There's a social scientist called Levi Strauss. He's a structuralist - and while he talks about ape and human societies, he similarly describes vertical and horizontal kinship structures - as opposed to mere dominance hierarchies. Jordan Peterson fans - take note! — karl stone

I didn't say what I said to undermine all notions of hierarchical organisation, I said it to undermine ones involving, even analogically, an outdated idea about wolves.

Just as a point of convenience, if you highlight a section from someone's post (from top to bottom of the desired section), you can click the 'quote' button that appears in the prompt and it will also notify them that you have responded, and any of your readers can click on the quote to see exactly what you're quoting from. Such tags make conversations much easier to follow.

Interesting hypothesis, but I think it's flawed, in that - there's a natural individual interest in academia and science in upsetting the applecart of accepted wisdom; and here we enter a hall of conceptual mirrors, because it's something this paper does - while under-estimating the tendency in others. And now, it's something I'm doing to this paper. Vertigo! — karl stone

The study that hypothesised alpha wolves based on wolf behaviour only used captive wolves. Wild wolves don't actually have the same social stratification. Even the person that came up with it has since rejected it.

To be sure, speech acts are acts, and hence subject to moral interpretation. I think we agree on this. — Banno

I agree with this, yes. But I think there's a pretty big distinction between the function of an imperative - how it imparts a norm and that it imparts a norm - and saying one ought to follow the same thing as a moral maxim. Having a single modal operator will not allow you to parse this distinction. It's important, as attending to the function of an imperative is not endorsing the act that imperative takes an affirmative stance towards.

The alpha thing, like iron and spinach turned out not to be true. Unfortunately both became popular and well cited enough to enter popular culture.

Triad? just to make sure we are on the same page - speaker, hearer and state of affairs? Words for activities have their use, perhaps, hen placed in such triads. — Banno

Aye. I figured that 'triad' would be less obscure than 'ternary predicate'. I don't have any goals here other than to brainfart into the thread, and I don't care so much about whether ethical statements are truth apt, about emotivism or cognitivism or the usual meta-ethical fare, I care more about paying attention to what we do with norms and imperatives and so on.

No. Nature and the fact that you have a penis, which is different than a woman, who has a vagina, is what allows you all to be equally men. — Harry Hindu

I will inform the Language Police all over the world to remove gendered constructions, people all over France need to know that whether a river has a vagina or not depends on whether they're talking about the bit flowing into the sea vs it being inland. Sailors all over the world no longer must furiously masturbate into socks when they can just fuck the boat beneath them. This will be incomprehensible to those who speak Tagalog, however, who must suffice with the usual biological bits - at least before their language was changed through their interactions with the Spanish. Eunuchs are no longer male, hallelujah!

There is an extra dimension of gender surplus to the biological ones, which are certainly still relevant. Their relevance is echoed by the relevance of the words 'trans', and the distinctions between 'girl' and 'XX genotype' (see XX male syndrome) and so on. The etymology of gendered words (and tropes) goes further back than contemporary understanding of biology, we should not be surprised to find mismatches between the two in correct use.

It isn't us who're misunderstanding gender, it's you who are misunderstanding language and normativity.

TO be candid, I would drop "meaning" from most philosophical conversation. It's far more productive to talk about what we do with words, how they interact with the world, and such, than to get bogged down in esoteric waffle about concepts and such. — Banno

I hope this wasn't directed at me, I tried so hard to put my analytic philosophy goggles on!

'One ought not kill': Killing is an element in the group of things we ought not do.

'One ought follow the imperative 'do not kill'': 'Do not kill' is an element of the group of things we ought do, and is an imperative. — Banno

I think I have to be picky here and say that it's quite a lot different to have 'ought' ranging over activities like killing and commands like 'Do not kill'. The grammar's quite a lot different. Imperatives have a structure something like the below account (for imperative speaker S, an agent H and an event E). Taken from here, I'm sure there are limitations of the account I won't understand.

a. S refers to an event (stipulated) E that can potentially be brought about by H
b. S takes an (affirmative) stance towards the actualization of this potential (S affirms that E should be brought about by H)
c. S presents this stance as relevant to H’s decisions about H’s future course of action.

