Is a dog with three legs a bad dog? Is a triangle with two sides still a triangle or is it a defective triangle? Perhaps if we just expand the definition of triangle a bit we can have square triangles.
There is a point of view that holds that to define something we must say something definitive about it and that to say that we are expanding or changing a definition makes no sense if we don’t know what it is that is being changed.
It is of the essence or nature of a Euclidean triangle to be a closed plane figure with the straight sides, and anything with this essence must have a number of properties, such as having angles that add up to 180 degrees. These are objective facts that we discover rather than invent; certainly it is notoriously difficult to make the opposite opinion at all plausible. Nevertheless, there are obviously triangles that fail to live up to this definition. A triangle drawn hastily on the cracked plastic sheet of a moving bus might fail to be completely closed or to have perfectly straight sides, and thus its angles will add up to something other than 180 degrees. Even a triangle drawn slowly and carefully on paper with an art pen and a ruler will have subtle flaws. Still, the latter will far more closely approximate the essence of triangularity than the former will. It will accordingly be a better triangle than the former. Indeed, we would naturally describe the latter as a good triangle and the former as a bad one. This judgment would be completely objective; it would be silly to suggest that we were merely expressing a personal preference for straightness or for angles that add up to 180 degrees. The judgment simply follows from the objective facts about the nature of triangles. This example illustrates how an entity can count as an instance of a certain type of thing even if it fails perfectly to instantiate the essence of that type of thing; a badly drawn triangle is not a non-triangle, but rather a defective triangle. And it illustrates at the same time how there can be a completely objective, factual standard of goodness and badness, better and worse. To be sure, the standard in question in this example is not a moral standard. But from the A-T point of view, it illustrates a general notion of goodness of which moral goodness is a special case. And while it might be suggested that even this general standard of goodness will lack a foundation if one denies, as nominalists and other anti-realists do, the objectivity of geometry and mathematics in general, it is (as I have said) notoriously very difficult to defend such a denial.
– Edward Feser. Being, the Good, and the Guise of the Good
This raises a number of interesting questions, by no means limited to the following:
What is the fact/value distinction.
Whether values can be objective.
The relationship between objective goodness and moral goodness.
And of course, whether a three-legged dog is still a dog.
Meanwhile:
Actually, I don’t see that it raises any interesting questions.
That you cannot have a triangle with two sides, is just the way things are in formal systems. In ordinary life, it is usually not that precise. In a natural language, words get their meanings from the way that we use them rather than by an explicit definition.
If by “triangle” we were to mean the musical instrument, then maybe you can have a two sided triangle as long as is can be played and has good tone qualities.
Hmmm. Could Mung be implying (inferring, suggesting, begging, pleading) that marriage without a male and a female is like a two sided triangle?
Same sex marriage is here to stay. Get on with your life.
It is your position that you cannot have a triangle that does not meet the formal definition of a triangle. So in the real world there are no triangles because there are no actual triangles that meet the formal definition of a triangle.
Further, you say that in order to make your position acceptable we have to act as if it’s false.
And for the third leg of your argument, you assert that if it sounds like a triangle it is a triangle.
Well Neil, that’s a defective dog of an argument. I grant you that.
Where I live same sex marriage was already here before the SCOTUS decision and I didn’t put my life on hold when it happened. I don’t think I even noticed.
Why don’t you run along now and help your friend Adapa build his/her case that I have “a long and sordid history of anti-gay bigoted behavior at UD.” The two of you seem to be of like mind and the evidence should be massive.
In the real world there are no actual mathematical triangles. But there are triangles, because we do not restrict the use of “triangle” to the formal case.
Adapa, if I’ve ever been persecuted by a “gay” person I am unaware of it. I’ve also explicitly expressed my opinion that “gay” persons are no less deserving of equal protection under the law than any other person.
Meanwhile, you’ve offered no evidence to substantiate your claim:
I await your case.
As long as we stipulate our coordinate system ahead of time — for example, that we dealing with a Euclidean space — it is necessarily the case that the sum of the interior angles is equal to 180 degrees.
It is tempting to think of triangles as a kind of object. But this is, I’ve come to realize, a profound error, because of Descartes. Descartes showed us to transform geometry into algebra, which means that a triangle is defined by a set of algebraic equations. But algebraic equations are not objects — they are relations. The deep insight that Descartes had — overturning millennia of mathematics going back to Plato — is that mathematics is not about objects, but about relations.
