GregoryNovember 04, 2019 at 03:538500 views54 comments
To ask what is nothing is to ask the wrong question. A better question is to ask if it's a state. Does nothing have boundries? Are there any works out there exclusively on this subject?
Comments (54)
Deleted UserNovember 04, 2019 at 04:16#3484440 likes
Sartre's Being and Nothingness is pretty interesting.
Deleted UserNovember 04, 2019 at 04:48#3484540 likes
Nishitani's Religion and Nothingness is interesting too.
I like sushiNovember 04, 2019 at 07:34#3484730 likes
Refer to Kant’s “positive noumenon”. It is basically a reference - pointing nowhere - to some contrariness of language that presents the illusion of ‘existent nothingness’.
Note: I’ve never read anything of Satre myself. I guess one day I’ll take a quick look beyond the superficial image I have of him.
Razorback kittenNovember 04, 2019 at 11:43#3485080 likes
I believe nothing can always have at least two features. It's size and shape for instance (presuming it's in a frame of reference of something). Or nothing can have a direction relative to something. It seems odd I know but I believe without having these features, nothing wouldn't be able to form something and nothing would be all there is.
Then again I believe I'm an eternal universe without a big bang, so who knows?
TheMadFoolNovember 04, 2019 at 13:26#3485310 likes
To ask what is nothing is to ask the wrong question. A better question is to ask if it's a state. Does nothing have boundries? Are there any works out there exclusively on this subject?
Always fascinated by the subject of nothing.
If I recall correctly nothing is defined as absence, a contraction of no thing. It's difficult if not impossible to understand something that negates everything after all for one to contemplate on anything at all it must first be a thing of either the physical or the mental.
Yes, it's a concept of course - this nothing. However it, because it negates everything, lacks any properties and since analysis, the way I understand it, is about properties, it becomes impossible to comprehend.
If there's anything I've learnt then it's the distinction between relative nothing and absolute nothing. The former is what describes our everyday notion of nothingness. We say an empty box has nothing inside or 3 applies - 3 apples = nothing/0. It's relative because there is a thing whose absence is noticed.
The latter, absolute nothing is a different creature. Being empty of all things real or imagined it defies any attempt to grasp it since, duh, there is nothing to grasp.
I think when people discuss nothingness they conflate the two - the relative and the absolute nothing - and though it's not a mistake for relative nothingness has greater utility it's far from a true understanding of the ultimate void of absolute nothingness.
Heidegger in Discourse on Thinking talks of regioning. We can only think I'm space and nature. Nature includes nothing\zero, so we can't think without nothing it would appear
Are there any works out there exclusively on this subject?
Exclusivity is a lot to ask for. Zhuangzi talked about different ways to refer to nothing. The distinctions made there are not arguments for what is or is not happening but a guide to how each expression has a situation that is meant to be conveyed.
Our different descriptions set against the background of what we cannot describe.
Mathematics says that objects are made of an infinity of zeros. So nothing, through the medium of infinity, creates something. Is this accurate?
Razorback kittenNovember 05, 2019 at 09:38#3489100 likes
If you replaced some water or air with a patch of nothingness, the surrounding body would undoubtedly collapse into the space. It creates a vacuum as we know. To create a near perfect vacuum takes a huge amount of energy. So if absolute nothing is no more than an impossible idea, why does it take so much force to create?
I think that if consciousness is the brain (identical), than we have to say that consciousness is a null set. The highest realities are the inversion, contradiction, or maybe just the negation of material being. Being seems to apply only to the material anyway
Reply to Gregory I don’t think that’s accurate to say that mathematics says things are made of an infinity of zeros,
but modern mathematics does construct all its objects out of nested sets of sets of ultimately empty sets,
and all of its functions can be constructed exclusively with nested application of the joint denial function (“nor”) which is basically a binary negation operation (“nor(x,x)” is the same as “not(x)”),
so it is fairly accurate to say that everything is made of negations of nothing.
I refer the OP to the Jerry Seinfeld Comedy series, which was a show about nothing. Very popular. Also, this on YouTube:
Nothin' from nothin' leaves nothin'
You gotta have somethin' if you wanna be with me
Nothin' from nothin' leaves nothin'
You gotta have somethin' if you wanna be with me
I'm not tryna be your hero
'Cause that zero is too cold for me, brrr
I'm not tryin' to be your highness
'Cause that minus is too low to see, yeah
"The linear series that in its movement marks the retrogressive steps in it by knots, but thence went forward again in one linear stretch, is now, as it were, broken at these knots, these universal moments, and fall asunder into many lines, which, being bound together into a single bundle, combine at the same time symetrically, so that the similar distinctions, in which each separately took shape within a sphere, meet again." Hegel
Our nada who art in nada, nada be thy name thy kingdom nada thy will be nada in nada as it is in nada. Give us this nada our daily nada and nada us our nada as we nada our nadas and nada us not into nada but deliver us from nada; pues nada [then nothing]. Hail nothing full of nothing, nothing is with thee.
