>Declares things to be at absolute rest.
>Appeals to unspecified sense of anti-realism for claim.

"It's like that if we think it's like that".

Ok. A is walking away from B. Find a coordinate system in which they are both stationary.

The "absolute" part is meant to take it out of our hands: make it something we discover rather than declare (so changing our minds doesn't alter the situation). — frank

Relative velocity isn't just "declared".

I just evoked absolute rest: a thing that never moves. X-Y axis. Does it exist? — frank

Probably not. But I don't really know what you mean.

Sure, but don't you believe the discussion could be broadened? Studies show the CEOs of fortunate 500 companies tend to be something like 3 inches taller than the average man, and that per every inch of height a man has it's an extra $800/year and that's not even digging into the inherent social respect given to height and romantic prospects. I think we can all agree that good-looking people are subject to preferable treatment and we could certain enact policies to at least aim to target this. — BitconnectCarlos

Treating the height difference as if it's causing that difference in income is extremely bizarre. Imagine the social programs that would come of it:

"We demand genetic engineering for height so that our children can become CEOs! For too long have people who are shorter than CEOs not been CEOs, and we demand equality of opportunity for height!"

In keeping with the Political theme relative to the OP, here in America we value compromise in our democratic process through the two party system. — 3017amen

Just an observation. If one party in a negotiation can always be assumed to compromise without fail and imposes no relevant sanctions when the other party fails to compromise, the other party can get more and more of what they want by being an obstinate, uncompromising git.

A: "We want to pay 2 dollars less tax"
B: "We want it to stay the same, how about 1 dollar less?"
A: "We want 2"
B: "We want 1 dollar less, how about 1.5 dollars less?"
A: "We want 2"
B: "We want 1.5 dollars less, how about 1.75 dollars less?"
A: "We want 2"
B: "We want 1.75 dollars less, how about 1.875 dollars less?"
...
A: "We want 2"
B: "We agree, good compromise."

Time passes.

B: "You know, last time, it was really unfair, you were an asshole, now we demand 1 dollar more tax. This is fair given your previous demand, which was unworkable."
A: "You know, now we want 2 extra dollars less tax, it should be as low as possible for our nation's prosperity. Be consistent and follow decorum, our noble nation demands no less!"
B: "Fuck, fine, we still want 1 dollar more tax, but how about 0.5 dollars more tax?"
A: "We want 3 dollars extra less tax."
B: "In the spirit of compromise, we accept."

Time passes, some levers have been pulled.

"We want to pay a further 2 dollars less tax"
"We still need tax, but our economy needs to reward consumer satisfying investment a lot at the minute, how about 1.5 further dollars less tax?"

Well, at least whoever's not sitting at the negotiating table has nothing but consistent interests...

Sure, but nature's inequalities manifest themselves in actual, everyday life whether it's a job hunt or promotions or social activity, etc. — BitconnectCarlos

Yes. Though nature only affords our societies with some of the differential, or enables/renders possible social costs which leverage distinctions in bodily properties, rather than playing a primary causal role for any of the social costs of having those bodily properties.

My main reason for this thread was just to point out that today's left seems to push for equality with, say, A, B, and C but they're not interested in X, Y, and Z which end up favoring/advocating for certain groups and basically ignoring others.

Having a certain height or skin colour can only be changed through interventions like eugenics; drown all babies that come out at less than a certain size or whose skin colour is not as desired, or otherwise prevent reproduction of those people, maybe kill all people under 1.2 meters tall on their 16th birthday. Things like average height of populations can increase over time through policies (or general collective action) that increase the availability of nutrition.

But, and this is a big but, the risks of differences height or differences in skin colour or disability (within a relevant sub-population) can only be addressed culturally and politically. You can't give poor people who can't walk back their leg function, but you can provide a safety net that allows them a wheelchair and make policies that require access ramps and elevators, and do what you can to aid their social and workplace integration.

It's really coming down to what the possibilities of political action are and which ones are most relevant; race, gender/sex and disability are differences between people which engender risks that both matter a lot and can practically be mitigated or stopped through intervention. Nose size, hand span, and whether you like marmite are not.

I still haven't come to a conclusion regarding metaphysics in the realms of science and mathematics. At times I feel that only scientists who are involved in or knowledgeable of research into a particular topic are qualified to delve into the metaphysics of that topic, and at other times I think that this requirement is too stringent. — jgill

I think the pictures of metaphysics you get if you immerse yourself in a field differ a lot from field to field, and even subfield. Dive into physics, maybe you end up seeing reality as a collection of coupled fields and asking questions like "are space and time emergent properties?"; much different from what is imagined in mechanics. Dive into politics, maybe you end up seeing a perpetual struggle for power between social institutions and groups of people. Dive into biology, maybe you see a self differentiating flow of biomass adapting to environments and its own internal conflicts. The entities stipulated differ, how they relate within fields differ, how you imagine the fundamental principles differs.

