23 Apr 03
Originally posted by bbarrI wouldn't want a philosophy unburdened by logic and your philosophical interjections are often helpful. But in this case all you were doing was arguing against an extreme position that few people actually hold (that there is no such thing at all as objective reality). That doesn't really tell us very much about the grey, ambiguous, in-between world in which we live. You presumably don't believe that we live in a wholly objective reality either (a statement equally extreme, to the extent that few people would bother making it). So to what extent do you believe that we can objectively know things?
Would you prefer a philosophy unburdened by logic? My claim is hardly mathematical, and still less reductive. If people want to converse in contradictions, fine. But if people want to explore issues without falling into nonsense, they would be wise to adopt standards of good argument. One very good standard is that one's claim ought not imply its own falsi ...[text shortened]... nversations to consist merely in the barking of various noises and not in the speaking of sense.
Rich.
23 Apr 03
1 edit
Originally posted by bbarrseems that it can work both ways though.
So, far from cutting off conversation, logical constraints steer conversation in more fruitful and ultimately more interesting directions.
without some logical constraints, there probably will be chaos with each individual 'barking' a particular point of view. while interesting discoveries may occur in this freeforall, it is very likely no one will notice because there aren't any parameters to mutually pay attention to.
on the other hand, rich's point is not a bad one either. the logical constraint can be very limiting, if it is followed blindly. if we consider the constraint that the earth is flat, then it would be unwise to explore beyond its edge. similarly, the constraint that the universe revolves around the earth produces a very different 'reality', than the constraint that the earth revolves about the sun.
i guess we all use logical constraints, but we need to modify them when appropriate.
23 Apr 03
Originally posted by pradtfYeah, that's very well put. I really wasn't intending to start a crusade against logic here - just demonstrating my usual knack of putting people's backs up without really meaning to.
seems that it can work both ways though.
without some logical constraints, there probably will be chaos with each individual 'barking' a particular point of view. while interesting discoveries may occur in this freeforall, it is very likely no one will notice because there aren't any parameters to mutually pay attention to.
on the other hand, rich's ...[text shortened]... the sun.
i guess we all use logical constraints, but we need to modify them when appropriate.
Rich.
23 Apr 03
Originally posted by pradtfIn cases like this we clarify what is meant by omnipotence. Omnipotence is not the power to do anything, it is the power to do any logical possible thing. It is logically impossible to create a rock an omnipotent being cannot lift, so it is not a threat to God's omnipotence that he cannot create a rock he himself cannot lift. Very few theologians have maintained that God is not bound by logical laws, as this seems to render him beyond all comprehension of creatures like us, creatures who can only conceive of what is logically possible. This is a peculiar aspect to Western religious thought, and it seems to rest on the assumption that the only way humans can relate to God is by an exercise of their intellectual capacities (what has been called 'Natural Religion'😉. In other, contemplative traditions (e.g., St. Theresa de Avilla, St John of the Cross, Meister Eckhart, more recently Thomas Merton, and these are just the Christian mystics) our relationship with God is not mediated by the accurate use of the concept GOD, but by direct access to the divine, or spiritual identification with the divine, or a transcendence of seprateness, etc., depending on who you read.
so how does logic deal with paradox eg.
god can do anything. can god create a rock so heavy, god can not lift it?
are there established processes to handle something like this? how is this sort of thing resolved?
23 Apr 03
Originally posted by pradtfBut these examples (that the Earth is flat, etc.) are not logical constraints. Logical constraints, when violated, entail a logical contradiction. Logical constraints just are logical truths. It is obviously not a logical truth that the Earth is flat. Equally, it's not a logical truth that the Earth is roughly spherical. The sphericity of the Earth is a contingent truth, no contradiction is entailed by its denial. What you are in fact claiming is that discussions are often unreasonably constrained by dogmatism, and I'll not argue that point as you are clearly correct. But logical truths are of a different sort than contingent truths. Although it is conceivable that the Earth might not have been spherical, or at some point could cease to be spherical, it is just not possible that, for instance, the Earth be BOTH spherical and not-spherical simultaneously. This is what I mean by logical constraint.
seems that it can work both ways though.
without some logical constraints, there probably will be chaos with each individual 'barking' a particular point of view. while interesting discoveries may occur in this freeforall, it is very likely no one will notice because there aren't any parameters to mutually pay attention to.
on the other hand, rich's ...[text shortened]... the sun.
i guess we all use logical constraints, but we need to modify them when appropriate.