"A Clean Well-Lighted Place" (1933)
:pray: :eyes:
PossibilityNovember 07, 2019 at 10:30#3498610 likes
Nothing, for me, can be understood in terms of actuality, potentiality or possibility (but then, I do tend towards ‘glass half full’). When there is actually nothing, there is still the potential for something. Likewise, even when there evidently can be nothing, we could nevertheless imagine the possibility of something.
‘Absolute nothing’ is a concept that refers to an absence even of the possibility of anything. We can approach an understanding of this ‘absolute nothing’, but ultimately there is no way of fully understanding it as such.
Any concept of ‘nothing’ is relative at least to some possibility: being whatever is striving to understand it...a possible ‘something’ to which this ‘nothingness’ matters...for whom ‘nothing’ has meaning...
If I recall correctly, Parmaneides argued that since nothing does not exist, change is impossible, because otherwise things like the past would cease to exist (become nothing which is impossible).
Lucretius used nothing to argue that something cannot come from it, otherwise anything would come into existence, which we don't observe. Therefore atoms must have always existed.
Nishitani's 'nothingness' is ??nyat?, 'luminous emptiness'. Not like Sartre's 'god-shaped hole'.
My personal spiritual development proceeded from depressed fascination with the Sartrean void to transnihilist saniassiform illumination. So I see a deep, weird link between the two.
In fact, I bumped into Nishitani's book while in pursuit of a syncretic view of voidness. Curious to know if you can recommend a book or philosopher who has assimilated the one void to the other.
Sartre is posed deliberately against nothingness as a nihilism. The point is an examination of our accounts of ourselves as given by concepts finds nothingness.
I am, in conceptual terms, nothing. All these philosophies and doctrines which have insisted what I am on account of some essence, some conceptual rule, I find empty. My existence or consciousness exists, extending beyond them all. For all their promises of who I am, all these doctrines have only recognised me as nothing, substituting me for whatever essence they wanted to ascribe me.
For Sartre, nothingness is the lie being told in every account insisting an are in an essence, rather than ourselves. It is the nihilism which disappears when we recognise ourselves as self-defined and responsible.
Deleted UserNovember 07, 2019 at 22:59#3501280 likes
Constructing fundamental mathematical objects out of sets is like constructing bricks out of houses.
I can see why you would think that, but that's how modern mathematicians do it.
The natural numbers, for instance, meaning the counting numbers {0, 1, 2, 3, ...}, are easily defined in terms of sets. First we define a series of sets, starting with the empty set, and then a set that only contains that one empty set, and then a set that only contains those two preceding sets, and then a set that contains only those three preceding sets, and so on, at each step of the series defining the next set as the union of the previous set and a set containing only that previous set. We can then define some set operations (which I won't detail here) that relate those sets in that series to each other in the same way that the arithmetic operations of addition and multiplication relate natural numbers to each other. We could name those sets and those operations however we like, but if we name the series of sets "zero", "one", "two", "three", and so on, and name those operations "addition" and "multiplication", then when we talk about those operations on that series of sets, there is no way to tell if we are just talking about some made-up operations on a made-up series of sets, or if we were talking about actual addition and multiplication on actual natural numbers: all of the same things would be necessarily true in both cases, e.g. doing the set operation we called "addition" on the set we called "two" and another copy of that set called "two" creates the set that we called "four". Because these sets and these operations on them are fundamentally indistinguishable from addition and multiplication on numbers, they are functionally identical: those operations on those sets just are the same thing as addition and multiplication on the natural numbers.
