Bo 'n Thigle

[bo198214]

Bo: "Ok, do you see the house there, I want do something similar but ..."
Thigle: "There is no house at all, it is an illusion."
Bo: "But nontheless you and me see the house, so lets progress with planning the new house."
Thigle: "It is impossible to plan a house when not regarding the actual stock market."
Bo: "I can plan the house anyway."
Thigle: "You can but then you are stuck."
Bo: "Thousands of masons have built a house with completely disregarding the stock market."
Thigle: "You are ignorant of my broadness (I could teach you so many things *sigh*) and dont get it at all."
Bo: "I want to plan a house."
Thigle: "There cant be a house, how will you plan it?"

[thigle]

hey bo, you project over what i said, and say i said what i didn't. that's why you misunderstood me.

and if the mirroring metaphor didn't clarify it, then i really don't know...

perhaps we can proceed from this:
do you accept a possibility of something being BOTH true and false at the same time?

(and btw, you do act ignorant, as the above dialogue is not true to what we discussed in nondimensional being & consciousness, it is biased. :wink: )

[bo198214]

Its only an allegory, its my mirror for you.

[thigle]

thank you. i missed the laughing emoticon at the end of your post.
so time to get less serious

i must appreciate now that your allegory has a certain elegance in catching the clumsiness of our trials at communication i the other post. it even makes me laugh now,

[wendy]

A statement is true relative to what its context. It is not intrinsic, or self-contained. If there is two possible contexts, then there are two different readings, and one can be true to one and false to another.

Some visual illusions, particularly the edges of a cube, rely on this.

W

[moonlord]

There are also some paradoxes whose truth value cannot be determined. Some could say they're both true and false in the same context. I personally make a difference between 'neither true, nor false' and 'true, but also false'.

[thigle]

wendy sais:

A statement is true relative to what its context. It is not intrinsic, or self-contained. If there is two possible contexts, then there are two different readings, and one can be true to one and false to another.

a statement in n contexts has n interpretations, and without dual aristotelian logic of excluded-middle, we can as easily as wendy does see a statement to be possibly true for <0,1,...,n> of those simultaneously
for n=5, these logical values could be charted :

00000
00001
00010
00011
00100
00101
00110
00111
01001
01010
01011
01100
01101
01110
01111
10000
10001
10010
10011
10100
10101
10110
10111
11000
11001
11010
11011
11100
11101
11110
11111

so there is a gradient of 31 truth values ('truth-shades') for a statement in 5 contexts.

but any number of (possible) contexts, they all have have a common context, a meta-context, the field of contexts, which make them all similar by their difference. (lived body, languague, worldview-structure,...)
so statements whose meaning is interdependent on contexts (not exclusively) are all connected from inside as well as globally from outside.

moonlord wrote:

There are also some paradoxes whose truth value cannot be determined. Some could say they're both true and false in the same context. I personally make a difference between 'neither true, nor false' and 'true, but also false'.

actually, that what is ordinarily understood under the label of 'logic' or 'logical', is only one kind of logic, the one we use to consider all-logic, what stemmed from aristotle's principle of identity, or sometimes called 'excluded-middle': that a thing is not identical to itself (that it lacks identity, or essence - that it ain't of its Kind) if it is both A and antiA. in other words, that a thing cannot be dead & alive at the same time, or white & black, or...
so the logical modalities of BOTH and NEITHER were excluded from western thinking for well more than a dozen centuries (and still are for many, as you can see even on these forums, even for some who claim logic to be one of their favorite subjects)

but, boole's logic of the last century (which is responsible also for the very ability of computers to get difference from 0s and 1s - the logical gates thing), as well as more than thousand years old logic of siddharta's tetralemma and nagarjuna's reaction to it & its transcendence, all consider the logical frame, or the structure of logic, to be at least such that a tetrahedron is a simplex of logic - a 4-tuple configuration with 4 vertices as A, antiA, Both, Neither values.