That's somewhat of a vertical picture; what you end up thinking about the principles of the entities from descending into a domain of study. But it's also possible to do metaphysics laterally, to draw connections between domains, come up with uniting metaphors and vocabulary, describe process commonalities between domains of study in an abstract manner. This can be productive, or as is common, produces short circuits of thought and impassable problems; or interpret the impasses of what you have thought as contradictions or omissions within or between domains. Often both happen at once; by insulating over a live wire, productive simplifications engender broader world views, unaware of the limitations of their pictures, believing they have written all that needs be written until the inevitable, fatal, shock. Holding the background fixed with a violated assumption residing within it; avoiding shocking revelations by papering over their source .

Such short circuits are common forum posts; people taking folk notions, dipping into the concepts of a field, then finding a something counter intuitive they declare as an impasse, or essential for understanding of, or as an internal contradiction of the domain. Professional philosophers are not immune to producing such impasses, however, and you can feel the tensions; the subject in phenomenology devouring the autonomy of nature, the contradiction between the universality of rationally revealed structures and their presence alongside contingent events, institutions, social norms and emotion , and the unbridgeable, but already crossed, chasm between mind and body.

Typically philosophy consists of both impulses; being drawn down conceptual rabbit holes and being drawn to dig sideways and make a warren of them.

For which collections of objects does a unified now make sense? — Isaac

Strictly speaking, none, but the approximation for there being a single sense of time common to all the objects gets better the slower they are moving.

What exactly does (relative) speed change?

How fast something is going (relative to something else) shows up in the coordinate transform in special relativity, measuring how much relativity weirdness is required to account for the change between two coordinate systems (one attached to a moving point from an object, one attached to the object). It's a scaling factor, so it contracts/expands what it multiplies. Specifically, time and space terms.

An object at rest is just not moving with respect to its surroundings. That is, its relative velocity to its surroundings would be zero.

An object at absolute rest, maybe, is then just not moving with respect to all possible surroundings. This means its relative velocity to all possible surroundings would be zero. Unfortunately, that would mean that the surroundings couldn't move either, as that would make the relative velocity of the object to its surroundings nonzero. (Or, they'd only be able to move in ways that did not make the object contained within them move with respect to any other surroundings. Motion with nothing going by anything.)

So if there's such a thing as "absolute rest", it would have to apply to everything (or be incoherent). That is, there'd be no motion. There is motion, so there's no such thing as absolute rest.

There's probably a neat conceptual paradox that's something like : the universal experience is always the failure to reach the universal. — csalisbury

Immediately reminded me of having sex. If you've had sex, you haven't just had sex, you've also lost your virginity.

A unified "now" only makes sense for collections of objects which are moving sufficiently slowly relative to each other. (Relative) speed changes how fast time flows; so there's no unique temporal succession of nows; "now" is attached to a coordinate system. Worse, there's more than one time; time flows more slowly at lower elevations on Earth compared to higher ones.

We could actually take steps to limit people's heights. It would involve limiting calories. It's also probably easier to make smart people dumb than dumb people smart, but why not try both simultaneously? You never really hear major social inequality of height, intelligence, or charisma in the world. — BitconnectCarlos

I guess the distinction you're looking for is inequalities that derive from features of political organisation with regard to resource access and distribution and inequalities that derive from other means. Seeing as we're talking about politics, it isn't so surprising that (allegedly at least) politically based inequalities are of concern to "leftists"; an umbrella term for a political sympathy.

I am not sure whether it can actually work out that way, but that was the idea, if I understand him correctly — SophistiCat

Regardless, I think the synthetic differential geometry pdf suggested an intuition closer to it. Roughly, augment the real numbers with some set of symbols $D$.

You then stipulate that any function $f$ defined on $D\rightarrow \mathbb{R}\cup{D}$ has some unique constant $b$ such that for all $d \in D$ $f(d)=f(0)+db$. There's also a property that $d^2 = 0$ for all $d \in D$. This looks like placing a family of infinitely small line segments around every point in $\mathbb{R} \cup D$. For functions, it gives a "tangent space" of a function at a point confined to infinitesimal neighbourhoods around it. It "smears out" the real line (and function values) into something that can't be element-wise disassembled in the same way (if you fix a point of $\mathbb{R}$, this corresponds to an infinitesimal neighbourhood around that point in $\mathbb{R}\cup D$)

Thanks!

However, it cannot serve as the basis for true continuity, because it requires discreteness at the outset. — aletheist

Do you know of any current mathematical objects that behave more like true continuity in your view?

I said that Quine makes no room for degrees in his dismissal of the analytic/synthetic divide. — frank

Rejecting (by undermining) the analytic/synthetic divide was a major part of Quine's disagreement with the logical positivists, spelled out in Two Dogmas. Quine makes reference to Carnap regarding the role this rejection plays in putting the questions of metaphysics on a level playing field with those of natural sciences.

Consider the question whether to countenance classes as entities. This, as I have argued
elsewhere,10a21b is the question whether to quantify with respect to variables which take classes as values. Now Carnap ["Empiricism, semantics, and ontology," Revue internationale de philosophie 4 (1950), 20-40.] has maintained11a that this is a question not of matters of fact but of choosing a convenient language form, a convenient conceptual scheme or framework for science. With this I agree, but only on the proviso that the same be conceded regarding scientific hypotheses generally. Carnap has recognized12a that he is able to preserve a double standard for ontological questions and scientific hypotheses only by assuming an absolute distinction between the analytic and the synthetic; and I need not say again that this is a distinction which I reject.

