The methods of modern research involves dissecting and focusing in on finer and finer details. We would be forever blind to these finer details if it weren’t for instruments such as the microscope and the telescope. These tools allow specialists to focus in on the parts and gain a tremendous amount of knowledge in narrow fields.
But if researchers don’t look beyond these isolated islands of existence they will settle for a fragmented view of reality. And this causes problems for building theories about development and evolution of life. Researchers begin by looking at the parts to try to understand how they “build” bodies. Viewing things from this perspective it was expected that humans would have many more genes than turned out to be the case.. This is the type of error produced by this way of thinking Initially they did not understand the way in which the organism used its genes because they approached it from the wrong direction. Genes are in reality never isolated from the context of networks, cells and organisms.
Jaap van der Wal argues that we have become accustomed to thinking the human organism is made by a process of cells multiplication. But there is another more realistic way of thinking about it. From conception to adulthood a human being has always been a complete organism with a form and function suited to its environment. A machine is assembled from parts and it can only function as intended when all the parts are in place. Organisms are not like this. Where the organism is concerned the cell or cells of which it is composed serve the whole organism throughout its existence. It is not gradually built from parts. Machines are always built from the parts to the whole but organisms are never anything but complete wholes.
It is time to start paying more attention to how the whole determines the parts within it and luckily this view is becoming more prevalent.
I trust your silence on TSZ in general and in particular on the issues of concepts and empiricism in this thread indicates that work on the book is going well. Or at least that your are dedicated to making it so.
I don’t know what “ideal triangle” is supposed to mean, but it’s not the concept of a triangle. The concept of a triangle has nothing to do with whatever mental images one can construct — if concepts were mental images, then people with aphantasia would lack conceptual understanding.
Moreover, mental images as psychological entities are just as private as sensations. I cannot know what someone else is imagining anymore than I can know what they are sensing. But what we want in our theory of concepts is an account of the public nature of normative standards that make any particular use correct or incorrect.
Once Platonic self-exemplifying idea or eidoi are transposed into the mind, they cannot function as objective standards. This is one of the big lessons to be gleaned from the trajectory of early modern philosophy that runs from Descartes through Locke and Berkeley to Hume.
This is why Kant abandons the pictures-in-the-head theory of concepts in favor of concepts as rules.
What later philosophers realized is that concepts as rules are constituted by their place within an inferential system. Triangularity has nothing at all with what one can or cannot imagine; it is entirely about the rules of a geometric system. A geometric system, whether Euclidean or non-Euclidean, will contain the rules (axioms, premises, definitions) necessary and sufficient for articulating the concept “triangularity”.
The question is, are the rules that constitute mathematical and empirical concepts themselves arbitrary? Are they grounded in social conventions?
No doubt some are — the concept of “coffee” would make no sense without the background practices that involve using the roasted dried berries of Coffea plants to produce a beverage — and that concept in turn is not separable from biological and chemical facts about the molecules that the plant contains and how those molecules affect human metabolism.
There’s a nice question about how to think through the differences between animal habits and human linguistic rules within a broadly inferential framework. I think that Sellars was basically on the right track he proposed that the key to this problem lies in cybernetics.
That depends on what you mean by “arbitrary”.
If “arbitrary” means random, then no they are not arbitrary in that sense. But if arbitrary just means that they could have been different — that different choices could have been made — then, yes, they are arbitrary.
Are they grounded in social conventions? Again, that depends on what you mean. I’m more inclined to say that they are grounded in social practices, but those practices could be said to be conventional. Some people think of conventions as propositional, but it would be better to see them as behavioral.
Arithmetic can be said to be grounded in the Peano axioms. And, in turn, those axioms can be taken to be propositional conventions. But it would be better to say that arithmetic is grounded in our conventional counting behavior. And, given that conventional counting behavior, there were some arbitrary choices made in coming up with a suitable set of axioms.
There’s a difference between mere contingency, as contrast with necessity — “could have been different” — and arbitrary in the sense of “could have been different as a result of different choices” . Cultural and linguistic variations are contingent, but not it is not as if some blokes decided to invent grammar on a lark.