All kinds of mathematical structures, by which I don't just mean a whole lot of different mathematical structures but literally every mathematical structure studied in mathematics today, can be built up out of sets this way. The integers, or whole numbers, can be built out the natural numbers (which are built out of sets) as equivalence classes (a kind of set) of ordered pairs (a kind of set) of natural numbers, meaning in short that each integer is identical to some set of equivalent sets of two natural numbers in order, those sets of two natural numbers in order that are equal when one is subtracted from the other: the integers are all the things you can get by subtracting one natural number from another. Similarly, the rational numbers can be defined as equivalence classes of ordered pairs of integers in a way that means that the rationals are the things you can get by dividing one integer by another. The real numbers, including irrational numbers like pi and the square root of 2, can be constructed out of sets of rational numbers in a process too complicated to detail here (something called a Dedekind-complete ordered field, where a field is itself a kind of set). The complex numbers, including things like the square root of negative one, can be constructed out of ordered pairs of real numbers; and further hypercomplex numbers, including things called quaternions and octonions, can be built out of larger ordered sets of real numbers, which are built out of complicated sets of rational numbers, which are built out of sets of integers, which are built out of sets of natural numbers, which are built out of sets built out of sets of just the empty set. So from nothing but the empty set, we can build up to all complicated manner of fancy numbers.
But it is not just numbers that can be built out of sets. For example, all manner of geometric objects are also built out of sets as well. All abstract geometric objects can be reduced to sets of abstract geometric points, and a kind of function called a coordinate system maps such sets of points onto sets of numbers in a one-to-one manner, which is hence reversible: a coordinate system can be seen as turning sets of numbers into sets of points as well. For example, the set of real numbers can be mapped onto the usual kind of straight, continuous line considered in elementary geometry, and so the real numbers can be considered to form such a line; similarly, the complex numbers can be considered to form a flat, continuous plane. Different coordinate systems can map different numbers to different points without changing any features of the resulting geometric object, so the points, of which all geometric objects are built, can be considered the equivalence classes (a kind of set) of all the numbers (also made of sets) that any possible coordinate system could map to them. Things like lines and planes are examples of the more general type of object called a space. Spaces can be very different in nature depending on exactly how they are constructed, but a space that locally resembles the usual kind of straight and flat spaces we intuitively speak of (called Euclidian spaces) is an object called a manifold, and such a space that, like the real number line and the complex number plane, is continuous in the way required to do calculus on it, is called a differentiable manifold. Such a differentiable manifold is basically just a slight generalization of the usual kind of flat, continuous space we intuitively think of space as being, and it, as shown, can be built entirely out of sets of sets of ultimately empty sets.
Meanwhile, a special type of set defined such that any two elements in it can be combined through some operation to produce a third element of it, in a way obeying a few rules that I won't detail here, constitutes a mathematical object called a group. A differentiable manifold, being a set, can also be a group, if it follows the rules that define a group, and when it does, that is called a Lie group. Also meanwhile, another special kind of set whose members can be sorted into a two-dimensional array constitutes a mathematical object called a matrix, which can be treated in many ways like a fancy kind of number that can be added, multiplied, etc. A square matrix (one with its dimensions being of equal length) of complex numbers that obeys some other rules that I once again won't detail here is called a unitary matrix. Matrices can be the "numbers" that make up a geometric space, including a differentiable manifold, including a Lie group, and when a Lie group is made of unitary matrices, it constitutes a unitary group. And lastly, a unitary group that obeys another rule I won't bother detailing here is called a special unitary group. This makes a special unitary group essentially a space of the kind we would intuitively expect a space to be like — locally flat-ish, smooth and continuous, etc — but where every point in that space is a particular kind of square matrix of complex numbers, that all obey certain rules under certain operations on them, with different kinds of special unitary groups being made of matrices of different sizes.
I have hastily recounted here the construction of this specific and complicated mathematical object, the special unitary group, out of bare, empty sets, because that special unitary group is considered by contemporary theories of physics to be the fundamental kind of thing that the most elementary physical objects, quantum fields, are literally made of. So everything in reality can in principle be arduously constructed out of empty sets, transformed through operations that can all be constructed out of repeated use of (basically) negation.
On a different topic, I have something else to say about nothing. Why is there something rather than nothing? Well, on a modal realist account, it's trivially because there exists no possible world at which there is no world, which translates back to normal modal language as saying that it is not possible for there to be nothing. Nothing can't exist.
All kinds of mathematical structures, by which I don't just mean a whole lot of different mathematical structures but literally every mathematical structure studied in mathematics today, can be built up out of sets this way.
So, then, instead, the existent cannot not be and so it is ever, with no more forthcoming, because it does not forth come, as never being made (from 'Nothing'). Plus, empty sets of 'nothing' have no being either.
So, what would the mandatory existent be like that just is, but has no direction put into it?
So, what would the mandatory existent be like that just is, but has no direction put into it?