Quine strongly rejecting the analytic/synthetic distinction and thus the (alleged) derived sharp divide between science and philosophy in Carnap's work does not immediately suggest that Quine advances a sharp divide between science and philosophy in Two Dogmas. Nor that he derives anything about the relationship of various sciences from this rejection.

The overall picture is that knowledge is a network of claims about posited entities related by links of logic and reason (that the links take a particular form in a particular network part is also part of what is posited), and only the exterior of this network need interface with our experiences by means of observation processes. The picture of ontology tracks the picture of what we know; what we stipulate to exist relates to our experiences sensorially and through observation and what else we stipulate to exist through propagating inferences. Despite this, epistemology and ontology remain distinct topics of inquiry. The work of epistemology consists of spelling out how entities are connected within the network: what the connections mean, how they are formed and their character; the work of ontology consists of furnishing the entities within the network with a general description technique in which they may be unambiguously expressed, and thereby delineating what form our ontological commitments take given our knowledge.

The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics or even of pure mathematics and logic, is a manmade fabric which impinges on experience only along the edges. Or, to change the figure, total science is like a field of force whose boundary conditions are experience. A conflict with experience at the periphery occasions readjustments in the interior of the field. Truth values have to be redistributed over some of our statements. Re-evaluation of some statements entails re-evaluation of others, because of their logical interconnections -- the logical laws being in turn simply certain further statements of the system, certain further elements of the field. Having re-evaluated one statement we must re-evaluate some others, whether they be statements logically connected with the first or whether they be the statements of logical connections themselves. — Two Dogmas

But the total field is so undetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to re-evaluate in the light of any single contrary experience. No particular experiences are linked with any particular statements in the interior of the field, except indirectly through considerations of equilibrium affecting the field as a whole

In this regard, knowledge is web weaved of different fabrics supporting each other; stipulated entities within the web play the same role insofar as they function within the web in the same manner. Because of this, the web has ambiguous constituents and ambiguous propagation of effects from observation. Collections of stipulations which play the same explanatory role and interface with the web's periphery of observation in the same way may exist, and moreover if there is an observation which is startlingly inconsistent with our knowledge, a range of re-evaluations of what we know will be possible to bring our knowledge into accord with this startling observation.

The overall role ontological commitments play here is a matter of efficiently coordinating our knowledge. They're like condensation nuclei for clouds of knowledge.

Positing does not stop with macroscopic physical objects. Objects at the atomic level and beyond are posited to make the laws of macroscopic objects, and ultimately the laws of experience, simpler and more manageable; and we need not expect or demand full definition of atomic and subatomic entities in terms of macroscopic ones, any more than definition of macroscopic things in terms of sense data. Science is a continuation of common sense, and it continues the common-sense expedient of swelling ontology to simplify theory.

The difference between fields of inquiry becomes blurred, as often there are overlaps in what entities they are connected to, though observations related to one field may be more distantly connected to those in another, and a re-evaluation through startling observation may get to work on near connected knowledge items to the observation process rather than ones situated further from it.

In light of Two Dogmas, it looks more plausible that differences between science and philosophy are differences in degree, as they're extremely interconnected parts of the same network (as Quine sees them). Nevertheless, there's some hint of an abstraction hierarchy involved; if we posit that some fields of study are more closely connected to and thereby more tightly constrained by the observational exterior of the network, the perceived increase in rigour by being close to this observational exterior may be concordant with an idea of tighter constraints on the number of theories consistent with those observations; in other words, for example, developmental psychology may be more underdetermined by observation than materials science. Having more varied ontological commitments and general theories consistent with the same observations may give a flavour of arbitrarity to a domain of study. But I don't think any of this necessarily follows from the paper alone.

In the future our unconscious will be used to mine Bitcoin.

so researcher's judgement on the value of other fields is fickle to say the least, — Isaac

This. Also even within the same field but different subfield. "What you're doing isn't history/anthropology/linguistics/psychology..."

In my experience academics involved in any kind of science generally separate themselves from philosophy. "What would make a neural net self aware?" - philosophical speculation, as it requires a what is seen as a non-scientific concept of self awareness.

Despite that, you can trigger academics when not-even-wrong philosophical speculation crosses over into the science, like "Does Evolution have a purpose?" annoys researchers.

The combined effect on academics I think is it's either useless, error borne from lazy thinking and lack of education in their field, or not related to their research at all.

Of course there are exceptions, and you can find authors who bridge gaps; like Dennet, Metzinger, Rovelli, Merleau-Ponty, Rota and Priest.

A set is a bottom-up conception, assembling a whole from discrete parts. True continuity is a top-down conception, such that the whole is more fundamental than the parts. — aletheist

Let's say I have some "True continuity" X. Like a line X=(0,1). Let's say I can take "parts" of it in the above manner; arbitrary subintervals. (0,a), (a-1/n,1) are subintervals for any a less than 1 and greater than 1/n. Since they're parts of a true continuity, the true continuity ensures the existence of their intersection; limit the process of intersection over n and get the limit {a}. If I take the union of all such limits, since a was an arbitrary member of (0,1), it produces (0,1). So starting from a true continuity, like a line segment, you can get discrete numbers, then build up the true continuity out of the individual numbers through a union. It's top down and bottom up at the same time.