but contrary to what is commonly believed, even aristotle knew of middle-terms reasoning. (he specifically says: "reasoning through middle-terms is credible but not real"(in Widdows:Geometry&Meaning))

so you work with BOTH and NOR values as well.
do you also meet with problems when communicating with ordinary people that cannot expand beyond OR ? what exemples do you give them to explain it ?

nagarjuna says that between sameness and difference of those 4 lies the shunyata - emptiness or openess. this corresponds to running out of 'logic' into the realm of alogical. similarly the division algebras disintegrate into zero-divisor algebras, after the 4 algebraic properties of Reals fall off by stepping through into imaginaries, quaternions, and finally from octonions out into the open of the zero-divisor algebras. 'algebra' comes from a name of a scholar that meant a 'stone' so i like to think of zero-divisor algebras as 'empty-stones', or 'open-algebras'.
also, nagarjuna's 5th 'alogical' logical position, his 'shunyata' concept, that is a name for an actuality of what can be considered a 5th point beyond (or with) the 4 points that represent the 4 logical parameters.
that is, it is at position [0.0.0.1], the 5th vertex added to 3d tetrahedron, making it into 4-simplex, a pentatope with its 5th logical vertex (or alogical from the position of any of the other 4 logical parameter vertices) that lays in 'beyond' the other 4 but is in equal relation to all of those.

i wonder, beyond that 4-d logical lattice, (which is a double diamond lattice) what lies there ? i mean: in 4-fold logic of tetrahedral frame, one gets a stella-octangula if each centre-vertex segment is taken to be positive axis-part, and the tetrahedron is inversed through centre to get negative values for each of the 4 parameters. so 2 tetrahedrons in a cube.
similarily, how many pentatopes(5-cells) fit into one hypercube ? it doesn't seem to fit. or should i fit them into the hamiltonian path between the 8 centres of the 8 3-cubes that form the 4-cube's hypersurface ? which would give a self-dual pair of 5-cells ?

[jinydu]

The existence of statements with different truth values depending on context does not refute duality, it only shows that you have to be careful enough to specify a context when posing questions. For example, the question: "Given a line L and a point P not on L, does there exist a line through P that does not intersect L?" has different answers depending on whether you're working in Euclidean or, for instance, elliptic geometry. However, the problem is not with Aristotelian logic; the problem is that the question was too vague. Had a particular geometry been specified, there would have been one and only one right answer.

Sorry thigle, but duality is (thankfully) the law of the land in both mathematics and natural science.

[moonlord]

Um, thigle, aren't there 32 values?

[wendy]

One must understand that there is a lot of cross-linking, and so there are many less possibilities than if all the values are freely settable.

W

[thigle]

moonlord: yep. 01000 is the 32nd. thanxalot :wink:

jinydu wrote:

The existence of statements with different truth values depending on context does not refute duality, it only shows that you have to be careful enough to specify a context when posing questions.

For example, the question: "Given a line L and a point P not on L, does there exist a line through P that does not intersect L?" has different answers depending on whether you're working in Euclidean or, for instance, elliptic geometry. However, the problem is not with Aristotelian logic; the problem is that the question was too vague. Had a particular geometry been specified, there would have been one and only one right answer.

Sorry thigle, but duality is (thankfully) the law of the land in both mathematics and natural science.

no need to apologize. i like duality, and there's no need to refute it. (which i never claimed). but duality is not dualISM. nowhere in this thread did i denied duality wholly, i just showed what it blocks from viewing, it's inappropriateness in certain contexts
so i just disagree when dualism is applied to issues essentialy more complex than dualism allows for and when such issues(questions) are forcibly(or blindly) tried to be fitted into(answered by) a concept(of duality) that is obviusly as inadequate as trying to fit a Klein's bottle into 3d space without a singularity of self-intersection. it's just not possible to do it without that singularity.

