G) On the spirituality of the 21st Century, Malraux revisited
In a less fortunate thread, Tristan said:
"Statements
(A) XXIth century will be spiritual OR will not be.... (André Malraux)
(B) The current debate is more and more spiritual AND is not a debate... (ok i assume, given the current material)
Deductions....
(a1) The current XXIth century is not a century OR it is spiritual OR it has not yet begun OR it is already ended [OR connector in natural language most of the times means \"mutual exclusion\", but not always]
(a2) ((a1) consequence): (because i assume it has begun and it is not ended yet and it is much spiritual) \"we don\'t care if XXIth century is not a century\"."
Now, l'ami Tristan was bravely battling pseudophilosophy, so we can't be too judgemental of his formulation. Nonetheless, when we consider the Malraux statement not under propositional logic but under first order, we see clearly that there's a problem :
i. the 21st century will be spiritual OR the 21st century will not be
which has the apparent form
i*. p v q
is now
ii. there is some x such that (x is the 21st century AND x is spiritual) OR ~(there is some x)
(ii) is not well-formed.
We could perhaps give (ii) as
ii*. there is some x such that (x is the 21st century AND x is spiritual) OR ~(there is some x such that x is the 21st Century)
(ii*) has the overall form of a material implication, and can be rewritten as
ii**. there is some x such that IF x is the 21st century THEN x is spiritual
However, (ii**) is only *not* the case if the 21st century exists, but is not spiritual - it holds perfectly well if there is no 21st century AND the 21st century is spiritual, which is an "intuitive paradox".
I'd therefore suggest that we read the operator as a biconditional:
iii. There is some x such that x is the 21st Century IFF x is spiritual
Firstly, (iii) allows us to quantify over the whole expression (rather than negating an existential quantifier in the second disjunct, as was the case in (ii*)) and also avoids the intuitive paradox of the 21st century both "not existing" and "being spiritual". From (iii), it follows that, (IF there is a 21st century, THEN it is spiritual) AND (IF it is not spiritual, THEN there is no 21st century) which, I think, better captures Malraux's intention.
***
To return to your conclusions:
a1. There is some x such that x is the 21st Century
This is debatable, as "the 21st century" is a conventional denomination. Let's nonetheless agree that some region of spacetime corresponds to "the 21st Century" and accept (a1)
a2. Therefore, it follows that EITHER the 21st Century is spiritual OR that Malraux made a mistake
This board is not a soapbox for cranks. Others are being far too polite with you.
Logic is not a matter of "point of view", but of formal rigour. I undoubtedly lack sufficient rigour at times, but - having been formally trained - I'm at least *aware* of my limitations. You, unaware of your limitations, have taken your fantasies for realities and thereafter attempt to pervert 'mathematics' to the ends of your pre-established objectives. You seem entirely closed to the possibility that you are in massive error - and a 'true' scientist is as open to the failure of his hypotheses as to their success. As you have already decided that God, or spirits, or some other supernaturalist claptrap, is "the case", why bother dragging maths in? Do you think it makes your thinking less magical?
"Spirits that are human essence" is meaningless obscurantism. Before basing a system on such nonsense, you'd do better to give a clear proof of your contention. And - unless you can formulate your proof in an accepted logical system - you'd do better to post it somewhere else.
This group was established for those of us who wanted to discuss logical questions without overcharging Emrah's group. If you have any remarks to make on logics or their application, we'd be pleased to read them. But if your sole objective is proselytism, you'd be better off elsewhere.
"First: Why i used OR when i knew i should have used IFF."
No "should" about it: it's an excellent - and real - illustration of indeterminacy. Any 'translation' into logical form is as good as any other, if we respect the syntax... we can then argue about *interpretation*, but - as we saw - we had to presuppose a semantics (the "intuitive paradox" is that we can *suppose* that p is false but still affirm that "p -> q" is true). If we were arguing the interpretation of a theory here, someone could easily decide to bite the bullet and accept that the most important message is that it cannot be the case that there be a 21st Century AND that it not be sipritual (and never mind those cases where there's no Century and it's still Spiritual or there's neither Century nor Spirituality).
Nonetheless, I'm looking forward to sharpening my logic again - I haven't done any for years.
***
"Second: Why the equivalence between your conclusion iii and my statement A is tautologic IF AND ONLY IF WE SUPPOSE AT A HIGHER LANGUAGE LEVEL that Malraux made a mistake OR(inclusive) that the 21th century isn't bothered by spirituality OR(inclusive) that the 21th century doesn't exist. (i am perhaps too quick with the goal and the demonstration will maybe offer an implication instead of an equivalence, wait and see)"
Now, let's see - can we formalise this a bit?