Do you agree this process is legitimate?

If not, do you reject sets as a concept?

Anything of lesser dimensionality is not itself a part (or portion) of that which is truly continuous, but rather a connection (or limit) between its parts. — aletheist

I think this would end up giving precisely the same mathematical theorems, no? You just restate things in terms of connections and parts.

Like: the metric topology on the interval (0,1) consists of open sets defined by: the empty set (a limit) is in the topology, the whole (0,1) is in the topology, unions of parts and connections/limits are in the topology, countable intersections of parts (be they connections/limits or parts) are in the topology.

The vocabulary of sets lets you phrase all these concepts already. "Parts of a line? They're finite intersections of its interval subsets which have cardinality greater than than 1".

Can you apply the same level of doubt to what's making you doubt all this?

Go eat something and find out?

You do stuff. Like doubt you exist. You probably also eat things sometimes.

Doubting's one thing you do. Try doing something else for a bit.

If you need an academic argument, this should take your mind off doubting like that for a while!

If I put on my Heidegger hat, I say that we can only break enframing by means of a radical antihumanist shift. Only a God can save us, because only a God can subordinate mankind in the way necessary for an antihumanist (thus post-technological) turn in society to occur. We are not post-Gestell until we are posthumanist, and this cannot occur in terms of a philosophy that smuggles in the old enlightenment conceits - and this is precisely where most contemporary attempts fail. — Pneumenon

Another way forward might be to find an instability within the enframing concept that sees humans within nature, or as always already inhuman. Human mastery over nature, seeing it as instrumentalised for us, invites a reverse position where we're (1) nothing but one type of its instruments and (2) thus have a duty of care for that which we're coextensive with.

Think it's hairy->airy which sounds like aerie which is a place where birds are kept. Presumably a joke about how British people are terrible at speaking English, or that standards for proper English aren't actually adhered to by some (many) British native speakers.

Where I grew up in Scotland, we'd mostly use one tense of the verb "to go", we'd say "gan". Gan could mean "I am going", "I went" or "I will go". Also "meet with", "date" and "have sex with". We have thoroughly ridiculous accents.

Falsifiable hypotheses are refutable by experiments.

What is really happening, I suspect, is that we have a different understanding of the relationship between rights and law. Law, on my understanding, exists in service of rights, such that rights have a logical priority over law. This is certainly the more ancient view, as far as I can make out. It is also the correct view: if we accept Friedman’s argument, which seems to me a good one, rights-respecting behaviour pre-dates the human species, and so a fortiori it pre-dates the State. — Virgo Avalytikh

I understand a natural right as way people morally ought to be treated based solely on their nature. For people, natural rights are to be derived solely from human nature, they thus apply to all people and at all times.

I understand a social obligation as a way people normatively ought/are expected to be treated within a social system or society. Social obligations are particularly strong norms. They vary widely over social systems and societies.

I understand a legal right as an enforceable claim within a legal system. Legal rights vary widely over legal systems. It is possible for these to be codified to a large degree, as we're used to, to be based largely on custom, as is older, or some mixture of the two, as in appeals to documented precedent.

Since legal rights are enforceable claims, they induce particularly strong social norms, and thus induce social obligations. Historically, codified legal systems arise much later than customary ones; all societies have rules which are enforced, whether or not they are codified, and whether or not they have a central government.

‘Natural rights’ theory has often been accused of espousing a flimsy ontology, where the content of our rights is simply stipulated. In fact, this comes from a failure to appreciate what kind of philosophical project ‘natural rights’ theory is: man has a nature, as a purposeful, creative and social agent, and there are ways in which we might think of rights which allow man to act in accordance with that nature, and ways that do not. Perhaps this would become clearer by reflecting on the many ways in which a proposed system of rights may be contrary to man’s nature, some of the ways in which the individual may be dominated or have her ends constantly frustrated. — Virgo Avalytikh

Everything humans have ever done is possible for humans, and is thus within our nature. From the most brutal of tyrannies to hippy communes, from pre-monetary societies to capitalist states. Natural rights, then, are not a constraint on what is possible for humans to do, they are a constraint on what we ought to do, what is proper for us. How does property fit in here?

Let's stipulate that so long as there have been tribes, there have been possessions in some sense; a society in which people may claim exclusive access to land is much different from one where people may not, a society in which people may claim exclusive access to other people's bodies (like slavery) is different from one where they may not. Even this stipulation does not confer a natural right of possession, as it only recognises a historical coincidence of human societies with rules regarding what humans can claim to possess within them. It is not a derivation from human nature to possession, it's a historical observation. Further, in each case, a society has existed which has customs of possession which may differ depending upon historical circumstance, so we cannot attribute a natural sense of possession to humanity on this basis alone - we cannot distinguish what someone owns in a society by virtue of its customs, like laws, and what someone owns in a society by virtue of natural right on this basis.