and therefore again: the problem is not ONLY, (or determinatively) the vagueness of (your exemple) question (or what might be called absence of context-specification, but ALSO the space(or attitide,ambience) frrm which the one who gives the answer does so, because when that attitude(perceptivity) tries to neglect or even deny the vagueness, when one tries to persuade others and itself that vagueness, or indeterminacy, or openess, or feminine or Wilderness or whathaveyou is a PROBLEM, in still other words, when the logic of the answer is habitually dualistic (not dual), then its just:
_ a sign of the answerer's inability to handle the undefiniteness of the question with only simple frames/tools (for exemple excluded-middle logic of Aristole's identity principle - which is just an overestimation of a Type(idea) of logic and then consequent misunderstanding that stems form taking that type as a Kind (essence) of logic, or even as the logic-as-such),
_as well as a sign of lazyness to readjust or omptimize, or evolve into new modes of functioning(answering). not being able to let go of the old & confortable and resistance to awareness..

so NO, it's not a PROBLEM of the context(lessness), nor of the meaning(answer logic) exclusively. it's a co-dependent function of BOTH of these.
so it is a POSSIBILITY for a more refined distinction, for adequacy, or accuracy.

for exemple, the vagueness of the question that you offer and then make a problem of it is not a problem at all!
it is a POSSIBILITY to give ALL 3 ANSWERS SIMULTANEOUSLY, thus answering wider context (of curvature), parallely with answering the question itself fully. to be wider is to be denser.

so you first state so clearly the context-dependency, but then you just flip to the other extreme and give accent on essence of an idea. which is a proper act of dualism. (=misaction on polarities, or dualities, that are so abundant in the world)

Sorry thigle, but duality is (thankfully) the law of the land in both mathematics and natural science.

again, did the above distinguish DUALITY and DUALISM ?
who do you thank to and why do you apologize ?
that land is just your dreamland, and it has myriads of solipsistic kings who proclaim this or that, duality, triality, quadrality, n-lity.
but when the snow falls, none of them goes out without a warm coat.
it's the land that invents actual laws. and look ! ther're no signs on Earth stating "mono-modal country: DUALITY-exclusive domain"

you know, wendy sais: "the dream you dream alone is a dream. the dream we dream together is reality."

so last time: duality is not dualism. dualism is a habitual tendency to overestimate one of the polarities over the other, master-slave, or winner-loser relationship preference.
instead (of dualism), to any duality, complementarity concept can be applied to. so that the mutual, or relational becomes the figure, and the balance or middle is included in the picture. it is just a different configuration of preferences, where the whole is at least as much important as the partial.

btw, dualism is what makes us killing ourselves by killing our environment - the inappropriate overestimation of will-to-power, of the ability to determinate, in denial of the importance of the soft, of the attunement, of the feminine.

[moonlord]

Maybe you should explain what exactly do 'dualism' and 'duality' mean, prefferably emphasizing the difference. I personally considered them synonims.

[bo198214]

I think I realized some of the incompatibilities between thigle n me.

There are two thinking modes (perhaps you can relate it to some
philosophical concepts):

• 1. Associative thinking is about beauty and association. Where
  I would describe association mainly as "reminds me on". Its an
  idealistic thinking style.
  
• 2. Grip thinking is about making things work. Mathematics
  uses only grip thinking (at least in its explanation, what every
  researcher does for its own - who knows ...). Its a pragmatic
  thinking style.

My parable (by associative thinking): When building a house (didnt
know how manifold this example can be used) grip
thinking corresponds to building it on proper ground, guaranty of
stability, using high quality substance. Associative thinking
corresponds to coloring the facade, tapestry in the rooms, appearing of
the house.

Both thinking styles are needed as one can see with actual houses.

Now there are some problems when applying associative thinking for
grip purposes. There are two errors of associative thinking crossing
my mind:
1. Keplers explanation of the planetary orbits by platonic solids.
2. Your statement: "you can not suceed in your attempts at finding 4d
magnetism rules, if you do not start to use quaternions".

Perhaps you can give some "dual" examples.

As I can see it, your thinking style is mostly associative, my thinking
is mainly grip style. You are thrilled by putting the greatest
philosophical principles together when regarding a given
problem (and probably to discover other associative philosophical
concepts). That is your drug. Quaternions and Self-Reference arouse
you. If you can not find some such principles somewhere you are not
interested.