╞ (There is some x such that x is the 21st Century IFF x is spiritual) = (the 21st century will be spiritual OR will not be)
IFF
There is some F such that F is the property of "supposing that Malraux made a mistake OR(inclusive) that the 21th century isn't bothered by spirituality OR(inclusive) that the 21th century doesn't exist" and we have F
???
Intriguing - I shall wait and see!
***
"Third: A high level consequence for the demonstration could be: existence of spirituality is not related to time and therefore spirituality may exist after the end of times.
If you agree, let's call it the Spiritual Paradox."
Now this, dear Tristan, is sailing dangerously close to my domaine de prédeliction. If we get as far as third, we might have to take the debate to the philsophy of time thread.
***
"And if you still agree after that conclusion (+infinite is spiritual), let's publish a best seller that will revolutionate the face of the world."
I aready have a title: "The Chronic Argonauts: Investigations into Time and Space". We can use my Facebook profile picture as the cover...
I must admit that I felt a bit pretentious in setting up this group - I've got a master's in philosophical logic, but anything beyond that is just a question of "research skills". I can handle most systems, and have a good grasp in a few; but I'm certainly no expert in the more formal areas. You're certainly far better in mathematical logic than I am...
All the same, *applied* logic is still the major tool of the analytic approach, so I'm looking forward to seeing what direction you'll take your 'discursive logic'...
Tristan - I will say that I was lucky to have as tutor Philippe de Rouilhan, who is an analytic philosopher of the old school - the kind for whom speculation of the metaphysical sort is entirely secondary to the understanding of the tools of analysis themselves...
It's also true that you can't do analytic philosophy without a good grounding in the most common logics (mostly first-order and modal). Fifteen years ago, you couldn't get a thing looked at if it wasn't full of analysed expressions...
I agree, you can't talk about a drawing a logical conclusion about football, save in the sense that football is already defined as a set of rules and a certain ontology (I'm being deliberately technical here). If we take "talk about God" to be loosely constrained by a certain set of descriptions and a certain ontology, we can indeed draw "conclusions about God". Mike Liccione, if he were to participate, would certainly talk about this far better than I can... Let's imagine that we hold certain descriptions of God to be true of him - that he is absolutely omniscient, for example. Now, we can draw certain logical conclusions - for example, that in order to be absolutely omniscient, God would have to know everything in every possible world. We can also ask logical questions - in order to be absolutely omniscient, must he know all possible events, or only those events which actually occur? The ontological jungle that opens up from such speculation is apparent in much of Scholasticism.
For that matter, the "problem of evil" is an an entirely logical problem: Let us postulate that God is omniscient, that he is omnipotent, and that he is all-benevolent. We can give these semi-formally as
i. there is no x such that God does not know x
ii..there is no x such that God cannot affect x
iii. there is no x such that (x is evil & God can tolerate x)
These could be formulated differently, but they'll suffice. Now imagine that, in (i...iii) above, x = 'Auschwitz'. The theological problems follow logically.
This board is not a soapbox for cranks. Others are being far too polite with you.
Logic is not a matter of "point of view", but of formal rigour. I undoubtedly lack sufficient rigour at times, but - having been formally trained - I'm at least *aware* of my limitations. You, unaware of your limitations, have taken your fantasies for realities and thereafter attempt to pervert 'mathematics' to the ends of your pre-established objectives. You seem entirely closed to the possibility that you are in massive error - and a 'true' scientist is as open to the failure of his hypotheses as to their success. As you have already decided that God, or spirits, or some other supernaturalist claptrap, is "the case", why bother dragging maths in? Do you think it makes your thinking less magical?
"Spirits that are human essence" is meaningless obscurantism. Before basing a system on such nonsense, you'd do better to give a clear proof of your contention. And - unless you can formulate your proof in an accepted logical system - you'd do better to post it somewhere else.
This group was established for those of us who wanted to discuss logical questions without overcharging Emrah's group. If you have any remarks to make on logics or their application, we'd be pleased to read them. But if your sole objective is proselytism, you'd be better off elsewhere.
Studies the formal behaviour of inference operations which, whilst not monotonic, may nevertheless satisfy various other conditions, notably that of cumulativity. Very widely cited in the literature.
Medium-scale-integrated (MSI) circuits consisting of up to 280 heterojunction bipolar transistors (HBTs) were designed and fabricated. These include an 8-bit universal shift register, a 3-bit register, and a gated full adder. The design considerations, HBT fabrication, and device characteristics are described. Correct operation was observed at cloc...