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Moody
Saturday, September 30th, 2006, 05:05 PM
In his 'An Introduction to Philosophical Analysis', John Hospers makes the distinction between three types of 'possibility';

i) Empirical possibility,

ii) Technical possibility, and

iii) Logical possibility

Unfortunately, much non-philosophical thinking stops at the first two, and sees things only in terms of either empirical and technical possibility.

However, Philosophy deals in the main with Logical possibility[LP].

Nietzsche's eternal recurrence of the same could be seen as an example of a LP.

The 'eternal recurrence' says that events from the past will recur again in the future in exactly the same way, and in exactly the same form, as they did in the past.

Those who recoil from this notion may not be aware of LP.

With LP the philosopher is able to open up the world of thought to untold possibilities.

But LP does not mean that 'anything' is possible, of course; it means that, as long as no self-contradiction is involved in a proposition, then the proposition is a LP.
In other words, anything 'logical' is possible.

Hospers argues for example, that time travel is not a LP.
However, in the process of so doing, he demonstrates that 'the eternal recurrence of the same' is a LP.

"It is logically possible that history might suddenly start repeating itself: that on January 1, 2006, all of our modern buildings & machinery would disappear & we would find ourselves among sand & pyramids & the world of 3, 000 BC.
This repetition is logically possible [though not empirically, to the best of our present knowledge], but it would be a repetition with a difference: the first time you were there [3,000 BC], you weren't there; & the second time [AD 2006], you were.
This would not be a case of literally going back in time to 3,000 BC: it would be a case of history repeating itself [with a slight difference], with the world of 2006".
[Hospers, ib., page 173-, slightly adapted]

So feel free to anounce your logical possibilities here in the Philosophy forums!

Wiki article;
http://en.wikipedia.org/wiki/Logical_possibility

Pervitinist
Saturday, September 30th, 2006, 10:48 PM
Is it logically possible that 5+5=11?

Janus
Saturday, September 30th, 2006, 10:51 PM
Is it logically possible that 5+5=11?
Of course it is! All we need to do is move away from a decimal system and take away a random number except 1 and 5 ;)

Pervitinist
Saturday, September 30th, 2006, 11:04 PM
Of course it is! All we need to do is move away from a decimal system and take away a random number except 1 and 5 ;)

Good point. But what if we keep the decimal system?

Janus
Saturday, September 30th, 2006, 11:28 PM
Good point. But what if we keep the decimal system?
Then we just change the order of the numbers ;)

Pervitinist
Saturday, September 30th, 2006, 11:37 PM
Then we just change the order of the numbers ;)

LOL! Well, let me put it differently: It is empirically impossible (at least without taking psychedelic drugs) to add five apples to five apples and get eleven apples. But is it also logically impossible? If so, why?

Janus
Saturday, September 30th, 2006, 11:42 PM
There are various ways:
For example one apple could suddenly due to a anomalia in the space-time-continuum or somebody completly unrelated throws an apple to your apples etc ;)

Tryggvi
Sunday, October 1st, 2006, 10:32 PM
LOL! Well, let me put it differently: It is empirically impossible (at least without taking psychedelic drugs) to add five apples to five apples and get eleven apples. But is it also logically impossible? If so, why? No, it is not logically possible. Logically possible is whatever can exist without logical contradiction. Thus, it's logically possible that you could have wings tomorrow and be able to fly, but it's not logically possible that 5+5=11 or that you are omnipotent and omniscient at the same time.

SuuT
Monday, October 2nd, 2006, 01:18 AM
1.) It is logically possible that we live in the best of all possible worlds.

2.) It is logically possible that the world, as we know it, is the creation of a consciousness beyond our own and governs what we believe to be our own consciousness.

3.) It is logically possible that this consciousness that governs our consciousness imposes restrictions upon the world as we know it, such that logical contradiction exists as logically possible in a world in which it is so, without us being able to say that x, which is a logical contradiction in the world as we know it, is a logical possibility in the world as it ontologically is; as the world as we know it is limited by the imposition of a higher governing consciousness.

The rub:

The governing consciousness imposing restrictions on our consciousness such that we unable to make logically possible a logical contradictory, limits our knowledge of the extent to which logical possibility applies to this world, which might be the best of all possible worlds, is metaphysically contingent upon access to what lay beyond the consciousness which governs our own: a world is possible in which logical contradiction is an illusion; it may be our own.

This does not involve a contradiction.

A particular, and more practical, illustration of uncertainty as a constant as seen in Quantum Mechanics:

http://plato.stanford.edu/entries/qt-uncertainty/

Pervitinist
Monday, October 2nd, 2006, 11:52 AM
Thanks for this enlightening line of argument!