Whereas activities aren't even language stuff. The deed isn't the promise or command to do it. Letting the domain range over imperatives and activities without an eye for their differences removes the distinctions between them. Relevant distinctions are that imperatives are performative relational triads, words for activities (in the context we're using them anyway) are singular and constantive. We can evaluate imperatives by substituting in S's E's and H's, 'killing' is always just killing and 'not killing' is always just not killing. You could view them from the same vantage point with the same (modal) operator, but this means that 'ought' actually ranges (partly) over speech acts!

Just some thoughts.

It looks to me like 'One ought not kill' and 'One ought follow the imperative 'do not kill'' might actually work through different modalities. The first is a modality that applies neatly to events, as if we are predicating 'ought not' to the event 'killing'. The second might actually be relational - between a speaker S uttering a command C and an agent A - in my book there either needs to be an utterer or some other structure S which applies C to A. Perhaps the first modality O might be interpreted as universal quantification over S and A - IE that an arbitrary A ought to follow C as uttered by an arbitrary S (aRcs). I don't trust that this would seamlessly lead to the equivalence between O(x) and (aRxs) as it seems to me there will be ambiguous cases between, say, the boundary of killing and the prevention of death. So it might be, say, permissible to divert the tracks in the trolley problem but 'one ought not kill' could still be true.

The water there is quite muddy, as it seems to require an analysis of the relationship of speech acts to the norms they require and establish (which presumably what all this rule following talk is working towards). But the ability to evaluate aRcs using norms; they may fail for some and obtain for others; lends aRcs a contingency not afforded to the raw statement 'one ought not kill'.

Another difficulty I can see is how we would extract propositional content from 'one ought not kill', say that we've abstracted 'ought' to an operator O on propositions, what proposition x would you write to translate 'one ought not kill' to the form O(x)? It looks to me like the easiest translation would be just to take 'not kill', but that is not a proposition - rather it's the negation of a verb, so it is not the negation of a proposition - what is the truth value of 'not kill'?. So rather than operating on propositions, O should be able to range over events and somehow the 'negation' of events. The easiest path I see here is to make O operate over stipulated events which either occur or do not occur, interpreting negation as nonoccurence of the event.

Edit: just to be particularly perverse, we might be able to imagine O as a mapping from events and non-occurrences to propositions; which are thus true or false. Ought-language and moral reasoning seems to be done with much the same moves as we would expect from logical discourse, even if the domain of O were not propositions.

1. A number in decimal notation can be written as d0+10d1+102d2+...d0+10d1+102d2+..., where d0,d1,d2,...d0,d1,d2,... are digits. — SophistiCat

I was playing about with modular arithmetic, mod 10 mod 100 etc, and I kept adding the remainders together. I completely forgot to write the number out in base 10 positional notation.

That's a really good hint as it also contains a strategy for other proofs about divisibility and digit sums (even in other bases). Beautifully tailored to the context, made my day, thanks. :grin:

I've not mentioned Marx, but usually Marx isn't far behind in these conversations about gender. It usually goes down as some argument that the existing power structure is wanting to maintain its control over its resources to subjugate the masses, all having been brought about by capitalist greed. Removing gender based pronouns is somehow the first step in pushing against the power structure. No longer will I be benefited by having a penis, and so I fight viciously to protect my power position. — Hanover

It depends who you're talking to, really. Marxist discourse can actually be pretty against what it sees as 'identity politics', though instead of complaining about liberals using it in a way that undermines civil liberties, they complain about liberals using it in a way that undermines the class identity of the proletariat.

Gender performativity and Marxism don't have to go hand in hand, there's no conceptual necessity between one and the other, it's just a statistical correlation of leftist ideals.

It doesn't help that 'postmodern Marxism' is a dead horse trope, I guess it's better to call it a zombie horse at this point.

Yep. And the lessened probability of being a Czech and a winner from the general population of ticket buyers would be P(W & C)=P(W)P(C) and P(C)<1.

The probability of a Czech person winning the lottery in the US is P(winning & being Czech), which is less likely because there are less Czechs than people in the total population of the US (and by assumption less in the lottery ticket purchasing group). But this doesn't mean you're less likely to win given that you've purchased a ticket, because P(winning given being Czech) is exactly the same as P(winning given not being Czech) - winning is independent of nationality.