Unfortunately thats not quite what makes me high. I go into awe if by
some ideas things can be done/thought that were not possible before.

[thigle]

well, it's not a big difference but it's a one that makes a difference. so let me try to find out how i mean it really.

dual.ity x dual.ism
doubl.ity x doubl.ism



actually i mean
by duality: a dual scheme projected over existence that is just that. a simple dual mode of perceiving/thinking of whatever. one can have a triality, or quadrality or n-ity projected over existence, it's like the valence of mind's way of distinguishing the yet-undefined raw experiential flow.
by dualism: an -ISM made of dual modality (of projection), with one of the polarities emphasized on disadvantage of the other, per definition.

a duality that is not "-ismed" is for exemple complementarity - another way of working with duality, where both polarities (or opposites from dualistic viewpoint) are each other's grounding, a mutual feedback of 2.

but yep, you're right it's not a common distinction perhaps.

philosopher kent palmer states that dualism(or more generally pluralism) and monism (from "mono") are duals that play together through history of our worldview -structure. in the sense of overemphasizing habitually (unconsciously) one of the natural polarities over the other one.

like for exemple, the yin-yang symbol is (doubly) dual locally, but is monistic globally. so it's not dualistic only or monistic only. so it's complementary. a closure over a unity of a duality of dualities. (a circle of 2 distinct processes, each being the essence it's complementary)

[thigle]

i see bo reacted posted while i had the mozzilaTab with my answer opened. so to react to what you wrote bo.

i think you make a good distinction. yes i could relate it to various (philosophical) concepts, but that's not the point here.

your associativeThinking and gripThinking concepts overlap with the perception/will distinction. it's like the letting-go mind and grasping mind. or attunement and will. so i found it useful and nice not because it functions but because it function because it distincts truly, it is a true distinction, a fragment of an Ideal mirror.

Both thinking styles are needed as one can see with actual houses.

not only as an architect, i agree. it's a feedback-loop workflow between these 2 that allows for a project and building (of a house).

btw, anyone here needs an architect ? (bo (and not only) might say "a guy to the associative side of the spectrum" )

Now there are some problems when applying associative thinking for grip purposes. There are two errors of associative thinking crossing my mind:
1. Keplers explanation of the planetary orbits by platonic solids.
2. Your statement: "you can not suceed in your attempts at finding 4d magnetism rules, if you do not start to use quaternions".

Perhaps you can give some "dual" examples.

as you rightly point out by asking for dual (rightly used ) exemples, there's also the problem with gripThinking for associative purposes.
abstractly stated: methods are context-dependent. (or 'paths weave through landscapes').

of your exemples: kepler's stepped aside with that, that's for sure. i like his 'on six-cornered snowflake' though, where he even mentions rhombic dodeca, though he didn't know it being a 4-cube's 'outer cover' yet. funny guy, Kepler. and were it not for his exhaustive observations, elliptic orbits model would not be found i think, as it was discovered by working with Kepler's observations, which were really massive (in terms of quantity if data he gathered.) so though he tripped on associativity on that one with orbits, he was nevertheless very pramatic and have done a lot of hands-on work. a 'star-geezer'. - now is that a pun ?

as for my statement, "...succeed...start using quats..." now that's blunt, isn't it ? why did i state such a thing in a discussion made of mostly equations ? let me feedback re-stating it into simplex, (associativeGrip(tm) thinking (called also 'ass-o-grip' ):
'you can not suceed in your attempts at finding 4d magnetism rules, if you do not start to use quaternions' >
... 'one cannot succeed at finding true (4d magnetism) rules without using quaternions.' >
... 'one cannot discover order without using certain algebra(operational rules) for orientation... { such that fits within the Cayley-Dickson process and thus connect to Clifford geometricAlgebras' }
...'one cannot suceed...without using 'poly-modal algebraicity' (now kill me for that, ass-o-grip is it called for not one reason) by which i mean, sounds it as weird as it may, something like :