This post raises interesting issues. I think it is helpful to separate some of them:
1. Concepts in the context of individual minds, eg concepts as mental representations (not necessarily images) or concepts as behavioural dispositions. This is an empirical question for psychology.
2. Concepts in the context of cultures: to what extent do cultures share a common standard? How are individuals judged and shaped to conform to any standard? How do such standards get established and evolve? These are questions for sociology and anthropology.
3. How do individual psychological concepts become aligned to a cultural standard for individuals participating in a culture within a community. This is is scientific issue crossing the domains of psychology and sociology/anthropology.
4. Do concepts, both in the psychological and the culture senses, require language? Ca we have psychological concepts in non-human animals? Can we have culture in non-human animals? Can culture shape the development concepts of non-human animals? These are question for the sciences of animal behavior and cognition.
I see 1-4 as scientific questions. So, associated with each will be the standard philosophy of science issues.
But the deepest and most difficult philosophical issue is to understand the nature of norms, that is of the standards referenced in 2, 3, 4. Norms do not seem to have simple causal descriptions. As norms are currently understood, they cannot be analysed by science alone.
Science requires more conceptual clarity to proceed effectively. Philosophical thinking by scientists and philosophers is needed.
Can we find a naturalistic, philosophical analysis of norms? Can that serve as the basis for further scientific investigation?
Of course you are right that CharlieM is confused about the difference between a concept versus what is being conceived of, eg the psychological concept of a triangle, which commonly which be seen as concrete (eg supervening on the brain/body), versus a triangle as an abstract object.
I’ve just reached the part of L&R where they try to dissolve the issue by making the case that it is wrong to separate abstract and concrete; both are both RPs in the sense of structure or information or something like that. That’s the best I understand them for now.
I am interested to see how you develop this idea.
Is it intended to be a historical analysis of the context of Sellars’s use of cybernetics in his thinking? Or are you taking the modern concepts of cybernetics and systems thinking and applying them to the problem of naturalizing norms? Or something else?
Do you want the answer given by classical physics or the answer given by quantum mechanics?
The composition of the observed world is dependent who or what is doing the observing.
I don’t think that anyone here can claim to have a complete, unambiguous concept of matter. But I do think that there are many here who can have a complete concept of a triangle. Its simplicity is what makes it such a good candidate for discussion.
We start from facts and take it from there. Thinking has taken you to the point where you associate thinking with the physical brain, but you cannot be sure of the connection. You may believe that thinking can only be a product of the physical brain but you are waiting for some sort of confirmation.
Thinking has brought you to a point of doubt. But you cannot doubt thinking itself.
Do you doubt that a triangle is a two-dimensional bounded figure with three straight edges and three vertices?
I do not speak German but I can agree that to the average German the concept dreieck will agree with my concept triangle. They are different words but they signify the same thing. And regarding physical triangles they are all different but they signify the same thing. You cannot say that the concept triangle signifies a physical triangle because the concept encompasses more than is contained in any physical triangle.
The concept triangle is not restricted to time and space so to ask where it exists is meaningless. All measurements are relative, the concept triangle is absolute.
What qualifies as non human? Suppose a bird is required to insert tokens of the correct shape and color into slots, and suppose the bird has no trouble learning to do this.
Does the bird have concepts of shape and color? Mental representations?
You are right the concept cannot be a mental image. As you say mental images are individual and private.
Why can’t the ideal triangle and the concept triangle be one and the same? Can you tell me what you think the difference is between my concept triangle and your concept or anyone else’s concept?
Classical physics please, since your average billard rack is larger than atomic scale.
Heehee, what is so complicated about matter? It’s literally just stuff. And of course we don’t exactly have a complete, unambiguous concept of “thinking” either.
Why do you fear doubt? It’s much better than false certainty.
Anyway, I thought thinking must be about something. We begin by thinking about what is given through our senses, the observed world. Hence, there can be no “thinking” in isolation, so no reason to grant it any primacy over physical stuff.
Let me take a shot at that but using a different example.
Can the concept of Pegasus exist even though Pegasus does not? I think yes. Obviously so in fact.