This question implicitly commits a logical error that predicate logic was invented to avoid. Consider the sentence "every mouse fears some cat". You might mean that for each mouse, there is some cat or another that that mouse fears, maybe not the same cat feared by all mice. Or you might mean that there is some one cat in particular of whom all mice are afraid. Saying the former doesn't imply the latter. In predicate logic we would distinguish these two sentences from each other as:
For every mouse, there exists some cat, such that the mouse fears the cat.
and
There exists some cat, such that for every mouse, the mouse fears the cat.
In our case, I'm saying that nothing can't possible exist, and therefore that something or another must necessarily exit; but you're taking that to mean that there is some one particular thing that must necessarily exist, which is not implied by the first statement. It's the difference between:
At every possible world, there exists some thing, such that the thing exists in the world.
and
There exists some thing, such that at every possible world, the thing exists in the world.
Cosmological arguments for God generally commit this same error, taking the generally agreed upon statement "everything comes from something", which is to say:
For every thing, there exists some other thing, such that the thing came from the other thing.
...which is perfectly compatible with there being infinite chains of creation or even loops in principle, and takes it to be equivalent to or at least to imply:
There exists some other thing, such that for every thing, that thing came from the other thing.
...and then they proceed to call that erroneously-inferred first cause (the "other thing") "God".
PoeticUniverseNovember 08, 2019 at 02:37#3501800 likes
It's not a matter of plurality or singularity. The point is that there isn't any special kind of thing(s) that has(/have) to exist at any possible world; just that some kind of thing(s) or (an)other must exist at each possible world. They can all be completely different things at every possible world, and it doesn't matter what they are, so long as there's something there.
PoeticUniverseNovember 08, 2019 at 02:44#3501830 likes
I'll take it as all possible worlds/paths granting all the specifics that would have to be all at once with no one in particular being able to be the only design.
TheMadFoolNovember 08, 2019 at 03:25#3501890 likes
Nothing, for me, can be understood in terms of actuality, potentiality or possibility (but then, I do tend towards ‘glass half full’). When there is actually nothing, there is still the potential for something. Likewise, even when there evidently can be nothing, we could nevertheless imagine the possibility of something.
‘Absolute nothing’ is a concept that refers to an absence even of the possibility of anything. We can approach an understanding of this ‘absolute nothing’, but ultimately there is no way of fully understanding it as such.
Any concept of ‘nothing’ is relative at least to some possibility: being whatever is striving to understand it...a possible ‘something’ to which this ‘nothingness’ matters...for whom ‘nothing’ has meaning...
How about a linguistic take on nothing.
It simplifies discourse quite a bit you know.
"I don't want anything" becomes "I want nothing"
"All things are inferior" becomes "Nothing is superior"
"Nothing" emerges when we reach limits. "Only unicorns will be discussed" becomes "Nothing other than unicorns will be discussed".
Reply to TheMadFool "Nothing", together with "something", "everything", and "not everything" (or, if you will, "neverything"), is just part of one of many sets of four DeMorgan dual concepts that all bear the same relationship to each other, the relationship of none, some, all, and not-all (or, if you will, "nall").
And since impossible = "at none of the possible worlds", possible = "at some of the possible worlds", necessary = "at all of the possible worlds", and contingent = "at none of the possible worlds:
And since impermissible, permissible, obligatory, and supererogatory bear all the same relations to possible worlds as those alethic modalities but with a deontic direction of fit instead:
There are probably others I'm overlooking too. Even the ordinary boolean operators NOR, OR, AND, and NAND are just two-place versions of some, none, all, and nall, so:
NOR = AND-not = not-OR = not-NAND-not
OR = NAND-not = not-NOR = not-AND-not
AND = NOR-not = not-NAND = not-OR-not
NAND = OR-not = not-AND = not-NOR-not
And I'd argue that in all of these cases, the first one, based on "none", is really the most primitive and fundamental, because all of the boolean logical operators, not just these ones but IF, ONlY-IF, IFF, XOR, and so on, can be built out of nothing but NORs. (True, they can also be built out of nothing but NANDs, but that just seems like a weird and convoluted consequence of NAND being the negation of the NOR of negations).
Reply to Pfhorrest
Thank you for your detailed account of how numbers can be derived from empty sets and I don't doubt that modern mathematicians consider it fundamental to mathematics, and even most physicists too.
However in terms of the philosophy of mathematics, does it actually achieve anything?.. well that depends upon what you are trying to achieve.
It would seem that they are trying to ling mathematical 'objects' to real objects in a logically rigorous way. But I don't believe that that is the best way to go.