You can visualise the first probability statement as randomly drawing people who purchase tickets from the total population - winners who are Czech are less likely.

You can visualise the second probability statement as stating your chances of winning given that you've purchased a ticket - which are the same as a non-Czech holding a ticket.

Is it not axiomatic that an even number added to another even number always gives an even number? — Tim3003

No. It is easy to prove though. Even numbers take the form 2k for some k (whole k). Take two even numbers 2n and 2m for any n and m. The sum is 2n+2m, which is 2(n+m), which is of the form 2k for k=n+m.

Thanks for the reference!

Eh, if you have a theory of history, if you make it constraining you'll be accused of being reductionist and unrealistic, if you make it loose you'll be accused of being unscientific. Marx is seen as having both sins for both reasons, depending upon the interpreter and sometimes the period of his writing. There are some predictions in his accounts though; like the tendency of the rate of profit to fall and the increased mechanisation that causes it. It's difficult to operationalise his theories - to take a concept and measure it with numbers -, but there have been lots of attempts to do so.

What do you think 'nature' means for Heidegger? What on earth is 'natural temporality'? Don't you think he wants it in scare quotes the way he puts 'reality' in scare quotes? That is to say, the notion of 'nature' as something that has any meaning or coherence outside of the structure of temporality seems to me to be something that Heidegger would argue against. — Joshs

There's actually a lot of capital N Nature in Being and Time. It's a name for a 'totality of entities' in a specific 'domain' - which tells us nothing of what Nature is for Heidegger, just that it is a certain domain of entities which may have a merely regional (rather than fundamental) ontology:

Being is always the Being of an entity. The totality of entities can, in
accordance with its various domains, become a field for laying bare
and delimiting certain definite areas of subject-matter. These areas, on
their part (for instance, history, Nature, space, life, Dasein, language,
and the like), can serve, as objects which corresponding scientific
investigations may take as their respective themes. Scientific research
accomplishes, roughly and naively, the demarcation and initial fixing of
the areas of subject-matter. The basic structures of any such area have
already been worked out after a fashion in our pre-scientific ways of
experiencing and interpreting that domain of Being in which the area of
subject-matter is itself confined. The * basic concepts' which thus arise
remain our proximal clues for disclosing this area concretely for the first
time. And although research may always lean towards this positive
approach, its real progress comes not so much from collecting results and
storing them away in 'manuals' as from inquiring into the ways in which
each particular area is basically constituted [Grundverfassungen] — an
inquiry to which we have been driven mostly by reacting against just
such an increase in information.

However, introduction 2 explicitly links the question of experiential temporality, and the 'clearing of the ground' he wants to achieve with his 'destruction of metaphysics', with the question of what it means to inhabit a world or nature in the broadest sense:

In other words, in our process of destruc
tion we find ourselves faced with the task of Interpreting the basis of the
ancient ontology in the light of the problematic of Temporality. When
this is done, it will be manifest that the ancient way of interpreting the
Being of entities is oriented towards the 'world' or 'Nature in the widest
sense, and that it is indeed in terms of 'time' that its understanding of
Being is obtained.

though there is also a connotation of Nature being thingly/must be understood as present-at-hand, as he contrasts beings of Nature to persons:

The person is not a Thing, not a substance, not an object. Here Scheler
is emphasizing what Husserl v suggests when he insists that the unity of
the person must have a Constitution essentially different from that
required for the unity of Things of Nature. 1 What Scheler says of the
person, he applies to acts as well: 'But an act is never also an object; for
it is essential to the Being of acts that they are Experienced only in their
performance itself and given in reflection. ' vl Acts are something non-
psychical. Essentially the person exists only in the performance of inten-
tional acts, and is therefore essentially not an object.

but he doesn't necessarily restrict the understanding of Nature to a present-at-hand understanding:

Even if it were feasible to give an ontological definition of "Being-in"
primarily in terms of a Being-in-the-world which knows, it would still be our
first task to show that knowing has the phenomenal character of a Being
which is in and towards the world. If one reflects upon this relationship of
Being, an entity called "Nature" is given proximallyas that which becomes
known. Knowing, as such, is not to be met in this entity. If knowing 'is* at
all, it belongs solely to those entities which know. But even in those entities,
human-Things, knowing is not present-at-hand.