Does the fact that someone has the concept of Pegasus mean that Pegasus exists? I think not. Again, this seems obvious.
Can two people differ on their what they think the concept of Pegasus refers to? I think yes. For example, one person may never have encountered the word. Or another may think it is part of Roman mythology instead of Greek.
If you disagree with my answers to the above three questions, why do you?
If you agree with my answers, why do you think the situation is different for abstract (“ideal”) triangles?
Does your concept of triangles include non-Euclidean triangles. Some people’s do and some don’t.
Primarily the former — a historical explanation of how Sellars himself tried to use cybernetics to naturalize normativity, an analysis of how successful he was in doing so, and then use that to motivate an account of how contemporary cognitive science and neuroscience advance upon the Sellarsian framework.
It’s certainly true that “Dreieck” and “triangle” mean the same thing, but we need to be really careful about “what meaning the same thing” means.
Here’s one view: to say that “Dreieck” and “triangle” mean the same thing is to only, and no more than, that the words have the same functions in their respective languages: the function of “Dreieck” in German is the same as the function of “triangle” in English. The sameness of function is determined by syntactical and semantic roles. No “abstract objects” required.
Yes — and once we have a distinction between Euclidean triangles and non-Euclidean triangles, we have to move the concept “triangle” up a level, so to speak — a genus that includes various species.
The concepts that I am interested in are not representations of anything physical although the concept triangle and an actual physical triangle belong together in the same way that a dog belongs with the concept canine. And no concept is isolated. Concepts are linked together in all sorts of ways.
We all have an understanding of concepts like “culture” and “standard” but because we all have incomplete knowledge our concepts will be incomplete too. This is where things become individual. How the concepts we hold align with reality depends on us as individuals and we often argue about these things. What can you argue about with the concept triangle?.
The concepts that humans share and can agree upon are very limited even with the availability of language, so I think that an understanding of concepts is beyond non-human animals. Many animals can certainly recognise and distinguish objects but that is a long way from understanding the concepts.
If all life were to be wiped off the earth would many river deltas still have a typical triangular shape? What is it about this shape that is dependent on human norms and conventions?
Can you clarify for me what you see as the difference between the concept triangle and the ideal triangle?
Having mental representations is not the same thing as understanding concepts as I am using the term.
I have driven a very routine route many, many times with very little awareness of the actions I undertook during the journey. Repeating learned activities, with variety in response to specific conditions, is no guarantee of being aware of those tasks.
If the concept of triangle and “the ideal triangle” were the same thing, it would be contradictory to talk about a triangle that isn’t “ideal.”
I did already, by the example of Pegasus. It shows the difference between concepts, what they refer to, and how people can differ on that.
The same argument applies to concepts of abstract triangles versus abstract triangles themselves.
We definitely can argue about the nature of the concept of triangles. We are right now.
You can claim I am wrong. But until you address the nature of the argument I made with the Pegasus example, you will not convince me.
Maybe you are claiming that no two people can differ on the essentials of what a correct concept of an abstract triangle would refer to (regardless of whether abstract triangles exist). But even with that approach, the issue is not simple.
The context for correctness matters. When is the disagreement taking place? Before or after the invention (discovery?) of non-Euclidean geometries?
But even assuming the time is now, context still matters. Are we taking about correctness for high school students? For sophomores majoring in physics? For post-grad mathematicians?
I’ll respond to any posts you may which engage my arguments. If you are not sure you understand my points, try paraphrasing in your own words.
The observed world consists of matter which takes the form of solid, liqiud and gas with various transitional states. The general triangular form of your average billiard rack is but one aspect of it. There is much more knowledge that could be gathered about it. We get a very incomplete picture of the world by observation alone.
And of course we all know stuff 🙂
The concept thinking is unique in that it is the same as the activity directed upon it.
Why do you fear doubt? It’s much better than false certainty.
I don’t fear doubt. If it wasn’t for doubt we would have o further questions to ask. And there’s a lot of enjoyment to be had in looking for the answer to questions.
There are many mathematical problems which we can think about without invoking anything physical.