In the 19th century, the great mathematics like Euler, Dedekind, Cantor, and Frege developed our contemporary understanding of what formal languages are, what they are for, and why they are so powerful. It has nothing to do with the properties of objects and everything to do with structures. By contrast. ancient Greek philosophers like Plato and Euclid thought that mathematical objects were like perceptual objects — only seen with the mind (more precisely, with the intellectual portion of the soul) rather than seen with the eyes. That’s a powerful metaphor for mathematical knowledge but it is not one that should hold us captive, when we have better philosophies of mathematics to guide and inspire us today.
By contrast, natural languages are fuzzy, vague, open-textured, and imprecise, and in natural languages, our concepts are generally speaking family-resemblance concepts (as Wittgenstein described), or radially structured with strong prototypes in their centers and weaker affiliations at the peripheries (as in prototype theory).
Thus it is as Neil said — there’s not much analogy here because of the important differences between natural languages and symbolic languages. They have different syntax, different semantics, and also different pragmatics — they are used for different purposes.
I have just some to realize much of this as a result of having started to read Macbeth’s Realizing Reason: A Narrative of Truth and Knowing. I’m going slowly and just started, so it will be a while before I know what I really think of it. Already I can tell it is a remarkable achievement, because it is neither more nor less than a completely Hegelian vindication of Frege. (Those of you who don’t know much technical philosophy might not appreciate what a stunning accomplishment that is.) Though I haven’t gotten very far, I believe this is the best book of philosophy published in 2014.
I hope to have finished reading it by the end of next week; I’ll know more then.
There are no actual triangles in the real world but there are actually triangles in the real wold. One hardly knows where to begin.
Where, exactly, do triangles exist, if not in the real world?
Neil:
Mung:
Mung,
That’s the kind of dickish misrepresentation that has earned you your dismal reputation online. If you don’t want to be regarded as a dick, then stop acting like one.
While that might be true, so what. It’s not about protection, it’s about rights. Do they deserve equal rights, the right to marry, the same tax breaks married couples currently get etc?
What’s really interesting is if you think that “gay” persons are condemned by the religion you follow as immoral. Are they? If so, do you agree? If not, why do you still follow that particular religion.
Mung, you are confusing the map with the territory again.
But quite apart from that: our brains are good classifiers. But Nature doesn’t always obvious joints for us to carve her at, and people will draw boundaries (e.g. colour boundaries) in different places, often in culturally determined ways. Also, people will use different properties for classification in different contexts, so something defined as a “box” in one context, may be included as a “chair” in another, or a “drum” in another. And it turns out that the way we classify objects, perceptually, turns out not to be in terms of “core” features that must be present in order for a candidate to meet our criteria for inclusion in a category, but rather a Bayesian process in which each of several properties raises the probability that we will classify an object in a particular way. So there may be no such thing as a “core chair feature” – no feature that all chairs must have in order to be classified as a chair – and yet, people will happily agree on which, of a series of candidate objects, are chairs and which are not.
Map-territory error. Very straightforward.
Here’s one for you mung, and it is absolutely true, involving map-territory confusion.
In the real world, there exists on every continuum, points such that:
A=B, B=C, and A<C
Same exact issue.
Doggedly dichotomous thinking appears to be something of a distinguishing characteristic among ID-supporters here. If you take a brush and remove its bristles one by one, at what point does it stop being a brush?
Chairs:
ACH!! BEWARE! The ALL-CONSUMING SORITIES! (The most powerful and deadly paradox of all.)
Not just dichotomous but ignoring the temporal dimension. Objects extend over space as well as time. A three legged dog was once a four legged dog and may yet be a two-legged dog, and a dead dog. It was also once a zygote, maybe.
And the idea of a “dynamic core” is, I would argue, key to a sensible understanding of consciousness. So without some kind of dynamic ontology, dualism is probably inevitable.
walto,
I am currently engaged in altering the Wikipedia article on ‘Sorites’ one letter at a time.
‘Species’ is an interesting category. Presented, as we are, with the modern results of an historic branching process (even YECs accept that it goes back some distance), we see their discreteness as essential, and the gulfs between unbridgable. But it ain’t necessarily so. You can go ‘the back way’, down through the temporal dimension and up the other side.
Well, now, you could get banned for saying that at Uncommon Descent!
