Dictionary of Arguments

Geach I 285
Practical Inference/Kenny: (Analysis 26,3,1966). Thesis: Theoretical and practical inference are radically different.
Geach: What they have in common is a certain asymmetry between premises and conclusions.
1. A lot of premises provide a single conclusion and cannot be achieved with any of these premises.
2. On the other hand, a set of conclusions follows from a single premise only if each individual conclusion follows from it on its own.
Carnap and Kneale have sought technical solutions to this asymmetry. GeachVs: one should leave the asymmetry.
It remains in Kenny's approach. If a set of conclusions would always be deducible together, but not individual conclusions...(s) then the set itself could not follow.

Practical Inference/Kenny/Geach: I present it in the style of Kenny:
From a set of commands

Fq, Fr, Fs... one can conclude the conclusion Ft,

provided that the phrastic of the conclusion entails the phrastic of a premise and that it is consistent with the phrastic of all other premises. I. e.

t ent q and the conjunction

Kt, Kr, Ks... is consistent.

Spelling: ent: entails, p ent q = p contains q, q follows q from p, entailment
Kpq: Conjunction p u q
Cpq Conditional p > q

It is about how a wish is consistent with other wishes.
This immediately means that no practical conclusion can be drawn from an inconsistent set of commands. When

Kq, Kr, Ks... is an inconsistent conjunction and t ent q, then
Kt, Kr, Ks... is inconsistent and then Ft is not valid deducible from the set FqFrFs....

Further difference to theoretical inference: practical inference can be cancelled. (>added premises).
Geach I 287
Definition Synthetic theorem/Peripathetics/Geach: the principle that if a conclusion t follows from its set of premises P, and if P plus t delivers the conclusion v, then the premises provide P v.
Only if the synthetic theorem applies, we get a chain of inferences. That is what we need in theory and practice.
Kenny's theory secures the synthetic theorem.

Practical Conclusion/Kenny/Geach: it is necessary for a correct conclusion Ft from a set of premises that (the phrasticon t ent the phrasticon v) from one of these fiats (commands) is compatible with the phrastics of all other fiats from the set.
We can omit the word "or" if we formulate it in this way:
t ent v, KtKpKqKr.... is a consistent conjunction if and only if
KtKvKpKr.... is consistent.
Proof: with the validity criterion in this practical form:

We have to show that from
(1) Ft is deducible from Fp, Fq, Fr...
(2) Fv is deducible from Ft, Fp, Fq, Fr...
from that follows that
(3) Fv is derived from Fp, Fq, Fr.....
(1) holds if and only if t ent (one of the phrastic p, q, r...)
I 288
and if the conjunction KtKpKqKr.... is consistent.
Without losing the general public, it can be said that t ent p.
Now (2) will hold if and only if v ent (one of the phrastic t, p, q, r...) and the if conjunction KvKtKpKpKqKr... is consistent.

But if v ent t, because t ent p (through (1)), then v ent p.
And no matter if v ent t or v ent (one of the phrastics of p, q, r...), v is always ent one of (p, q, r...).
Now if KvKtKpKqKr... is a consistent conjunction, then also KvKpKqKr is ...
Then v ent (one of p, q, r...) and KvKpKqKr... a consistent conjunction. (3) Q.E.D. holds.
Premises/Added/Deleted/Inference/Conclusion/Concluding/Inference/Geach: although the modus ponens becomes invalid by added premises, a conclusion from the modus ponens will remain valid if it does not become invalid by an added premise.
Because we do not get any conclusions from inconsistent practical premises.
But if p and Cpq are consistent, it is also p and q. So Kpq will be consistent. And q ent cpq. But then Fq is a correct conclusion of Fp and FCpq!
Practical Inference/Kenny/Geach: surprising result: in practical closing, the FKpq command is not deductively equivalent to the pair Ep, Eq.
But this is not really paradoxical: the equivalence would lead to an absurd result, because for the same reason the set Fp, Fq, Fr... would be deductively equivalent to FKpKqKr...
But this latter order could only be fulfilled if it were guaranteed that all our wishes could be fulfilled at the same time.
We therefore need further closing rules for practical closure.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kenn I
A. Kenny
A New History of Western Philosophy

Gea I
P.T. Geach
Logic Matters Oxford 1972

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