We'd have to abstract from all societies and all senses of possession within them, to see through mere historical circumstance and its contingent forms of ownership, to something basic and shared for all humanity for all time; but notice that due to this historical variability of customs of possession, we cannot infer that such a natural right of possession is ever sufficient for the customs to reflect that right. Is there a sense of ownership from which all the others are derivative? In the sense of enforceable claims and consistency with custom, no then, there is always a gap between what ought to be, what is legitimate, and what is. If we are to derive a criterion of legitimacy for a mode of social organisation, it must be independent of the contingent features of all of them; firms haven't always existed, states haven't always existed. But within those, human bodies have, and have remained roughly the same.

Based on this, a promising candidate for the derivation of natural property rights seems to be the sense of possession one has over one's body; let's call that autonomy. Can we derive from autonomy conditions of possession which actually hold or have held? No, see the above, human bodies have been much the same for all this time, but the historical circumstances regarding possession vary wildly. In some customs of possession; like slavery; autonomy does not even entail the possession of one's body to be ensured in a social custom.

There needs to be a principle to bridge autonomy to social customs of possession; equating the senses of possession in each will not do. Each person stands in a unique relationship with their own body, nothing like dominion over any object. For stipulation's sake, let's say that a person possesses an item they have produced solely through their own labour in the same sense that they do their body. Then by what criterion do we judge social acts of production within an economy's division of labour? What about items produced through machines, ought the person who turns the plugs on at a factory own everything? Maybe the electricity is what is doing the work... As soon as productive labour requires any sense of teamwork or social dependence, the principle would no longer apply. Read. it has never applied, since as you say we are intrinsically social. It would also be impossible to ought to own anything regarding land or what is produced from it without intervention, as it is not produced solely through a person's labour since it is not produced by labour at all. Impossible to ought to own on the basis of autonomy alone.

It seems like what we need to transfer from autonomy to more abstract and socially mediated senses of possession is an equivocation between my possession of my own body and possession within a social custom. To think that Amazon is owned by Jeff Bezos in precisely the same sense he owns his body is insane; bodies do not have shareholders or corporate headquarters, human bodies do not coordinate within themselves entire other human bodies. If Jeff Bezos has a shit, someone does not poop for him.

The idea that the Principles Of the Free Market can be derived and legitimated through human nature alone is just as nuts. "See this contingent social form in which production and exchange are organised? Yeah, that's the one true human nature, the only social form consistent with it. Btw, it has never existed."

I apologize for interrupting a productive flow of thought. But I was curious what you guys were talking about. Seems pretty esoteric. :chin: — jgill

What do logic and topology have to say about each other?

Specifically; if a logic has a model is there a correspondence between a topological space on the set which models it and how proof works in the logic?

If yes, can you please try to explain this in a better way? I don't even have much time for this, sorry. I have even to go to the hospital for a couple of days next week. — Mephist

The Heyting algebras are for intuitionist logic (of some sort). I wrote that previously.

Hope you feel better soon.

I would agree that we have obligations to each other in absence of the law, though. And would further stipulate that something being legal is not the same as it being moral. I'd also stipulate that something being socially obliged does not entail it is moral, though it would surprise me if there weren't things in a three way overlap of what is legal, what is socially obliged and what is moral. I'm going to continue to frame that what's illegal is outside of the set of what's socially obliged though; in particular, we're socially obliged not to do that which is illegal. We may be morally obliged to do that which is illegal sometimes.

The axiom of extensionality defined what it means for two sets to be equal. They were equal if they contained the same things.

An analogy - shopping lists. Two shopping lists are the same if they have the same items in them.

The next axiom is the axiom of pairing, which states that if you have two sets, you can make a another set which contains only those two sets as elements.

Shopping list wise - this means that if you have two shopping lists for different shops, you could make a shopping list for both shops by combining them.

Then there's the axiom of (restricted) comprehension - if you have a set, you can take a subset of it whose elements are the only elements which satisfy some property. If A = {1,2,3,4}, we can construct the set.

{x in A, x is even}

and get {2,4}. All the axiom of comprehension does is ensure the existence of a subset of a set which satisfies a specified property. It's called the axiom of restricted comprehension because it requires that we begin with a set (like A) then apply a property to it to get a subset (like {2,4}). If we could 'conjure up' a set into the language of set theory solely by specifying a property:

{x , x satisfies P}

Then we can make P whatever we like. Notoriously, this gives

$\{x, x \notin x\}$

The Russel set. This must exist if we stipulated "we can conjure up a set through a property", and P is a property of set theory since it's a well formed formula of the language of set theory. If something belongs to the set, it doesn't belong to it, if something does not belong to the set, then it belongs to it. The reason why mathematicians rejected this axiom was because it entails a contradiction, and through the principle of explosion (discussed earlier), makes the theory prove everything it can state, even the falsehoods. Restricted comprehension saves the theory from the paradox by making sure you start with a set to apply properties to, rather than conjuring up a set from the logic using a property. If you change the underlying logic to one that is more resistant to contradictions, you might still want the unrestricted version (like in a paraconsistent logic).

Shopping list wise - this says that we can select sub lists by specifying elements. "What vegetables will we buy?" is answered by the sub list of vegetables.

The next is the axiom of union. This says that for every collection of sets, there's a set which consists of the elements of all of them taken together.