In short - the story of Nature in B&T is fucking complicated.

To my mind the question of whether normativity is part of the essential constitution of Dasein for Heidegger of B&T is distinct from whether it's part of our essential constitution. There's an exegetical question, then there's a question of its truth (or of the strength of the account). They're also mostly separate questions from how to relate natural temporality to experiential temporality - with the qualification that nature still unfolds (also for Heidegger) even if there are no clocks or clock-time.

With regard to the time question, which is a nature question in disguise: just because there's experiential temporality doesn't mean there is no possible account of natural temporality. Heidegger's critique of present-at-hand/scientific time doesn't absolve the work of a responsibility to account for natural temporality - and struggling with this kind of question. with lingering doubts about framework of B&T inquiring from the wrong vantage point (questioning towards being as it is implicated in the existential structure of Dasein does not necessarily mean questioning towards being simpliciter), is definitely part of the turn.

With regard to the normativity question; perhaps Heidegger does think authentic modes of being are more important ontologically -'anxiety is an ontological mood' (paraphrased)-, but this is far from denying the importance of inauthentic modes of being to Dasein's essential constitution. Is it really more true to say of Dasein that it is anxious than that it is constantly being influenced by others? How could being-with work without normativity?

The thread's clearly supposed to be about Heidegger exegesis and criticism, specifically about the relationship of his account in Being and Time to nature. While there is a relationship to physics (which Josh provided uncommented quotes for and perpetuated the myth that the Heisenberg uncertainty principle has anything to do with uncertainty rooted in perspectival variation), the ontology of nature, and how scientific understanding constrains and enables metaphysical speculation, your discussion isn't really on any of these topics.

:clap:

I am therefore not in favor of our hoisting a dogmatic banner. Quite the reverse. We must try to help the dogmatists to clarify their ideas. In particular, communism is a dogmatic abstraction and by communism I do not refer to some imagined, possible communism, but to communism as it actually exists in the teachings of Cabet, Dezamy, and Weitling, etc. This communism is itself only a particular manifestation of the humanistic principle and is infected by its opposite, private property. The abolition of private property is therefore by no means identical with communism and communism has seen other socialist theories, such as those of Fourier and Proudhon, rising up in opposition to it, not fortuitously but necessarily, because it is only a
particular, one-sided realization of the principle of socialism...

Nothing prevents us, therefore, from lining our criticism with a criticism of politics, from taking sides in politics, i.e., from entering into real struggles and identifying ourselves with them. This does not mean that we shall confront the world with new doctrinaire principles and proclaim: Here is the truth, on your knees before it! It means that we shall develop for the world new principles from the existing principles of the world. We shall not say: Abandon your struggles, they are mere folly; let us provide you with true campaign-slogans. Instead, we shall simply show the world why it is struggling, and consciousness of this is a thing it must acquire whether it wishes or not. — Marx, from The Ruthless Criticism of All That Exists

Not sure I follow this. I don't see Heidegger allowing for a conditioning model of social shaping in his earlier work. — Joshs

Explicit analysis of social structure would be more similar to anthropology, which Heidegger takes care to distinguish the aims of his inquiry from. However, he does care a lot about sociality and how the experiential world is natively occupied by other people; being-with as an existentialia. He cares less about the (ontic) specifics of social organisation and more about what it is about humans that grounds (ontological) our capacity for social organisation. We're shaped by others in the account, through discourse and das-man, and this capacity to be shaped by others is a fundamental moving part in the account of Being and Time; distinguishing inauthentic expectation from authentic anticipation, distinguishing being-toward-death from fleeing into the-they/discourse, and partially constitutes fallen-ness in its linguistic/normative aspect.

"Ice cream is good"
"That doctor is good"
"That researcher is good"
"That teacher is good"
"That game is good"
"Pleasure is good"
"Knowledge is good"
"That example is good"

Ice cream does not share the virtues of a doctor or a researcher, but it might be good because it is usually found pleasurable to eat. A good game might be one with a set of rules that inspire engaging play, but it cannot have an analytical mind, pleasant bedside manner or be delicious. Any equivalence which invites us to ask "How do the rules of chess taste?" is a silly one.