23 Apr 03
Originally posted by bbarrwhen did logic get involved? logic is simply rules and information that we hold to be true and unbreakable, until we find a better set of truths.
But these examples (that the Earth is flat, etc.) are not logical constraints. Logical constraints, when violated, entail a logical contradiction. Logical constraints just are logical truths. It is obviously not a logical truth that the Earth is flat. Equally, it's not a logical truth that the Earth is roughly spherical.
1000 years ago, the earth was logicaly flat, those who held claim to a shperical earth were illogical/insane/dangerous individuals.
the world is black and white, we blur it.
so anyway, 2nd sence, hearing.
hearing is a simple sence, a small bone some tiny hairs and you got audio reception, again impulses detected by the ear are converted to electricity, which is interpreted by the brain into what we are told is sound.
but sound is vibrations carried along a medium, vibrations caused by movement. Therefore our ears are simply motion detectors.
so why is it wuestioned when people can "see sounds" after all their brains are simply responding to movwment.
23 Apr 03
Originally posted by nktwildLogic got involved when you originally posted a logical falsehood. Moreover, 1000 years ago the Earth was not logically flat (whatever that means) it was contingently spherical. What you mean is, presumably, that 1000 years ago people held that it was a logical truth that the Earth was flat. But, of course, even if they did hold this (and I doubt they did) this just shows that what they mean by 'logical truth' is something radically different than what I, and the rest of the educated world, mean by 'logical truth'. You are assuming that logical truths are just those that we really really believe, so that any belief we are unprepared to give up would count as a logical truth. Again, this is just a misunderstanding on your part. Logical truths are NOT just strong beliefs. Logical truths are propositions that are necessarily true. The denial of logical truths entails a contradiction of the form (P & ~P). Your original statement entailed a contradiction, and it was your realization of this that lead you to modify your position (instead of the incoherent claim that all facts are subjective, you're now claiming that our access to the objective world is constrained by the subjectivity of experience).
when did logic get involved? logic is simply rules and information that we hold to be true and unbreakable, until we find a better set of truths.
1000 years ago, the earth was logicaly flat, those who held claim to a shperical earth were illogical/insane/dangerous individuals.
the world is black and white, we blur it.
24 Apr 03
Originally posted by bbarri wasn't intending anything theological, but thanks for the info anyway.
In cases like this we clarify what is meant by omnipotence.
here's my understand of what you are saying:
the paradox exists only because the two sentences are mutually illogical. in other words, we have a P -> ~P situation.
here's where my confusion lies though:
the statement "X can do anything" is valid as a proposition (therefore, the ensuing question will inevitably create the paradox). however, you are suggesting, i think, that it should not be valid because "do anything" isn't 'logically' valid - it has to be qualified in such a way, so that paradoxes can't take place.
so is this the right idea?
if it is, i guess it is similar to dividing by zero in math. there are certain things that are undefined in a system of logic such as math, so there may be certain things that are undefined (or lead to undefinability) in any system of logic.
24 Apr 03
2 edits
Originally posted by bbarrfrom what i understand from http://www.rbjones.com/rbjpub/philos/logic/001.htm
But these examples (that the Earth is flat, etc.) are not logical constraints. Logical constraints, when violated, entail a logical contradiction.
a contingent proposition is like
"the population of new york is over 1000000"
and is true in some worlds and false in others (eg consider the world when new york was just starting out as a city). because it is contigent upon the particular world, it is not a necessary proposition and therefore not a logical truth.
a necessary truth would be
"either the population of new york is greater than 1000000 or it isn't"
this is not contigent on any worlds (or reality), but is quite logically self-sufficient. hence, it is a necessary proposition. (it is essentially the same as P or ~P).
so facts that are established inductively (by observation) are contingent (because they are dependent on the world they are in) while those established deductively (from axioms) are necessary (because they are independent of worlds - they sort of have their own the one of logic).
now i've forgotten what i was getting at!
it again has to do with the statement "all facts are subjective" (which was not what ntkwild said at the begining - it was "fact cannot exist in the universe because of the way we process info ..." which may be a different story), but that's what we are talking about now - so be it.
ok so the statement
"all facts are subjective"
is a necessary proposition because it is independent of worlds. in this case, it is a necessary untruth, because its existence necessitates its nonexistence supposedly. but the falsity of this statement does not invalidate that some facts are subjective, only that there is at least 1 objective fact.