...it's impossible to discover true order {of 4d magnetism} without acquiring true operational polymodality of discovering/creative process. (due to the multidimensional nature of information processing in nature, due to the cyclical nature of creative process, where qualitative phases roll time through).

or one cannot discover order(=true rules) without acting and participating multidimensionally ( on the ground of discovery.)

by true i mean perhaps way too much, in other words, such rules that are not satisfying approximations, but such rules that fit all the other rules.
i mean rules that fit into some (even if just potential) TOE.

and i see i was giving categorical statement on grounds of implicit requirement for all-context (cosmicNarrative) compatibility. which i would find a rather positive sign if i were an associationist only, but i find it rather positive anyway.

so what for a gripper is enough and applicable concretely, for an asser might be inadequate and incompatible with the cosmicAss.

as for the dual exemples (of gripThinking misapplied to associativeDomains that weave throughout the grippedDomains, caressing these gently):
1. all the machine-life analogies and discourse, even most part of AI research,
2. that (DNA) structure codes the mind (in the softer version it is supposed to personality, and so some people can even believe that from einstein's DNA there could be brough up same Einstein.
...

As I can see it, your thinking style is mostly associative, my thinking
is mainly grip style. You are thrilled by putting the greatest
philosophical principles together when regarding a given
problem (and probably to discover other associative philosophical
concepts). That is your drug.

yep. let me have some more of it, it's free and has desirable side-effects like getting rid of wordGrip, letting-go of nihiGrip, instigating glowASS and others.

Quaternions and Self-Reference arouse you. If you can not find some such principles somewhere you are not interested.

no no. there are so many threads without these where i posted and in which there ain't a single imaginary nor a feedback-loop.

i am so boring.

*

sorry for being not fully serious this time, a side effect of my drug-addiction

[bo198214]

Oh what a surprise, consent!

not only as an architect

Though I read it in the presentation thread, it was not present to me anymore. So I intuitively nearly overstressed the house building example for Thigle the architect!

it's like the letting-go mind and grasping mind.

That is a judging statement (at least for buddhists), so I disagree (without further ambition to discuss). On the other hand associative and grip thinking is both still *thinking* and in that way grasping mind.

'one cannot'

is for me anyway a statement that is only applicable to maths, where one can prove that something is *not* existing. In every other case I would say, 'one can not' is a statement of limited capability of imagination.

2. that (DNA) structure codes the mind (in the softer version it is supposed to personality, and so some people can even believe that from einstein's DNA there could be brough up same Einstein.
...

though for me this is not grip-thinking but wish-to-have-control-thinking.

[jinydu]

I interpreted "duality" to mean "having only one objectively right answer"; I'll admit that I'm not too familiar with the word, since it is not often used in math or science.

As I have stated elsewhere, there are, unfortunately, some questions (thankfully, none in science) that cannot be answered in this way. In these cases, one admittedly has no choice but to resort to subjective and inferior methods.

[bo198214]

"having only one objectively right answer" ... there are, unfortunately, some questions (thankfully, none in science) that cannot be answered in this way.

Then maybe you are not well-informed. Three examples cross my mind:
1. What is the proof for the fundamental theorem of algebra?
2. Which color has my car?
3. Can every set be well ordered?

Explanation:
1. There are several proofs to the fundamental theorem of algebra.
2. I have no car.
3. This question is undecidable in the Zermelo-Frankel set theory (which is considered the base of mathematics).

Though the second question is not really a question of science, all 3 demonstrate how one can ask wrong questions in science, that 'must have only one objectively right answer', by relying implicitly on some misassumptions. The trouble is only, that one can not recognize the (hidden) misassumption, if one insist on the existence of THE objective answer.

[thigle]

thigle is an architect with small letter 'a', so you didn't overstress, i like the house analogy.

it's like the letting-go mind and grasping mind.