Exactly. They are only discrete cross-sectionally, not longitudinally. That misunderstanding lies at the heart of the “edge of evolution” fallacy – that somehow evolution can’t produce “new species” as though there’s some discrete step that is necessary and beyond the capability of incremental change.
The idea of speciation as a process rather than species as a set of categories depends on being clear about whether you are talking longitudinally or cross-sectionally.
Also, not a million miles away, is the “anti-evolutionist” argument about nested hierarchies. It remains a striking fact about organisms (at least multicellular organisms) that their features have a nested distribution. Whether you agree with Darwin’s proposed mechanism, or even with his proposed explanation in terms of a family tree, it remains an explanandum. Ditto the intriguing violations of nesting at the genetic level, for which, again, an explanation had to be found.
It’s an example of Nature having remarkably clear joints. Even where you have superficially apparent violations (batwings; bird wings) closer inspection of the homologs reveals that inerrant nesting.
@KN
In the other thread you made a bunch of untrue assumptions about my metaphysical background, disputing and doubting what’s not there. A few key points here.
“As a result of [rejection of essential versus accidental properties], definitions of terms do not specify essential properties. Instead definitions are partial, context-dependent specifications of rules of use.”
Both approaches are legitimate. Neither of them can be discarded. A thing can be defined one way as a list of its properties so that it’s exhaustively described. Another way to define a thing is to state its relations, to say what it’s similar to, what it’s opposite to, and to what class it belongs. Cold can be defined as opposite to warm, i.e. it’s nothing in itself, it’s not a certain range of temperature, but a logical opposite or perception difference contrasted with warm.
“This is why meanings can shift over time — because there is nothing over and above the linguistic norms at a particular stage in the history of a discursive community to tie them to anything.”
True. Basically, meanings shift because things change and ultimately there’s nothing that remains the same. However, there’s a further point that I have been making throughout – there’s a logic to this change. Things don’t change haphazardly and not without further consequences. When one thing changes, it inevitably changes other things that are in direct connection with it. You may want a particular change in something, but if you ignore its connection to another thing that you don’t want changed, you will end up with an undesirable result. Change, while being inevitable, can be either good or bad, and there are choices to be made in the process. We can make it more painful by failing to understand the process and making the wrong choices.
“(In philosophical terms, I’m suspicious that there are natural kinds specifiable independent of any inquiry.)”
This is the key difference between Aristotelianism and (Neo-)Platonism as far as I know. Aristotelians talk about things like “the form(al cause) of the dog” as if they were immutable reality. On Thomism, creation exists as a reflection of “exemplar causes” (a type of formal causes) imprinted in God (or imprinted by God in the fabric of the universe). The “exemplar causes” are basically natural kinds.
On Platonism (particularly Neo-), instead of natural kinds there are divisions in the (single omnipresent) substance and the divisions have a relative stability. By “relative stability” I mean the distinctions of so-called natural kinds are stable vis-a-vis each other, i.e. a cat is different from a dog, and the cat is a cat and the dog is a dog not just because each of them is what it is, but also because each of them is different from the other the way it is. From this follows that when one of the “kinds” or “forms” is gone, e.g. the species of cats vanish, then the species of dogs and others capable of doing what cats used to do, they take over the void left behind by cats in the local ecosystem. As far as I know, Aristotelianism (and consequently Thomism) rejects this relative interdependence and adaptability.
All this out of the way, it should be evident where my arguments against same-sex marriage came from. Marriage is directly connected to family. Marriage is the cultural institution that signals “family is the nucleus of civilization”. When marriage is redefined, then the status of family is directly affected. The disregard for family is clearly seen from how same-sex marriage advocates “define” family – they see no problem in declaring that family is perfectly fine without a father or a mother or a child. But when mother, father and child are irrelevant to family, then what is relevant? Clearly, they don’t care.
Yet there is also similarity – they are both languages, usable and used for describing reality (everything that is thought relevant). Where (culturally) given distinctions of (natural) languages fail, formal analytical distinctions can be devised on the spot from the material of the same language. This is on plain display when you read e.g. Aristotle, a/the father of formal logic, who conjured up things like “horseness”.
Yes. But not, I think, much different from the branching of trees in that respect. And most people, including creationists, don’t see tree growth as particularly problematic.
I never thought it particularly paradoxical. I treated it as a source of amusement.
Good one (and good example of sorites as a source of amusement).
for what? ANyway, I haven’t looked much at uncommon descent since dave scot left.