When we take something quite abstract, like pleasure or knowledge, and say that it is good, it seems to express a commitment to the abstraction as being in some sense valuable. Knowledge might be something a society could be geared to produce, just like ice cream, but I believe we would only say a society is good because it produces ice cream flippantly, whereas if it values knowledge and knowledge's production we might say it is good in a deeper sense and with more commitment. We also do not behave as if our commitment to a thing is why that thing is good, as this equivocates a personal sentiment with being good; why that sentiment was held in the first place.

Which is not to say we also cannot use 'is good' to express mere approval or personal sentiment, we do frequently, I imagine it's probably the most common use of "is good" - its use in "that's good".

Analysing "is good" on its own terms removes all the contexts that give it its sense. Which is not to say that it can't be analysed or that good cannot be demarcated from its opposite, just that context is key and the boundaries of the application of "is good" are of necessity not sufficiently clear to facilitate an exhaustive definition.

Maybe if we asked "what makes a teacher good?" or "what makes an ice cream good?" we could have a more productive discussion, but unfortunately by supposition this would be off topic.

What I am confused about is whether, in raising this question, Heidegger is concerned with the fundamental nature of reality, or rather (merely) with the reality of the human experience/condition. That is to say, is Heidegger concerned with what reality is like, in the sense that a physicist can be said to be, or is he concerned with what it is like to be a human being, more in the sense that an existentialist can be said to be? — philosophy

A distinction I'd like to highlight is between experiential temporality and time. Heidegger's analysis in Being and Time links three fundamental aspects of human experience (which he calls existentialia): projection, thrown-ness and fallen-ness.

Projection: expectation/anticipation of what is to come; the temporal modality of the experiential future / futurity.

Thrown-ness: your life history insofar as it is relevant to your currently lived situation; the temporal modality of the experiential past / historicality.

Fallen-ness: the understanding of your currently lived situation: the temporal modality of the experiential present / presence.

These different components are always active; one's expectations are mediated through your understanding of the present and constrained by what you have lived until now. Their joint function is called ekstasis, which embeds every human in their lived experience by providing the contours for the past, present and future. The three modalities co-implicate, projection requires an understood past and an uncertain future, thrown-ness requires anticipated consequences from understood actions, fallen-ness requires understanding of what may be through what has already been; so the three are aspects of one unitary phenomenon, existential temporality or temporalising ekstasis. This temporality is more similar to the development of a narrative in a story rather than the unfolding of events over time as measured by a stop-watch.

The later Heidegger, after what's called the kehre or the turn, changes his emphasis from existential temporality to a notion of unfolding. His motivating questions are no longer asked from the perspective of a human; a methodology which the earlier Heidegger strongly adopts - he's trying to get at Being as what underlays Being-in-the-world, and stops at existential temporality in Division 2 of Being and Time; now the notion of unfolding places humans alongside the world, now the becoming of nature and the existential temporality of humans are seen as equally foundational questions for ontology.

This change in questioning style changes the fundamental topic of analysis from the human/Dasein to the event/ereignis, Being itself is given a more active interpretation - it arrests/appropriates humans to it. The shift in emphasis changes the subject of interpretation from a socially/culturally/experientially conditioned understanding of being distinct from nature to one where human being spans social/cultural/experiential structures and patterns extrinsic to human being which nevertheless can constrain us and our experiences - what was extrinsic can become embedded.

Why Heidegger makes the methodological decision to frame his analysis after the kehre in terms of poetry and somewhat mystical categorisations of nature and culture (earth/sky and mortals/divinities respectively), I don't have much of a clue. The reliance on the interpretation of art in his pursuit of these questions might be related to how he thinks technology occludes/transforms our essential relationship with nature, but I don't have enough knowledge to pursue the exegesis here further.

Sorry for not continuing with the exegesis, I've been busy IRL and sitting down to concentrate for the length of time required to understand what's going on in the next paragraph has been difficult. I have tomorrow off and intend to give it a try.

It's pretty sad that we have more love for fishing territory than third generation (AKA natives with not-white grandparents) Pakistani immigrants.

Tax Justice Network agrees.