That is a judging statement (at least for buddhists), so I disagree (without further ambition to discuss)

i agree you're right, it's a judging statement, not only for buddhists.
but to buddhists (you mentioned them) a clear judgement is equal to clear distinction, and there's nothing wrong with that, all languague is (in its ordinary modality of use) a judgement. (sorry to all the poetic people who don't fit this languaue-judgement: they re-discover languague continually)

On the other hand associative and grip thinking is both still *thinking* and in that way grasping mind.

sure. but beware, there is nowhere in buddhism an attempt to get rid of thinking, only if in certain techniques, temporally, to discover the underlying space where any thinking (grip or ass) take place.
but realized beings don''t stop to think, they just think in different way - they dont grasp at all.

'one cannot'

is for me anyway a statement that is only applicable to maths, where one can prove that something is *not* existing. In every other case I would say, 'one can not' is a statement of limited capability of imagination.

well you would, and you're right, but you change context to general one.
i wouldn't. for me math is music is buddhism is life is one's Self study. (godamn associationist )
it is safe to say 'one cannot' outside of math-exclusive domains. like you can't (actually) pass through a wall (or can you ?). i mean the actuality of situations is such that we often really cannot, this or that.
ideally, virtually, or potentialy, in imagination, it is possible, yes, i have no propblem with people passing through matter, science this science that, i don't care, my imagination shows me it's not that far out anyway, BUT actually, ('to DO it' as you said) one (particular someone) is in situation of relativity, where one's body/voice/mind are perceived and used in their relative states, so i can think/know virtually that we're light-pulse in space, but that doesn't allow me to actualize it directly, to become a light-body and fly off in rainbows through the sky.

though for me this is not grip-thinking but wish-to-have-control-thinking.

yep. though for me, wish-to-have-control-thinking is close to grip-thinking, it's further 'freezing'..

you know, i perceive assThought as abstract, space-like, cetrifugal, absorbtive,...
while gripThought as specifying, light-like, centripetal, concentrative,...

so 'wish-to-have-control-thinking' seems than to be attribute that anyone(grippers/assers) can depending on his position(attitude) towards his (prefered) thinking style,
but it seems to me that as it manifests (in the actions of our 'civilisation'), i mean the will-to-power', is more of a result of gripThinking, overused beyond sanity, than of assThought.
or maybe not ?.
i mean, though assThough might be said (in its 'degenerate' mode) to be unpragmatic, intentless, goalless, it is harder for it to do bad action as it is more about continually trying to go back to the primal ground of the thinking itself, it's like negative entropy, backwards in time,
while gripThinking is causal, consequential, and directed on 'results', without much questioning of its intentions..

but still, abstraction/concentration is a feedback-loop. we understand things by going close then far then close than far, the concentration happens in space.

i love these unintentional discussions. (meanwhile i see bo reacted to jin's fear of presence of undecidability in 'proper science', so i don't have to do so anymore). but i cannot resist: first "duality is the law of the land(of science)" then "it's not often used in math or science". i love you jin :wink:

[bo198214]

Everything agreed. But two notes:

1.

like you can't (actually) pass through a wall (or can you ?).

Yeeees, I can! In lucid dreams (light context shift)! Often first thing I do is stretching, reaching the ceiling, passing one hand through the ceiling, passing both hands through the ceiling, sliding through the ceiling Ah this is quite gorgeous like a lot of other things in lucid dreams, except one becomes stuck amidst the ceiling

2. using the "ass" prefix might quite irritating in regard of the possible interpretations. Better change into "asso".

[thigle]

1. oh no ! we agree !

what a nice and relaxing feeling.

indeed, in lucid dreams one can do without the bounds of karmic traces of material body, perception/expression & mind. i really like things like inversing the dream-space, or making it transparent or whatever.
i don't walk through walls often, but i really like your technique.

but being in a dream, one can indeed do anything as far as his will is strong enough and his awareness balanced enough to not wake up..

btw, it's really an uplift whenever i come across a lucid dreamer.
you ever do any (multidimensional) geometry in lucid dreams ?