First off why should a set of nothing be any more fundamental than zero or even 1.
Second it creates a mountain out of a molehill.
Mathematics existed and was eminently useful long before anyone invented the concept of 'sets'
what is meant by an 'object' anyway? It is just a label or category if you like for those things that are considered to have objectivity.
Indian art is primarily about dear of nofhing, but fear can be santified. And this is my final point. Buddhists i think are Hindu. They say there is no soul because they believe the soul is the void. That is, God. There is no soul of Aristotle for them. They emphasize the nothingness of being. The truth of psychedelia is that God created the world thru the dying of God's subconscious.
João RodriguesNovember 09, 2019 at 16:25#3506700 likes
Without nothing you can't have something, because they're the yin-yang. The nothing, the absence like someone mentioned, like the nothingness of space, but without that nothingness of space, matter couldn't exist, without nothingness everything would be matter and you wouldn't be able to see the beginning and end of something. Correct me if I'm wrong, but the origin of the Buddhist concept of reincarnation comes from the idea that, if we came from nothing, the nothingness before we were born, and when we die we go to that same nothingness, what happened once (being born), can happen again.
I think nothing in the most general sense can be defined as an "object" that is logically inconsistently defined. For example: a circle that is not a circle. There are objects that are circles and there are objects that are not circles, but there is no object that both is and isn't a circle. That's why I put the word object into scare quotes in the first sentence; there is no such object, and the inconsistent definition as a whole has no referent.
Why is there something rather than nothing? Well, on a modal realist account, it's trivially because there exists no possible world at which there is no world, ...
I prefer an actualist interpretation: there isn't any possible way the world could not have been the world or can be described as 'not the world'. (A distinction without a difference?)
[quote=Pfhorrest]... which translates back to normal modal language as saying that it is not possible for there to be nothing. Nothing can't exist.[/quote]
CiceronianusNovember 11, 2019 at 16:50#3513180 likes
Is there a difference between "nothing" and "the nothing"? As I recall, The Nazi wrote that we encounter "the nothing" only when we're "suspended in dread" but in referencing the nothing he may not have meant just any old nothing, which presumably we could encounter without being suspended in dread. Just curious.
Comments (54)
Note: I’ve never read anything of Satre myself. I guess one day I’ll take a quick look beyond the superficial image I have of him.
Then again I believe I'm an eternal universe without a big bang, so who knows?
Always fascinated by the subject of nothing.
If I recall correctly nothing is defined as absence, a contraction of no thing. It's difficult if not impossible to understand something that negates everything after all for one to contemplate on anything at all it must first be a thing of either the physical or the mental.
Yes, it's a concept of course - this nothing. However it, because it negates everything, lacks any properties and since analysis, the way I understand it, is about properties, it becomes impossible to comprehend.
If there's anything I've learnt then it's the distinction between relative nothing and absolute nothing. The former is what describes our everyday notion of nothingness. We say an empty box has nothing inside or 3 applies - 3 apples = nothing/0. It's relative because there is a thing whose absence is noticed.
The latter, absolute nothing is a different creature. Being empty of all things real or imagined it defies any attempt to grasp it since, duh, there is nothing to grasp.
I think when people discuss nothingness they conflate the two - the relative and the absolute nothing - and though it's not a mistake for relative nothingness has greater utility it's far from a true understanding of the ultimate void of absolute nothingness.
Yes I think there is something to say about nothing. But there also appears to be nothing to say about something (ineffable).
I wonder if there is an irony or paradox there somewhere...
Exclusivity is a lot to ask for. Zhuangzi talked about different ways to refer to nothing. The distinctions made there are not arguments for what is or is not happening but a guide to how each expression has a situation that is meant to be conveyed.
Our different descriptions set against the background of what we cannot describe.
(a) No referent (i.e. non-sense) re: semantics, cognition
(b) No information (i.e. tautology) re: logic
(c) No thing (i.e. formless, void) re: physics
(d) Null set (i.e. zero) re: mathematics
(e) Random (i.e. patternless, noise) re: computation
(f) Omni-symmetry (i.e. non-being, nothingNess, absolute absence (of possible worlds)) re: metaphysics, or meontology
and so I wonder: to which sense(s) of the word does the OP refer?
You appear to have said quite a lot about nothing.
The OP seems to be answering the title question in speaking the title too, a rhetorical aphorism for the ages, I think.
You don't say.