Shopping list wise, this says that you can make a larger shopping list out of any collection of shopping lists. A shopping list of meat items taken with a shopping list of vegetables becomes another shopping list which consists of the meat items and the vegetables.

The next is the axiom of powerset. This says that for every set, there exists a set which consists of all the subsets of that set.

Shopping list wise, if we have the list:

Carrots
Potatoes
Eggs

This says we must be able to construct the lists

Carrots, Potatoes, Eggs, {Carrots, Potatoes}, {Carrots, Eggs}, {Potatoes, Eggs},
{Carrots, Potatoes, Eggs}, and the empty list (what you would buy if you bought everything on a blank page).

Then make a list of all those shopping lists and the blank bit of paper. That whole new list is the powerset of the original shopping list.

The powerset of a set is always larger than the original set. If you had a set of infinite size (to be introduced later), this makes there be more than one size of infinity. If we considered an object which would be a model of set theory, because of the power set axiom, intuitively it would have to have a size larger than any set, in particular larger than the natural numbers! Unfortunately this does not hold, there are countable models of ZFC (called Skolem's Paradox). Such a model does not satisfy the intuition, but entails no contradictions; a model in some sense sets out a meaning of terms, a countable model of ZFC doesn't have the statements in it mean precisely the same thing.

‘Rights are produced by social norms; laws are social norms; therefore rights are produced by laws.’ — Virgo Avalytikh

More precisely; people have no rights except for the ones afforded to them by social systems. If you want to know what a person is entitled to in a social system like ours, look to its laws, and look at how they may change. When the laws change, the rights changed. I assumed you believed this, perhaps you are arguing that there is some non social system by which people are afforded rights? Perhaps by some divine agent like the Free Market, the purveyor of all Goods, Services and Natural Rights?

If you could find me a natural right which is not merely stipulated to hold as a contingent feature of a social system, and which is not an enforceable claim when and only when it also holds in a social system or a legal system (which is a particular type of social system), I would believe they exist.

And these rights apparently

can be bargained up to in the absence of centralised State dictum; indeed, without any communication at all — Virgo Avalytikh

can be bargained, without any communication, and are not purely social or legal in character? Despite that they resemble how ownership works in a market society in almost every respect, except that they are somehow "legitimate"? Nonsense on stilts!

This is not true. In my original post, I cited an article of David Friedman’s, ‘A Positive Account of Property Rights’, in which he argues – convincingly, to my mind – that a set of non-overlapping rights domains, as well as a set of self-enforcing contracts, can be bargained up to in the absence of centralised State dictum; indeed, without any communication at all — Virgo Avalytikh

Let me see if this jibes with you, as a summary of your argument.

(1) Legitimate rights are of form X.
(2) All legal rights afforded by a state are of form Y.
(3) Y precludes X.
(4) Therefore all legal rights afforded by a state are illegitimate.

Y are "incompossible" or "coercive" or "do not satisfy the non-aggression principle".

And all this time you've been arguing about natural rights? Presumably they also flow from God The Free Market, the hitherto inexistent paradise on the hill.

Why these persons, in distinction from all others? Why this territory, in distinction from all others? — Virgo Avalytikh

You're looking for a philosophical (precisely moral) justification rather than a historical or political one, why must history have gone the way it did? I can't answer that, a state is as contingent a social form as a tribal council. What legal rights we have are ultimately a function of politics and history. Since there are no natural rights, what rights we have simpliciter are a function of politics and history. Why would different people in different countries in different time periods have different numbers of different rights if it worked any other way?

This won’t do, even as a partial definition, since a State is not necessary for the production of law. — Virgo Avalytikh

You're right, it is sufficient for the production of law. A collection of legislative bodies which produces codes that entitle select people to enforceable claims is necessary for the production of law. If you can find a social system with laws that does not have such a collection, I would be extremely surprised.

Sometimes, we might speak of groups as though they were an organism with their own inherent capacity to act, but this is non-literal. The Greeks called this linguistic phenomenon synecdoche, the improper predication of a property of a part to the whole. We do this in sport, when we say ‘Portugal has scored a goal’ when in fact it is not true that a country has kicked a ball into a net. — Virgo Avalytikh

I have not even mentioned legal responsibility as a precondition of personhood, or of being an agent of purposeful action. So I fail to see how any of this could be a faithful reconstruction of my position. — Virgo Avalytikh

What I have denied is that aggregations of agents of purposeful action – persons – may be counted as ‘extra’ agents of purposeful action, above and beyond the members.

You may not have explicitly stated that legal responsibility is a precondition for personhood. But you have denied responsibility to aggregates, like firms, on the basis that responsibility applies only to individuals (humans). I just flipped the implication; if responsibility applies only to individuals (humans), then firms must be humans, on the basis that they are legally responsible for things. Clearly you don't believe that, which is inconsistent.

It's much more plausible that the only rights things have are of the same character; legal ones, socially mediated ones, and it doesn't matter whether they apply to agents or aggregates.

Bleh, constructing the connection from the set theoretic side is extremely indirect. I think there're three components.