2. you're goddamnright on that 'ass-' ! :wink:

[moonlord]

I am a lucid dreamer too, but incorrectly thought my experiences to be related to VRI's. My favourite is lying on the back staring into the ceiling and experiencing a free-fall for a few seconds. I managed to get through walls, but not through the ceiling... I'll keep practising, though.

I didn't experience anything multidimensional yet, but that's probably due to my limited understanding of tetraspace.

[bo198214]

is lying on the back staring into the ceiling and experiencing a free-fall for a few seconds

so you can consciously induce lucidity? quite cool.

you ever do any (multidimensional) geometry in lucid dreams ?

No, pretty plain 3d, i am not really a geometrician, like Wendy. Most of the time I was anyway involved in sex escapades, though some lucid dream researcher still doubt the possibility (Green/McCreery). What is most annoying that I can not read in dreams, it is so volatile that 2 times reading the same thing gives different results (no objectivity ). This was my usual criterion whether I am dreaming or not (taking a newspaper/book and try to read ...). Though I really would like to take some books or so from dream land into earth land (and every time I then wake up: damn it again didnt happen! :wink: )

[jinydu]

Though the second question is not really a question of science, all 3 demonstrate how one can ask wrong questions in science, that 'must have only one objectively right answer', by relying implicitly on some misassumptions. The trouble is only, that one can not recognize the (hidden) misassumption, if one insist on the existence of THE objective answer.

Good point there. I agree that if a question relies on incorrect assumptions, it isn't meaningful to talk about what the correct answer to the question is.

Nevertheless, we can solve this problem by first asking whether the question relies on any incorrect assumptions; clearly the answer is either yes or no. If the answer is yes, then we don't even bother to ask the question.

first "duality is the law of the land(of science)" then "it's not often used in math or science". i love you jin :wink:

Perhaps that is because, under my definition of duality, it is so obvious to scientists that it doesn't even have to be stated explicitly. Either it is meaningful to talk about force, mass and acceleration, and F = ma for a given system, or one of the two premises is false.

[bo198214]

we can solve this problem by first asking whether the question relies on any incorrect assumptions;

This is only the first-come-to-mind-fix, but indeed you make the already done error a second time:

clearly the answer is either yes or no.

Though I have no good example for this, the question about incorrect assumptions can again rely on incorrect assumptions. There is anyway no decision algorithm for propositions. So how long will you wait to pose the question, if no one did show yet that it relies on correct assumptions (i.e. is decidable)?

[moonlord]

Jin: What if the question is based on correct assumptions? "3. Can every set be well ordered?"

[jinydu]

Jin: What if the question is based on correct assumptions? "3. Can every set be well ordered?"

No, take the set of complex numbers, for example.

[moonlord]

Well, there is something trichy here... Why can't the complex be ordered? First by real part, then by the imaginary. Or first by argument, then by real, then by imaginary?

[bo198214]

Jin: What if the question is based on correct assumptions? "3. Can every set be well ordered?"

No, take the set of complex numbers, for example.

Oh, silly. The complex numbers can not be linearly ordered compatibly with addition and multiplication. I.e. with the conditions:
a < b => c+a < c+b for all c
a < b => ca<cb for all c>0
The proof is simple: Assume we can compare 0 and i:

• 0<i then (multiply i) 0<i*i=-1 then (multiply i) 0<-i then (add i) i<0, contradiction
• 0>i then (add -i) 0<-i then (multiply -i) 0< (-i)*(-i) = -1 then (multiply -i) 0<(-1)*(-i)=i, contradiction

But without this compatibility assumption we can arbitrary order the complex numbers. For example lexicographicly (as moonlord stated).
Assume we have a well-ordering on the real numbers (well order means linear order and every set has a smallest element). Then the lexicographic order of the complex numbers (first compare real part, then imaginary) is also a well-order on the complex numbers.

Unfortunately the usual linear order of the real numbers (which is compatible with addition and multiplication) is not a well order, for example consider the set of all real numbers greater than (and not equal to) 0. Then there is no smallest element in it: r/2 is still smaller than r for each r>0. Indeed whether the real numbers are well-orderable depends on whether we admit the axiom of choice or not.