Found this
but modern mathematics does construct all its objects out of nested sets of sets of ultimately empty sets,
and all of its functions can be constructed exclusively with nested application of the joint denial function (“nor”) which is basically a binary negation operation (“nor(x,x)” is the same as “not(x)”),
so it is fairly accurate to say that everything is made of negations of nothing.
Nothin' from nothin' leaves nothin'
You gotta have somethin' if you wanna be with me
Nothin' from nothin' leaves nothin'
You gotta have somethin' if you wanna be with me
I'm not tryna be your hero
'Cause that zero is too cold for me, brrr
I'm not tryin' to be your highness
'Cause that minus is too low to see, yeah
and so on. Nothing has been done already.
"A Clean Well-Lighted Place" (1933)
:pray: :eyes:
Nothing, for me, can be understood in terms of actuality, potentiality or possibility (but then, I do tend towards ‘glass half full’). When there is actually nothing, there is still the potential for something. Likewise, even when there evidently can be nothing, we could nevertheless imagine the possibility of something.
‘Absolute nothing’ is a concept that refers to an absence even of the possibility of anything. We can approach an understanding of this ‘absolute nothing’, but ultimately there is no way of fully understanding it as such.
Any concept of ‘nothing’ is relative at least to some possibility: being whatever is striving to understand it...a possible ‘something’ to which this ‘nothingness’ matters...for whom ‘nothing’ has meaning...
Nishitani's 'nothingness' is ??nyat?, 'luminous emptiness'. Not like Sartre's 'god-shaped hole'.
Lucretius used nothing to argue that something cannot come from it, otherwise anything would come into existence, which we don't observe. Therefore atoms must have always existed.
Constructing fundamental mathematical objects out of sets is like constructing bricks out of houses.
Yes. Nothingnesses in need of a hieros gamos. From what I've read of him, Sartre never came close to illuminating his nothingness.
My personal spiritual development proceeded from depressed fascination with the Sartrean void to transnihilist saniassiform illumination. So I see a deep, weird link between the two.
In fact, I bumped into Nishitani's book while in pursuit of a syncretic view of voidness. Curious to know if you can recommend a book or philosopher who has assimilated the one void to the other.
Look into Brook Ziporynn. I don't much care for him but he might be right up your alley.
Sartre is posed deliberately against nothingness as a nihilism. The point is an examination of our accounts of ourselves as given by concepts finds nothingness.
I am, in conceptual terms, nothing. All these philosophies and doctrines which have insisted what I am on account of some essence, some conceptual rule, I find empty. My existence or consciousness exists, extending beyond them all. For all their promises of who I am, all these doctrines have only recognised me as nothing, substituting me for whatever essence they wanted to ascribe me.
For Sartre, nothingness is the lie being told in every account insisting an are in an essence, rather than ourselves. It is the nihilism which disappears when we recognise ourselves as self-defined and responsible.
Can you support these claims with a direct reference to Sartre's works?
I can see why you would think that, but that's how modern mathematicians do it.
The natural numbers, for instance, meaning the counting numbers {0, 1, 2, 3, ...}, are easily defined in terms of sets. First we define a series of sets, starting with the empty set, and then a set that only contains that one empty set, and then a set that only contains those two preceding sets, and then a set that contains only those three preceding sets, and so on, at each step of the series defining the next set as the union of the previous set and a set containing only that previous set. We can then define some set operations (which I won't detail here) that relate those sets in that series to each other in the same way that the arithmetic operations of addition and multiplication relate natural numbers to each other. We could name those sets and those operations however we like, but if we name the series of sets "zero", "one", "two", "three", and so on, and name those operations "addition" and "multiplication", then when we talk about those operations on that series of sets, there is no way to tell if we are just talking about some made-up operations on a made-up series of sets, or if we were talking about actual addition and multiplication on actual natural numbers: all of the same things would be necessarily true in both cases, e.g. doing the set operation we called "addition" on the set we called "two" and another copy of that set called "two" creates the set that we called "four". Because these sets and these operations on them are fundamentally indistinguishable from addition and multiplication on numbers, they are functionally identical: those operations on those sets just are the same thing as addition and multiplication on the natural numbers.