(1) Showing that the open sets of a topology are a Heyting algebra (or associate with one).
(1a) This should obey some restriction property, so that if we restrict the topology to a subspace, it will also be a Heyting algebra. This should follow from (1) directly, as if all open sets in any topology form a Heyting algebra, then so too will the subspace topology induced through a restriction. This probably turns out to let us take subsets of a language, like individual well formed formulae, and give them models in exactly the same way. Such a restriction would probably be continuous, as if we endow the subspace with the subspace topology and treat the mapping between them as an indicator function, the pre-image of every open set would be open just by definition. So the "continuity" of the interpretation looks to be a by product of (1) and the continuity of the inclusion map from a space with a topology to a subspace which is the image of that map with the subspace topology. The restriction map is probably quite similar to a subobject classifier, since it is a characteristic function for the set being used in the restriction. The overall intuition I have is that if we have a model, we can go to a larger model by "pushing back" along the restriction map.

(2) Showing that a model of intuitionist logic is a Heyting algebra (or associates with one)
(2a) The ordering relation in the Heyting algebra respects syntactic entailment, since we're using a Heyting algebra as a model, the logic is complete, it also respects semantic entailment. If it "respects semantic entailment", it should "respect the mapping from the logic to the Heyting algbra", because that's how we provide the formulae with models.

(3) (1) and (2) together give us that the open sets of a topology are a model of intuitionist logic. The interpretation function would then be taking the well formed formulae of the logic and associating them with their corresponding open sets, which are isomorphic to set "domains" that satisfy the formula, and have their own Heyting algebra.

The category theoretic construction lets you come at this some other way. If we re-parse everything in category theoretic terms the same things would hold. But it is probably true that it holds more generally for topoi that aren't representable as sets.

Edit, trying to translate between @Mephist's intuitions and our stodgy old analysis ones: if we drew out a category-theoretic diagram that had intuitionistic logic models on it as a category, then topological spaces as a category, then the syntax of intuitionist logics as some other object, we could construct the arrows:

Intuitionistic logic syntax ---interpretation>> intuitionistic logic models
Topological spaces ---replacement of union and intersection by join and meet and other stuff>> intuitionistic logic models
We could construct a model of an intuitionistic logic through a pullback of the interpretation and the other map? So that the "fibres" (pullback elements) are the open sets which model our specified syntactical objects. The topological space would model the whole logic when and only when the whole space is in the fibre product, maybe anyway.


There's a comment that goes through some of the construction here.

Still unclear, but I'm starting to see how it could be the case.

So, anyone may transform the land, in whole or in part. They are then within their rights to resort to force to defend their property. — Virgo Avalytikh

Indeed! The owners of the Dakota Access Pipeline were well within their rights to beat the shit out of protestors and Native American land residents on the land to defend their property. The protestors, in an attempt to deprive the firm of what was rightfully theirs, initiated brutal force. It was only right for protestors to be stripped naked and ogled by police, beaten and pepper sprayed, consistent with the defending the property rights of who rightfully owned the property. The violence of police was not coercive as they did not initiate it, the fault goes to the protestors and Native American residents. The owners were only defending themselves.

But you are right, in an ideal world, the State would not have provided police officers, the owners of the Dakota Access Pipeline would have hired a mercenary group, or hired a private security firm, for a modest sum, who spend their time freely due to agreeing to the contract. Strictly speaking, these mercenaries could never have been coercive, as they did not initiate the violence. They were simply protecting the owners of the Dakota Access Pipeline's right to transform the land...

f you are going to insist on identifying 'social norms' with 'what is written on a piece of paper by these particular persons in this particular territory', then you must give an account of political legitimacy. — Virgo Avalytikh

Why do I have to give an account of political legitimacy? I've never been arguing that states or markets are inherently moral institutions, I've been arguing that your criticisms of them are incoherent.

There's no more to a system of property rights than how it's set out in the law and how that law's enforced. A claim that you seem to believe, as you seem to believe that ownership is determined by social systems. The law is certainly a social system that determines who owns what. So, the state has the benefit of actually existing here, your proposed social system does not, it provides no enforceable claims to property, it cannot decide what is expropriative and what isn't.

I've never been arguing that "We ought to follow every law because it's written on a piece of paper" or "We ought to follow every social norm because it's there", I've been arguing that what it means for a person to be subject to a law is to be in the territory of a governing body, or other social form, that has that as its law. Laws are social customs, in the sense that laws are a subset of social customs, they can be changed. They're codes. Ought one follow a law? Depends on the law. Ought one follow a mandate from a political body? Depends on the mandate. The normative force follows both from social customs (the widespread belief and teaching that we should follow the social codes, which includes the law, and so includes private property) and from some social customs being enforceable claims (when they're laws). This says nothing about whether the social customs, laws, states, etc are somehow "legitimate" or "moral".

What it does say, however, is that how you're criticising them is based on category errors. If a law or social custom holds, it holds whether it is moral or not. Ought it not hold if it is not moral? Sure. Ought it not hold if it not holding for a specified reason cannot happen? No, ought implies can, cannot implies not ought. My argument strategy has been to show that what you're talking about couldn't possibly happen, or is based in category errors. Hence the argument about what it means to own something being solely a legal matter, or a matter of social custom.