It is through thinking that we are able to make distinctions between physical stuff and abstract stuff. We don’t think because we have a brain. We know we have a brain because we can think.
The concept of a triangle does not depend on the existence of the ideal non-physical triangle any more than the concept of a dog depends on the existence of the ideal non-physical dog.
It is not at all clear what you are agreeing about. From my way of looking at it, concepts are private and we have no ability to compare our concepts with those of other people. At most, we can compare the way we use concepts with the ways that other folk use concepts.
I see them as philosophical questions.
Yes, they have a superficial appearance of being scientific questions. But they are not questions that science can solve. So they could only be philosophical questions.
The basic point, here, is that science is systematic. If humans were a race of identical robots, then there could be a systematic account. But we are all different, so no systematic account is possible.
There are, however, some underlying principles. And those could be examined. But that would be mostly philosophy rather than science.
Huh.
I think most neuroscientists, psychologists, and sociologists would disagree with that claim. Maybe not so many anthropologists proportionally , but many would.
ETA: What do you think about KN’s above claim (as I understand him) that with the advent of non-Euclidean geometries, the meaning of ‘triangle’ “moves up a level”, to capture something common to triangles across axiom systems (I think that is what he means).
For mathematicians, is there an overarching, mathematical concept of triangleness that captures something common to all the relevant axiom systems.
I could see a common language concept, like three-sided polygon. But does that work in mathematics?
I realize I am using ‘concept’ and ‘meaning’ loosely in the above. I hope that my point is still clear despite that.
Yes, there are. But while they may see themselves as working on your questions, they are not making serious progress in solving those questions.
How can something exist but not be restricted to time and space? Sounds like a big old oxymoron to me. Do you have any evidence for this? Do you have any clue as to how one might obtain such evidence? As a self-confessed empiricist surely you must have thought about this?
I think you are just making this up, as we all make up stuff from time to time. How can you demonstrate to us that you are not?
This is not hard – your concept triangle consists of thoughts in your brain, and his concept triangle consists of thoughts in his brain.
The shape would be the same as it is now, but there wouldn’t be anyone around to consider it ‘triangular’. The concept of triangles was wiped off the earth when the humans went.
Charlie,
Haven’t we had this conversation before, but about the “ideal tetrahedron” instead of the “ideal triangle”?
There are, of course, ideal multidimensional figures — four, five, six or more dimensions.
It’s rather easy to deal with mathematically, but difficult to visualize.
Does manipulating such objects qualify as conceptualizing them?
Sure, and matter is unique because you can make billiard racks out of it. Many things are unique in some sense, but why is the one more important than the other?
100% agreed.That’s why “you cannot doubt thinking itself” sounds like an utterly boring stopper.
That contradicts your previous statement that we need “what is given through our senses, the observed world”, to have something to think about. In addition, consider that we once had a world without any conscious beings in it, but I don’t think we have proof of an episode where the universe was filled with disembodied minds thinking through math problems.
Ah good, you have overcome your doubt that you actually have a physical brain. My thinking tells me your statements above are not mutually exclusive. Agree?
Is it breaking the forum’s rules to ask someone in all seriousness whether their posts are intended as some kind of conceptual art trolling?
IMO, by taking a different example you are avoiding my questions.
Yes it can exist even if there is no such animal. But we need to go further and explain exactly what the concept of Pegasus consists of.
Yes Pegasus exists, but in what form? I arrived at the concept Pegasus through thinking. I know that Pegasus exists as mental pictures in the minds of those who have knowledge of Greek mythology and images of it have been portrayed by artists. I too can form a mental picture of Pegasus and have seen it portrayed.
In order for me to have an accurate concept of Pegasus I need to first have the concepts, horse and wings both of which are physically real. And I need to add to this the concept of mythical beasts in order to understand exactly what Pegasus is. It doesn’t exist as an actual animal as far as I’m aware but it does exist as a mental construct.
Yes. We need to combine several concepts in the right way in order to have an accurate idea of what Pegasus is. Here I am using “idea” to mean what we have in our minds once we arrange a number of concepts that we have gained previously.