You can't divide by zero. Dividing by zero is just shorthand for the limit of a/b where b tends to 0. Whether a/b tends to infinity when b tends to zero depends entirely on a and b. EG, if a = x^2 and b=x then a/b tends to x^2 / x = x tends to 0. Or a=2x^2, b=x^2 similarly produces 2.

Your reasoning's good, but the maths isn't there. Think you'd be able to prove P2 (and thus P3, which is just a restatement of P2) given that the link between the last digit in decimal notation of numbers and their even-ness is a consequence of the following:

any number can be written in the form 10*k+r, where r is the last digit in their decimal notation

?

Well I'm fucked.

Well, because there are sensible ways to think of subsets of sets as having 0 size, that does go against parts (subsets) of wholes (sets) necessarily not having 0 size. Really though the formulation is wrong, because there's not just one size concept which can be neatly applied to everything.

{1} has cardinality 1, but measure 0 in the real line. The size depends on the measure. See this vs this.

Ahhh....that’s what you meant before by involving sets or elements of sets. OK, fine. I can dig chopping off sets of zero size; that’s just an empty set. And by association, the totality of the divisible quantity is undiminished, which seems to sustain the OP. — Mww

The empty set has size 0, but so does any finite or countable set as a member of the real line. Even the rationals.

The OP stipulates a infinitely divisible quantity. Number lines do not exist in Nature, but one can be imagined a priori, consisting of an arbitrary, progressively conceivable set of real numbers (the numerical totality of the set cannot be imagined). Because it’s an abstraction, the guy chopping off numbers one at a time is itself an abstraction, but sustains the conclusion he is not chopping off parts of zero size, because the number line must be conceived as getting shorter — Mww

Being unable to shave off parts of zero size is precisely the limitation I spoke about. You can shave off sets of zero size easy, say {x in [0,1] except for 0.5}. I'd say that since it can be done mathematically, and in a consistent manner, it's certainly conceivable, and we shouldn't therefore privilege intuitions of discreteness in nature over intuitions of continuity - what holds where and to what degree is a matter for investigation; conceptual work and experiment.

The idea of chopping something into units requires a countable number of chops. You can half, quarter etc. The real line instead is an uncountable union of real numbers, so the analogy doesn't apply.

A part can have different sizes depending on its whole, assuming you allow this discussion to involve sets and elements of sets. EG, the number 1 has size 1 as a cardinal number, but it has size 0 as part of the real line. So long as we understand the sense of size which is currently operative there is no contradiction here.

First order logic is logic with quantification over variables. It's an expansion of propositional (or zeroth order) logic. It's been a while since I studied logic, but I can recommend the book 'Logic with Trees', it goes through propositional and first order logic thoroughly and includes some stuff on soundness/completeness/other things in meta-logic. Lots of exercises too.

They're the same thing, since propositional logic is complete and has the deduction theorem.

You just have to be careful with what those iffs work like. It's true in propositional logic that If P=>Q this yields P |- Q and P |=Q, but the 'this yields' isn't the same thing as material implication. Saying P |- Q (syntactic derivation) <=> P |= Q (semantic derivation) can be flat out wrong since the <=> biconditional is syntactic. When you're dealing with languages and metalanguages at the same time it pays to be careful with your symbols.

Propositional and first order predicate logic both have the deduction metatheorem. They also have the property of completeness, so that semantic entailment (truth tables or tableaux) and syntactic entailment (proofs in the logics using the inference rules) are equivalent.

For 1 maybe something like:

1. ~(PvQ)
2. Assume P.
3. PvQ (2, disjunction introduction)
4. ~P (1,2,3, contradiction).

Repeat for Q, though it might just give you the => implication. In case that's true, something like:

1: ~P and ~Q
2. Assume P v Q
3. Assume P
4. ~P from contradiction
5. Assume Q
6. ~Q from contradiction
7. ~(P v Q)

would probably work for the <=.

For 2.
1. ~P or ~Q
2. Assume P & Q
3. Assume P
4. ~Q (disjunctive syllogism, 3,1)
5. Assume Q
6. ~P (disjunctive syllogism, 4,1)
7. ~(P & Q) (2, contradiction)

Same qualifying remark for the reverse implication - this might not be a reversible proof.

I don't know if these strategies are actually valid in the logic you're working in, but perhaps they might inspire you to find a strategy which works.