I do not. I have objected, with no small amount of philosophical rigour, to the identification of 'social customs' with the State's edicts. Government and society are not the same. It is not us. — Virgo Avalytikh

You're right, governments aren't identical with the societies that they're in. Governments are (minimally) a collection of legislative bodies in a society.

Why I've been arguing is because if laws are social customs, private property is also a social custom. What you own and how you own it is determined by the laws that apply to where you live. There's no further sense of ownership for private property above and beyond how the law says private property works. Does that mean how people own things and who owns what is moral in any particular social system? No. It does mean that an impossible social system (such as you've described or elided to describe), where property ownership is not just legally mandated social relationship irrelevant of how moral it is or how expropriate it is is an inappropriate standard to judge societies by, by virtue of being logically contradictory.

Does the government own your tax?
Yes.
Is it expropriating your property when you pay it?
No.

When a loan shark legally reclaims all your stuff for failed repayments, are they expropriating your property?
No.
Because the law entitles them to reclaim their damages from what you own, they have their choice of what you own up to a specified value. They already owned it.

That is, in neither circumstance, no one is violating any property rights, because they're defined by the law.

When two people claim ownership for the same thing in a legal dispute, do they have conflicting items of property?
No, they have conflicting property claims. Who owns the thing is decided in the legal dispute. If the second person won, and the first person was preventing the second from access, maybe the first person has to pay damages, because the second person already owned it.

That's all there is to ownership of commercial private property. It's determined by the law, which is a kind of social custom - albeit a social custom that few affected by it can change. Your use of "expropriation" and the like are merely poetic (insofar as laws are sufficient to define who owns what!)

Are you really suggesting that the pieces of paper on which the State writes determines metaphysics? — Virgo Avalytikh

No, it's our capacity to form social institutions that can be held responsible for things that makes such a thing a necessary part of our social ontology. As far as the law goes, corporations are legal persons; they can be held legally responsible for things. What I'm doing is feeding facts like that into entailments you've suggested to show they're incoherent.

If your claim goes: "if X can be held legally responsible for something, then X has a mind", then corporations have minds because they are held legally responsible for things. If your claim goes "if X can be held legally responsible for something, then X is an agent", then I guess corporations are agents, so agents need not be humans at all.



In general, you continue to criticise the state for failing to behave the same as something which does not and cannot exist, you agree that who owns what is determined by a system of property rights - like our system of property law - but you continue to criticise the state for "expropriating" what it already owns by that standard.

If anything, I'd hope that you pay your taxes with glee now, now that you know you're giving someone their own property back when they demand it. Hell, you are initiating force when you deprive them of their property! Non-aggression requires you pay it.

Isn't there a missing premiss? Something like humans are the only entities with agency... then agency is only applicable to humans. — creativesoul

Yeah, that makes sense. I think @Virgo Avalytikh's presentation suggests they agree with this premise.

How did you get there from where you were? — creativesoul

If agency is only applicable to humans, and legal responsibility is only applicable to entities with agency, then agency is only applicable to humans. No agency => No legal responsibility. Flip that about. Legal responsibility => agency. Firms themselves can be a party in legal contracts. So firms can be legally responsible for things.

I don't believe they have agency in the sense humans have agency, but they do have causal powers and their own kind of existence, recognised by law, distinct from each of their employees (you could change every employee with another and keep the legal responsibilities intact, though this is not necessarily independent from employee roles within the firm (who signs the contracts for the firm.)

In your model the topology of omega is not used, and there is no topology defined on the space of all propositions (how do you define the set of open sets of propositions?) — Mephist

So you get a discrete space of points split in two equivalence classes: true propositions and false propositions. — Mephist

I was hoping you'd be able to tell me, as it seems defining what a topology is in terms of the logic is precisely where the missing intuition is. I assumed there was some topology on the space of propositions, and tried to see if "pushing back" the open sets of the topology on $\times_K \Omega$ through the interpretation $I$ made sense to you.

Something like, if we have a logical connective's truth function $f$ from $\times_K Q \rightarrow \Omega$, and we glue together open sets on $\times_K \Omega$ 's discrete topology through the fibre $\{ I(a)=1=f(c) | a \in \times_K Q , 1 \in \Omega, c \in \times_K \Omega \}$. I guess inducing a topology by pulling back a topology through a continuous function and a connective (dunno if that works at all).

It perhaps doesn't make much sense. Do you know the analogous construction for classical (or intuitionist) propositional logic? So we don't have to deal with the interpretation being a complicated set valued function. It should be in there somewhere and easier to talk about to exhibit a connection between a topology on the logic and a toplogy on the Omega product.

and open sets are naturally represented as types in type theory — Mephist

If we continued with the propositional classical logic in my example, and we have an interpretation from $\times_K Q$ (the symbol set product-ed with itself $K$ times) to $\Omega=\{0,1\}$, and if we gave $\Omega$ the discrete topology as I said. If we then stipulated that the interpretation was "continuous" in the sense of topological spaces (the pre-image of every open set is open), would the pre-image of any open set of $\Omega$ with the discrete topology be a type, and thus a proposition? Or a collection of propositions which co-satisfy/are equivalent?