Your third does not follow from your first two, which are in any case arbitrary choices. You could just as easily write: “Marriage is directly connected to the pair bond. Marriage is the cultural institution that recognises the life-long nature of the pair bond”.
And neither your version nor mine leads to the the third, because a family can consist of many many configurations, and many of us belong to more than one, and which members of it are married to each other can change over time.
Take a look at these, by my friend (and former teacher and colleague), Steve Schwartz:
http://philpapers.org/rec/SCHWII-3
http://philpapers.org/rec/SCHVAI
http://philpapers.org/rec/SCHIAS-2
Don’t worry about it. But I do think that an ID antipathy towards any kind of logic other than binary classical logic is part of the reason why ID arguments so often run into sand.
To be fair, map-territory errors are common in everyone. I think it’s a matter of convenience. 🙂
Edit: But that a=b, b=c, a<c bit throws most people. Explaining it can be fun sometimes.
Well, go on then.
:colbert: Is this one of those times?
Take a ruler, look at it. There is a point at which you can’t distinguish a from b or b from c but can still distinguish a from c.
Poincare’ said it far more eloquently but I figured I’d give you the quick and dirty version.
Edit: It can be fun when I purposefully introduce map-territory confusion at the onset. In this case, that would have been tough since it was the subject of my post.
Which is as arbitrary as it gets. It has been clear quite a while that you think absolutely any “configuration” can be declared family according to the method of Humpty Dumpty. Which only proves my point: You don’t care about family, you don’t care what family is, and you don’t care whether it is.
P.S. It’s doubtful you even care about “pair bond”. After all, can’t it consist of “many many configurations”?
For the first and third, I could only see the titles. For the second, there was at least an abstract.
What little I could see does not suggest anything particularly interesting.
Reality cannot be paradoxical. So if it looks paradoxical, there is something wrong with the way that you are looking at it.
Erik because a word can mean many things doesn’t mean it can mean anything.
I know English is not your first language, but you seem familar with it enough to understand that many people belong to several families? And that a family does not cease to be a family when one or both families die?
As I may have mentioned, my father, a widower, died a couple of months ago. I have three siblings. We still regard ourselves as part our shared family-of-origin, despite that fact that for 18 years we only had one living parent, and now have none. Also, each of us has family “of our own”. We regard each other’s families as part of our “extended family” – but on the other hand, I doubt my sister regards my Australian in-laws, or my son’s Australian cousins as part of hers.
And we regard brother, who has no children, as nonetheless having a family, i.e. him and his wife, and his wife’s extended family.
Had my husband and I adopted children, which looked likely at one point, they too would have become part of several of these families.
And we also regard my cousin as part of my family, as well as his half-brother, who, as it turns out, is no blood relative, being the son of my cousin’s mother’s second marriage.
None of this makes the word “family” assigned according to “the method of Humpty Dumpty”.
And having some of the marriages involved in all this marriages between two members of the same sex affect the “status” of any of those families. If my cousin’s brother, who is gay, marries his partner, I hope we will be invited to the wedding – and if so, we will go as family members.
Well, not all that many, given approximately two genders, and the fact that “pair” means “two”.
I make basically three combos. You?
Do you have access to JSTOR?
Are you referring there to Hume’s point about indistinguishability, or are you maybe making a statement about simultaneity?
Yes, I am referring to Hume’s point about indistinguishability. Although i am using a bit from Poincare.
Edit: Actually, it works the same for simultaneity I think,, assuming a single reference frame.
Thanks. Dunno about simultaneity, but I think that putting Hume’s point as
A=B, B=C, and A < C
could itself be called a map/territory error. That is, A isn’t really equal to B or B to C: it’s just that they seem like they are because they can’t be told apart. Simultaneity is a bit different, I think.
Well, it’s really Poincare’s point about the way we intuit the mathematical continuum.
I’m not really sure. I used to via a campus library computer. But I am now fully retired so that’s less certain.
Thank you for the brief description of the difference between Aristotelianism and Neoplatonism.
When Aristotle thinks about “horseness” — the morphe of horse that explains why there are perceptible horses, where new particular horses come from, and why they have the properties that they have — he does so in analogy with perceptible objects. Just as we see perceptible primary substances with the eyes, we “see” forms with the soul. On the hylomorphic account of perception, to perceive something is for the Form of that thing to enter into the intellect through the senses. (When I see a frog as a frog, it is because frogness has entered into my intellect through my senses.)