If you disagree with my answers to the above three questions, why do you?
I disagree that Pegasus does not exist. There may not be such a physical animal as Pegasus but it does exist as a mental construct. And the ancient story tellers had their reasons for constructing it.
I don’t see the concept triangle and abstract triangle as the same thing. The concept triangle is intimately connected with actual physical representations of the triangle. The concept contains the laws of the triangle. As abstract triangle are mental pictures the concept triangle is intimately connected with them in the same way that it is connected to physical triangles.
I’ve rushed this reply more than I would have liked but I’m pushed for time and don’t want to delay it any longer.
I believe it is a shared concept of a triangle which is understood as being bounded within a two-dimensional flat plane which is the form at its simplest. Any non-Euclidean triangles will have further concepts to consider.
So can you tell me what you think the difference is between your concept of triangles in Euclidean space and my concept of it?
Sure. My concept supervenes on my brain/body and yours supervenes on your brain/body.
To help explain that, I think (as per SEP), concepts are the building blocks of thought. and thoughts are processes that supervene on brain/body. The nature of those processes and the roles of concepts in them are topics for the cognitive sciences.
To be more expansive: I think one has to separate things that as best I can tell your posts do not clearly separate.
Issue 1: Need to separate (1) the concept, (2) the content (or reference) of the concept, and (3) whether or not that content exists in some sense. Example: concepts of abstract triangles, abstract triangles as the content of those concepts, and abstract triangles as entities which may or may not exist in some sense.
Issue 2: Need to separate (1) abstract entities from (2) concrete entities. So we have abstract triangles and particular instances of triangles in regions of spacetime, such as the shape of a river.
Issue 3: Need to understand the difference between concepts and accurate concepts. Adding the adjective ‘accurate’ could imply many things, but I understand your posts as saying that a concept of a triangle (whether abstract or concrete) is accurate if it aligns with the majority view of triangles as meeting the Euclidean axioms. I’ll just take that as a stipulation if you want, but remember that it is not what knowledge-area experts (ie mathematicians) would say. I suspect they would say accurate only applies once an axiom system is selected. I am not sure if they would accept any overarching standard of accuracy as I think KN does.
Issue 4: The issue of the existence of abstract math entities is an open one. Many physicalists think abstract math entities do not exist in any sense, but there are also several physicalist arguments that support their existence. In any event, merely being able to have concepts with the content of abstract triangles says nothing about whether the content of those concepts, ie abstract triangles, exists.
Based on my above post, I will say tha there is no difference in the content of two people’s accurate concepts of abstract triangles, using your stipulated version of accuracy.
If I was being extra careful, I might need to be explicit and say that content implies extension (ie the list of elements in the set of triangles). It is possible for different people to know different theorems in Euclidean geometry so that they have different ways of defining that set of triangles. Some might say that the content of their concepts hence differs. I have not thought that issue through, but I am mentioning in in the interests of ass-covering (specifically, mine).
BruceS,
That’s certainly helpful.
I think that a good deal of trouble arises (not least of which for myself) by confusing language-dependent and language-independent concepts. (I am not happy with that distinction but it will do for now.)
It seems mostly clear to me that my cat have something like a concept of their food bowls; they can always walk over to them whenever they feel hungry, they meow when near their bowls which indicates their implicit grasp of the correlation of being at the bowls and eating, etc. And while this behavior could be explained by conditioning, my guess is that they do have cognitive maps of the apartment — they just don’t do very much with those maps because the apartment is small and the environment is highly ordered and predictable.
If Carruthers and Camp are right about non-human animals like birds and bees, I’m pretty sure that cats have concepts too — or at least wild cats.
Now, someone of a Thomistic or Cartesian disposition might want to say that while birds and cats have concepts of concrete particulars, they cannot have concepts of abstract universals. (We can treat concrete particular/abstract universal as a single distinction, though it is two distinctions — abstract/concrete and universal/particular.) To have concepts of abstract universals, e.g. triangularity, requires cognitive abilities that non-human animals lack and which are taken, in some quarters, as evidence of a transcendence of biology.
