Re: Logic must "look after itself"
- From: translogi <wilemien@xxxxxxxxxxxxxx>
- Date: Wed, 3 Sep 2008 05:42:18 -0700 (PDT)
On 3 Sep, 00:35, John Jones <jonescard...@xxxxxxx> wrote:
Logic must "look after itself", or so Wittgenstein tells us...
A PROPOSAL
Logic borrows a number of ideas from our dealings with the world which,
if stripped of their original metaphysical and metaphorical intent,
leave us with objects that alone can express a logic that can "look
after itself".
DISCUSSION
Accordingly, "P" ought to say no more than P; here, we might say,
nothing is hidden and logic "look(s) after itself". In respect of that,
we would not expect "P" to entail P and Q. Yet, I argue, by assumptively
lumbering logic with a world baggage, we demand that P should indeed
entail Q. I list these instances:
1) While "P" says only P,
"not-P",
and
"P is true (or false)"
entails P and Q.
This is because negation, truth, and falsity, offer additional logical
object(s) to P: for P to be established either way, other cases must be
considered (cases which I have here generically termed "Q")
(I might add that the existential or ontological status of logical
objects that is indicated by these examples is, if logic is to look
after itself, a matter of indifference.)
2) Laws and axioms, such as the law of non-contradiction, excluded (or
included) middle, etc., also demand extra-logical objects. We can
embrace these objects in a logic provided we sieve out their
existential/ontological/sentential baggage:
For example, applying the law of excluded middle against P we have: "P
cannot be neither true nor false". Yet truth and falsity can only be
asserted in respect of P if an alternative is explicitly on offer (an
alternative which I have here generically termed "Q"). This is because
if we want logic to look after itself we must not assume an implicit
world of objects in support of its operations.
CONCLUDING
Laws, axioms, truth values, logical operations, etc., are worldy
performers which we mistake for the workings of a clear logic. The
logical objects that they introduce are invariably hidden; the explicit
expression of these objects and their structures alone can bring clarity
to those endeavours that should look after themselves.
Logic must "look after itself", or so Wittgenstein tells us...
Where?
(I guess he said something like that but what did he say exactly and
where)
Guess you mean
'There can be no surprises in logic' (Tractatus Logico-Philosophicus
6.1251)
But that has been overruled by Goedels theorems...(Or was that not a
surprice)
Axioms and rules are part and parcel of logic,
whitout them logic becomes useless.
For example if you don't believe modus ponens
(If P and P-> Q then Q )
it is hard to do logic.
(but there are some substructural logics uncovered where even this
doesn't hold, I haven't study them)
Logic is just (literally) to uncover these (hidden) axioms and rules.
So they become visuable and we can think, reflect and argue about
them.
There are many logics where the law of the excluden middle doesn't
hold
see Intuitionistic logic and super intuitionistic logics.
(But here modus ponens still hold)
(super intuitionistic logics are intuitionistic logic + an extra
axiom. but still not implying the axiomschema (A v ~A)
For the rest i support your proposel.
(but what is left of it)
.
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