The governing consciousness imposing restrictions on our consciousness such that we unable to make logically possible a logical contradictory, limits our knowledge of the extent to which logical possibility applies to this world, which might be the best of all possible worlds, is metaphysically contingent upon access to what lay beyond the consciousness which governs our own: a world is possible in which logical contradiction is an illusion; it may be our own.

This does not involve a contradiction.

To draw a conclusion for my question whether it is logically possible that 5+5=11:

Since it is logically possible that what we hold to be logically possible is the outcome of a higher consciousness - or let's be traditional and call it a Cartesian genius malignus - restricting our epistemic access to the realm of actual logical possibilities, the claim that it is logically impossible that 5+5=11 is logically possible is unfounded.

But does that mean that it is logically possible that 5+5=11?

We can't make this claim either, because in order to do so we would have to exclude the logical possibility that e.g. the genius malignus G that restricts our access to the realm of logical possibilities might himself be subjected to another genius malignus G* restricting G's access to the realm of logical possibilities.

As long as the logical possibility of G being deceived by G* cannot be excluded, G might be wrong in thinking that he is deceiving us about the logical possibility of 5+5=11.

So, provided that there is no third genius malignus G** fooling around with G* - our conviction that it is logically impossible that 5+5=11 might be not only


(a) induced by the genius malignus G

but also

(b) true due to G's being misled by G*.


Conclusion:


(1) We cannot positively claim that 5+5=11 is logically impossible because we cannot exclude the logical possibility of being misled in our judgement by a genius malignus G.


(2) We cannot positively claim that 5+5=11 is logically possible because we cannot exclude the logical possibility that G is misled by another genius malignus G*.

Still,


(3) We have the strong intuition that 5+5=11 is in some sense impossible (provided that we use the decimal system, the common semantics of mathematical symbols etc.)

The question is: Is this impossibility logical or merely mathematical?

Another question is: Does the concept of logical possibility make sense after all in view of skeptical arguments like the ones sketched above or does it rather reduce to some kind of common sense/intuitive or pragmatic possibility?

SuuT
Monday, October 2nd, 2006, 09:03 PM
...


To draw a conclusion for my question whether it is logically possible that 5+5=11:

Since it is logically possible that what we hold to be logically possible is the outcome of a higher consciousness - or let's be traditional and call it a Cartesian genius malignus - restricting our epistemic access to the realm of actual logical possibilities, the claim that it is logically impossible that 5+5=11 is logically possible is unfounded.

But does that mean that it is logically possible that 5+5=11?

We can't make this claim either, because in order to do so we would have to exclude the logical possibility that e.g. the genius malignus G that restricts our access to the realm of logical possibilities might himself be subjected to another genius malignus G* restricting G's access to the realm of logical possibilities.

As long as the logical possibility of G being deceived by G* cannot be excluded, G might be wrong in thinking that he is deceiving us about the logical possibility of 5+5=11.

So, provided that there is no third genius malignus G** fooling around with G* - our conviction that it is logically impossible that 5+5=11 might be not only


(a) induced by the genius malignus G
but also
(b) true due to G's being misled by G*.Conclusion:


(1) We cannot positively claim that 5+5=11 is logically impossible because we cannot exclude the logical possibility of being misled in our judgement by a genius malignus G.
(2) We cannot positively claim that 5+5=11 is logically possible because we cannot exclude the logical possibility that G is misled by another genius malignus G*.Still,


(3) We have the strong intuition that 5+5=11 is in some sense impossible (provided that we use the decimal system, the common semantics of mathematical symbols etc.)The question is: Is this impossibility logical or merely mathematical?

Another question is: Does the concept of logical possibility make sense after all in view of skeptical arguments like the ones sketched above or does it rather reduce to some kind of common sense/intuitive or pragmatic possibility?

This is a great example of the Uncertainty Constant in action.

With respect to question #1.) The possibility is metaphysically contingent upon access to what genius malignus knows that we do not. There is no contradiction involved in saying that we can--we just don't know how.

I may be genious malignus. You may be him. However, he may not know that I/you/we are he! (a conundrum...)

Mathematically, however, it doesn't matter how complex it gets from 1+1: the mathematics behind String Theory still work within the rules, the laws, of the known universe (even though malignus may have exactly the ontological status we have applied to him in this example). Therefore, its mathematical impossibility is, and will remain, that. (Think Newtonian physics/Relativity: math 'works').


With respect to question #2.) Logical possibility has the leisure to operate in the highest levels of abstraction (ergo its necessity in Traditionalist Metaphysics), as well as the most banal deductions of probability and deduction (e.g. the sun dawned today, it will do so tomorrow): it is both pragmatic and 'useless'.

Moody
Wednesday, October 4th, 2006, 02:36 PM
Since it is logically possible that what we hold to be logically possible is the outcome of a higher consciousness.

What is the logical argument for the "logically possible" 'higher consciousness'?