All kinds of mathematical structures, by which I don't just mean a whole lot of different mathematical structures but literally every mathematical structure studied in mathematics today, can be built up out of sets this way. The integers, or whole numbers, can be built out the natural numbers (which are built out of sets) as equivalence classes (a kind of set) of ordered pairs (a kind of set) of natural numbers, meaning in short that each integer is identical to some set of equivalent sets of two natural numbers in order, those sets of two natural numbers in order that are equal when one is subtracted from the other: the integers are all the things you can get by subtracting one natural number from another. Similarly, the rational numbers can be defined as equivalence classes of ordered pairs of integers in a way that means that the rationals are the things you can get by dividing one integer by another. The real numbers, including irrational numbers like pi and the square root of 2, can be constructed out of sets of rational numbers in a process too complicated to detail here (something called a Dedekind-complete ordered field, where a field is itself a kind of set). The complex numbers, including things like the square root of negative one, can be constructed out of ordered pairs of real numbers; and further hypercomplex numbers, including things called quaternions and octonions, can be built out of larger ordered sets of real numbers, which are built out of complicated sets of rational numbers, which are built out of sets of integers, which are built out of sets of natural numbers, which are built out of sets built out of sets of just the empty set. So from nothing but the empty set, we can build up to all complicated manner of fancy numbers.
But it is not just numbers that can be built out of sets. For example, all manner of geometric objects are also built out of sets as well. All abstract geometric objects can be reduced to sets of abstract geometric points, and a kind of function called a coordinate system maps such sets of points onto sets of numbers in a one-to-one manner, which is hence reversible: a coordinate system can be seen as turning sets of numbers into sets of points as well. For example, the set of real numbers can be mapped onto the usual kind of straight, continuous line considered in elementary geometry, and so the real numbers can be considered to form such a line; similarly, the complex numbers can be considered to form a flat, continuous plane. Different coordinate systems can map different numbers to different points without changing any features of the resulting geometric object, so the points, of which all geometric objects are built, can be considered the equivalence classes (a kind of set) of all the numbers (also made of sets) that any possible coordinate system could map to them. Things like lines and planes are examples of the more general type of object called a space. Spaces can be very different in nature depending on exactly how they are constructed, but a space that locally resembles the usual kind of straight and flat spaces we intuitively speak of (called Euclidian spaces) is an object called a manifold, and such a space that, like the real number line and the complex number plane, is continuous in the way required to do calculus on it, is called a differentiable manifold. Such a differentiable manifold is basically just a slight generalization of the usual kind of flat, continuous space we intuitively think of space as being, and it, as shown, can be built entirely out of sets of sets of ultimately empty sets.
Meanwhile, a special type of set defined such that any two elements in it can be combined through some operation to produce a third element of it, in a way obeying a few rules that I won't detail here, constitutes a mathematical object called a group. A differentiable manifold, being a set, can also be a group, if it follows the rules that define a group, and when it does, that is called a Lie group. Also meanwhile, another special kind of set whose members can be sorted into a two-dimensional array constitutes a mathematical object called a matrix, which can be treated in many ways like a fancy kind of number that can be added, multiplied, etc. A square matrix (one with its dimensions being of equal length) of complex numbers that obeys some other rules that I once again won't detail here is called a unitary matrix. Matrices can be the "numbers" that make up a geometric space, including a differentiable manifold, including a Lie group, and when a Lie group is made of unitary matrices, it constitutes a unitary group. And lastly, a unitary group that obeys another rule I won't bother detailing here is called a special unitary group. This makes a special unitary group essentially a space of the kind we would intuitively expect a space to be like — locally flat-ish, smooth and continuous, etc — but where every point in that space is a particular kind of square matrix of complex numbers, that all obey certain rules under certain operations on them, with different kinds of special unitary groups being made of matrices of different sizes.
I have hastily recounted here the construction of this specific and complicated mathematical object, the special unitary group, out of bare, empty sets, because that special unitary group is considered by contemporary theories of physics to be the fundamental kind of thing that the most elementary physical objects, quantum fields, are literally made of. So everything in reality can in principle be arduously constructed out of empty sets, transformed through operations that can all be constructed out of repeated use of (basically) negation.
So, then, instead, the existent cannot not be and so it is ever, with no more forthcoming, because it does not forth come, as never being made (from 'Nothing'). Plus, empty sets of 'nothing' have no being either.
So, what would the mandatory existent be like that just is, but has no direction put into it?
This question implicitly commits a logical error that predicate logic was invented to avoid. Consider the sentence "every mouse fears some cat". You might mean that for each mouse, there is some cat or another that that mouse fears, maybe not the same cat feared by all mice. Or you might mean that there is some one cat in particular of whom all mice are afraid. Saying the former doesn't imply the latter. In predicate logic we would distinguish these two sentences from each other as:
For every mouse, there exists some cat, such that the mouse fears the cat.
and
There exists some cat, such that for every mouse, the mouse fears the cat.