However, if one eschews any such transcendence of biology, and doesn’t wish to inflate the ontology with “abstract entities” such as triangularity and justice, then one needs a different way of understanding the difference between what non-human minds can do and what human minds can do. This leads us back to the question, what difference does language make, and how?
One thing we definitely need to be careful about is striking the right balance between (1) assuming that non-linguistic concepts must have all of the semantic features that we think linguistic concepts have, such as a distinction between sense and reference, a compositional role in judgment, etc. and (2) assuming that non-linguistic concepts cannot have any of the semantic features that we think linguistic concepts have, such as playing a role in material inference.
One specific point:
I’m not quite sure what you had in mind here, but I don’t think that axiomatic systems can, all by themselves, represent the environment. I think of them as cultural tools that facilitate improved collective representing. But taken by themselves, decoupled from any relation to perception and action, axiomatic systems don’t represent anything; they are just self-contained formal inferential systems.
While a Thomist or Cartesian might say that, they would surely be mistaken. Particulars are harder than universals.
To a first approximation, a universal is a category. And a particular is a small category.
Consider your cat, and it’s food bowl:
(1) the food bowl viewed from the north;
(2) the food bowl viewed from the east;
(3) the food bowl seen by natural light at daytime with light coming through the windows;
(4) the food bowl seen by artificial light (as at night);
(5) the food bowl when empty;
(6) the food bowl when full.
We could, of course, mix and match, to get a larger list.
The pattern of light received will be different in all of those cases. Unless your cat is using something beyond vision, the “particular” can only be a category.
This gets back to J.J. Gibson’s view, that perception works by tuning into invariants. In this case, the invariants would have to be properties that are the same for all 6 of the listed examples. It seems to me that such invariants are unavoidably abstract. The cat might not consciously think about the abstraction, but it has to be there underlying its perceptual abilities.
Thanks. Yeah, it’s basically finished. But finding a publisher is no day at the beach.
This is what I had in mind:
“Yes — and once we have a distinction between Euclidean triangles and non-Euclidean triangles, we have to move the concept “triangle” up a level, so to speak — a genus that includes various species”
— http://theskepticalzone.com/wp/from-reductionism-to-wholeness/comment-page-6/#comment-259959
I can see what you mean from a natural language perspective. I am not sure if that also works from a mathematical perspective. That’s one for Neil.
The issues your post raises also interest me. Thanks for the thoughts.
You should definitely read Frans de Waal’s latest book. Mama’s Last Hug. Anecdotes are all very well but folks are doing real work on animal cognition.
I think this example brings out something quite important (though I’m not sure how Gibsonian it is): the ability to reliably re-identity an affording feature throughout changes in the optical array requires a hierarchically organized model of the environment, where some levels of processing are more generalized than others, or (put otherwise) less immediately tied to sensory stimulation. The predictive processing approach has been really helpful in conceptualizing what this kind of computational architecture can look like, though the jury is still out as how biologically realistic it is.
I know of that work — I’ve read relatively recent work by Peter Carruthers and by Liz Camp. The past few months I’ve been reading more history of cognitive science than animal cognition studies but I’m not a stranger to it.
If we take the structural homomorphism approach to the representational aspects of the models created by the PP process, then the abstracting process in Neil’s post is consistent with PP. The invariants are the aspects captured by the homomorphism between the structures in the model and in reality (as accessed by the organisms sensory systems)
I agree that the properties involved in the models are abstract. And that the entities involved in the math of the model are abstract. To say such entities are somehow manifest in the cat’s perceptual processes would seem to require scientific realism used to support abstract entities realism. I think both are non starters for Neil.
One for you on related aspects of human cognition.
https://www.colum.edu/news-and-events/articles/2019/a-philosopher-and-a-psychologist-discuss-the-emotional-mind.html
I’ve read an interview with the author of Mama’s Last Hug, but find books like that spend too much time on anecdotes and stuff I already know. I prefer articles or interviews that focus on their new ideas.
Hmm.
I’ve read previous material by de Waal and this is his best. He’s advancing ideas and supporting them with evidence.
Meant to say definitely an argument against human exceptionalism.