Well, my argument was all along that the inference from the exception
to the existence of the general rule is logically valid. As all
logically valid inferences are indeed tautologies, saying that my
inference would be tautologous is essentially saying that I'm right, no?
In particular you can always rewrite in classical logic a valid
inference as a single sentence, that's because it is sound and complete.
So of course having inferred the existence of a general rule from that
of an exception then allows you to restate the rule as a single sentence.
So the process of reasoning that leads us from the known "no parking
between "9-12" to the unknown "Parking is generally allowed" can then
afterwards rewritten as " Parking is generally allowed unless the
council prohibits it for a limited period of time and announces this
limitation to the public" The "unless" part states the exception, now
simply incorporated into a more complex rule, but that is exactly what
we expect in logically valid inferences.
Furthermore, I gave above the full quote of the principle, not the
truncated version that is often cited:
"exceptio probat regulam in casibus non exceptis" and in
that full version it makes more sense: an exception establishes the
existence of a rule in those cases where the exception does not apply"
Note the plural of "cases". The exceptional cases are governed by the
rule that creates the exception, and from this limiting rule we can
infer the general rule
>
>
>> Typical example is the law of murder:
>>
>> General rule: you must not kill
>> Exception in the form of a rule: unless you act in self-defense which
>> is permitted
>> Exception to the exception, in the form of a rule: unless the
>> self-defense is excessive, which is not permitted
>> Exception to the exception to the exception: unless you rationally
>> believed that your act was proportionate, given what you knew at the time
>> Exception to the exception to the exception to the exception: unless you
>> intentionally caused your lack of knowledge to avoid responsibility.
>>
>> Very typical which is why we use non-monotonic logic (those of us who
>> still do GOFAI) to represent them.
>>
>> And the same in science - the example of Newton's first law I gave you
>> has a general rule (things at rest stay at rest) and then an exception
>> in the form of a rule (all things that are acted on etc...)
>>
>> The distinction is in the scope of the quantifier, the exceptions
>> restrict the scope fo the rule it is an exception to
>
>
> Your examples above use a different meaning of "exception" than the
> meaning you used before, to argue "the exception proves the rule".
> Your latest examples are part of a general rule, while your previous
> examples were exceptions outside the general rule, ex. Balbus.
Don't think so, my usage is the same in all scenarios.
First, just to be clear, Balbus wasn't the exception, it was his case
that established the principle that the exception proves the rule.
The exception in the Balbus case was the practice of the Senate to
accept as a clause in various treatises with the German tribes a
"non-interference condition". This demonstrated a legal rule: If so
agreed through a treatise between Rome and a vassal state, the Roman
senate can not confer citizenship unilaterally to any of the subjects of
that state without explicit permission of the King of that state." In
modern parlance, an international treaty can limit the sovereignty of
the Senate to act unilaterally
Cicero argues that the only way to make sense of this rule is to see it
as an exception to a general rule: The Senate has the power to confer
unilaterally citizenship to the citizens of vassal states.
If, hypothetically, the senate didn't have the power to confer
citizenship to subjects of a vassal state to begin with (e.g. because
only "naturally born" Romans can be citizens), it would not make sense
to agree not to use this (non existing) power in an international treatise.
The exception, which both sides agrees exists (the evidence are the
treatise) thus proves the existence of the rule that is contested
between the parties - the general power of the senate to confer
citizenship.
Of course, as above, once this argument has been successfully made, you
can then restate the law:
The Senate has the power to confer citizenship on subjects of a vassal
unless there is a treatise between vassal and Rome where Rome agrees not
to use this power.
Cadiz did not have such a treatise with Rome, hence the case of Balbus,
the exception did not apply, hence he had validly acquired citizenship
by a unilateral act of the Senate.