In our case, I'm saying that nothing can't possible exist, and therefore that something or another must necessarily exit; but you're taking that to mean that there is some one particular thing that must necessarily exist, which is not implied by the first statement. It's the difference between:
At every possible world, there exists some thing, such that the thing exists in the world.
and
There exists some thing, such that at every possible world, the thing exists in the world.
Cosmological arguments for God generally commit this same error, taking the generally agreed upon statement "everything comes from something", which is to say:
For every thing, there exists some other thing, such that the thing came from the other thing.
...which is perfectly compatible with there being infinite chains of creation or even loops in principle, and takes it to be equivalent to or at least to imply:
There exists some other thing, such that for every thing, that thing came from the other thing.
...and then they proceed to call that erroneously-inferred first cause (the "other thing") "God".
I worded it such that "existent" could be plural, too. Perhaps "existent(s)" would have been better.
So what is an existent like that can't have a any design going into it?
I'll take it as all possible worlds/paths granting all the specifics that would have to be all at once with no one in particular being able to be the only design.
How about a linguistic take on nothing.
It simplifies discourse quite a bit you know.
"I don't want anything" becomes "I want nothing"
"All things are inferior" becomes "Nothing is superior"
"Nothing" emerges when we reach limits. "Only unicorns will be discussed" becomes "Nothing other than unicorns will be discussed".
None = all-not = not-some = not-nall-not
Some = nall-not = not-none = not-all-not
All = none-not = not-nall = not-some-not
Nall = some-not = not-all = not-none-not
Since nothing = "none of the things", something = "some of the things", everything = "all of the things", and neverything = "nall of the things":
Nothing = everything-not = not-something = not-neverything-not
Something = neverything-not = not-nothing = not-everything-not
Everything = nothing-not = not-neverything = not-something-not
Neverything = something-not = not-everything = not-nothing-not
And since impossible = "at none of the possible worlds", possible = "at some of the possible worlds", necessary = "at all of the possible worlds", and contingent = "at none of the possible worlds:
Impossible = necessary-not = not-possible = not-contingent-not
Possible = contingent-not = not-impossible = not-necessary-not
Necessary = impossible-not = not-contingent = not-possible-not
Contingent = possible-not = not-necessary = not-impossible-not
And since impermissible, permissible, obligatory, and supererogatory bear all the same relations to possible worlds as those alethic modalities but with a deontic direction of fit instead:
Impermissible = obligatory-not = not-permissible = not-supererogatory-not
Permissible = supererogatory-not = not-impermissible = not-obligatory-not
Obligatory = impermissible-not = not-supererogatory = not-permissible-not
Supererogatory = permissible-not = not-obligatory = not-impermissible-not
There are probably others I'm overlooking too. Even the ordinary boolean operators NOR, OR, AND, and NAND are just two-place versions of some, none, all, and nall, so:
NOR = AND-not = not-OR = not-NAND-not
OR = NAND-not = not-NOR = not-AND-not
AND = NOR-not = not-NAND = not-OR-not
NAND = OR-not = not-AND = not-NOR-not
And I'd argue that in all of these cases, the first one, based on "none", is really the most primitive and fundamental, because all of the boolean logical operators, not just these ones but IF, ONlY-IF, IFF, XOR, and so on, can be built out of nothing but NORs. (True, they can also be built out of nothing but NANDs, but that just seems like a weird and convoluted consequence of NAND being the negation of the NOR of negations).
Thank you for your detailed account of how numbers can be derived from empty sets and I don't doubt that modern mathematicians consider it fundamental to mathematics, and even most physicists too.
However in terms of the philosophy of mathematics, does it actually achieve anything?.. well that depends upon what you are trying to achieve.
It would seem that they are trying to ling mathematical 'objects' to real objects in a logically rigorous way. But I don't believe that that is the best way to go.
First off why should a set of nothing be any more fundamental than zero or even 1.
Second it creates a mountain out of a molehill.
Mathematics existed and was eminently useful long before anyone invented the concept of 'sets'
what is meant by an 'object' anyway? It is just a label or category if you like for those things that are considered to have objectivity.
I prefer an actualist interpretation: there isn't any possible way the world could not have been the world or can be described as 'not the world'. (A distinction without a difference?)
[quote=Pfhorrest]... which translates back to normal modal language as saying that it is not possible for there to be nothing. Nothing can't exist.[/quote]
Don't 'holes in things' exist?
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