In Aristotle’s time, this was unquestionably the best theory anyone had about how conceptually structured perception operates. The problem is that it relies on a whole host of assumptions that simply don’t make sense in light of the past three or so centuries of empirical scientific research. We know a lot of stuff about how brains do things like process visual stimulation, and we also know a lot of stuff from empirical psychology about how concepts are structured. We also know a lot of stuff about how formal languages are organized, and what makes them different from natural languages, which is why we can conceive of and build computers.
The distinction between formal and natural languages that we rely on every second of our waking lives — given how pervasive computers are in First World cultures! — would have been unthinkable to Aristotle (or to Plato, for that matter), because it only begins to come into view with Frege’s invention of formal syntax, and without Frege, we couldn’t have had Turning and von Neumann.
You are probably right about Turing, but perhaps not about von Neumann. I see von Neumann’s work on computers as coming from the needs of scientific and engineering computation, particularly large matrix computations, rather than from Frege’s work.
You might be right about that. At some point in my life I will need to learn something about the history of computing.
Still, my basic point was this: natural languages and formal languages carry out very different functions. The function of a natural language is to facilitate successful coping in cooperative contexts. The function of a formal language is — if Macbeth is right! — to model the basic structure of reality. (She doesn’t mention Every Thing Must Go but the two accounts mesh perfectly well together.)
In some sense, we have a “pair bond” with each and every FB friend. Two is the core, but there’s no upper limit.
As to family, there’s also no upper limit, so in this sense yes, there are “many many configurations” of families. Therefore the actual definition of family lies in its core, in its irreducible heart. You have not managed to define it. “Many many configurations” evades the point.
http://users.rcn.com/rathbone/lw65-69c.htm
Well, you seem to have totally evaded mine. How do same gender marriages affect the status of any family?
At this point I have a dismal track record of understanding Erik’s arguments, but let’s see how well I do.
(1) Marriage is legal recognition of the biological conditions for being a family;
(2) The essence of being a family is biological reproduction;
(3) Only heterosexual couples can reproduce biologically;
(4) Hence, only heterosexual couples can themselves be a family;
(5) Hence, only heterosexual couples need the legal recognition of marriage;
(6) Hence, same-sex marriage requires denying either (1) or (2).
How’s that, Erik? Did I get your view right this time?
I think you are grossly underestimating Aristotle and Plato. The “horseness” that I mentioned was not ordinary Greek, but neologism devised by Aristotle to explicate a metaphysical point. And he’s the father of formal logic, so he was clearly well aware of the value of meticulous organisation of the elements in language.
Even more aware of the distinction of ordinary and formally organised language were Indian linguists. Panini grammar employs a a thoroughly analytical approach and is composed as a list of terse rules, each derived from the former and logically ordered accordingly, so that when you remove (or forget – this work was to be learned by heart by students, same as everything important in Sanskrit) one of them, you cannot continue with the rest – the entirety falls apart like a pack of cards. These people definitely knew very well the power of formal rigour.
(4) needs no “hence”. It’s such a self-evident biological fact that reproduction of humans occurs heterosexually that it should have no need for any premises of its own. It’s more like,
(1) Heterosexual reproduction (husband and wife) forms the basis of family (parents and children).
(2) Families provide to society the continuity of its population.
(3) If society values its own continuity, it protects families as its basic reproductive unit.
(4) Marriage is one of the symbols of such protection (i.e. given the premises, it’s a good idea to celebrate the union of husband and wife)
Same-sex couples are not husband and wife. Simple enough?
Well, in fact it just takes some work on the database schema.
http://qntm.org/gay
It’s an interesting read.
I suspect from now on database designers who think in terms of decades will be building in all sorts of flexibility….
(1) Heterosexual reproduction (husband and wife) forms the basis of family (parents and children).”
What about a heterosexual couple who adopt? Do they not also form the basis if family? If so, then why can’t same sex couples who adopt firm the basis of family?
“(2) Families provide to society the continuity of its population.”
No, unprotected sex does. Biology 101.
“(3) If society values its own continuity, it protects families as its basic reproductive unit.”
And it does. Opposite sex families and same sex families.
“(4) Marriage is one of the symbols of such protection (i.e. given the premises, it’s a good idea to celebrate the union of husband and wife)”
And it is a good idea to celebrate the union of husband and husband, and of wife and wife.
“Same-sex couples are not husband and wife. Simple enough?”
But they can be spouses.
An open mind is a wonderful thing. I highly recommend it.