24 Apr 03
Originally posted by pradtfMost of that is right on target.
ok so the statement
"all facts are subjective"
is a necessary proposition because it is independent of worlds. in this case, it is a necessary untruth, because its existence necessitates its nonexistence supposedly. but the falsity of this statement does not invalidate that some facts are subjective, only that there is at least 1 objective fact.
But propositions are not necessary because they are independent of possible worlds, they are necessary because their denial entails a contradiction. It is OK to say that necessary truths are true in all possible worlds. It's not right to say that the claim 'all facts are subjective' is a proposition whose existence entails its nonexistence. Existence and nonexistence are not properties (as Kant showed in his attack on the ontological proof of God). It's better to say that this claim entails its own falsity.
24 Apr 03
Originally posted by royalchickenThat's an interesting statement. To me it seems that maths is fundamentally a way of checking that none of your sheep have gone missing, or that you have one loaf to give to each of your guests. That would make maths a way of dealing with the physical world in a logical way (ie both your appliations combined in one).
Good way to get me mad 😉. Maths is FIRST a logical system of thought, and SECOND a method for dealing with physcial science.
Of course maths can exist in the abstract, but even there it is only comprehensible by reference to the physical world. For example "1" ultimately represents one physical thing.
Does that sound correct? 🙄
Mick 🙂
24 Apr 03
Originally posted by bbarrI find this interesting too. The Christian faith is hardly logically self-supporting, so I would have thought it was natural for theologians for state that God is beyond comprehension.
Very few theologians have maintained that God is not bound by logical laws, as this seems to render him beyond all comprehension of creatures like us, creatures who can only conceive of what is logically possible.
Mick 🙂
24 Apr 03
Originally posted by mikado1 does not necessarily mean "one physical thing". To give an idea of how abstract maths can get, and how far removed from being a "physics of missing sheep" (I like that 😉) it can be, suppose one wishes to logically construct what we call the positive integers while using as little reference to actually counting objects as possible. One could proceed like this:
That's an interesting statement. To me it seems that maths is fundamentally a way of checking that none of your sheep have gone missing, or that you have one loaf to give to each of your guests. That would make maths a way of dealing with the physical world in a logical way (ie both your appliations combined in one).
Of course maths can exist in the abs ...[text shortened]... xample "1" ultimately represents one physical thing.
Does that sound correct? 🙄
Mick 🙂
1. For some set X, let F(X) = X U {X}. Call F(X) the "follower" of X.
2. Define a 'natural number" in terms of this:
0 -> E (E is the "empty set"😉
1 -> F(E)
2 -> F(F(E))
...
3. A set Y is "inductive" if it contains E and for all X in Y, F(X) is in Y.
4. Then assume, axiomatically, that such a set exists. Now we define our nonnegative integers as the set of sets defined above that are contained in every inductive set.
After this, we might go on to define operations and relations on our set of nonnegative integers, but we have rigourously defined them without really counting anything, which is what maths is really for.
24 Apr 03
Thanks for that reply, but I still don't completely understand.
As I understand your post, F(X) is defined as the "follower" of X. What do you mean by "follow"? Outside my window I can see a queue of traffic, with a red car followed by a blue car, followed by a green car, etc. However I wouldn't want to make the sequence of colours in the traffic outside my window the basis of all mathematical theory. Your logic only appears to work if you define "follow" to mean "follow at increasing integral intervals" which would make your definition of "integer" a tautology.
If I imagine an alien born without senses of any kind (and without any inbuilt capacity to imagine sensory perception) then I cannot imagine how that alien could formulate maths, having no reference points to work from.
I'm certainly not suggesting that maths exists in order to support the science of "physics". It is stretching things to suggest that simply counting things (like sheep) is "physics". But I'm interested in the concept that maths can be purely abstract without reference to a physical world.
I trust I'm not either misinterpreting you or stating the bleeding obvious!! 😀
Mick