Last night I was talking with an old friend of mine, an atheist Jew, who is now in the best relationship of her life with a devout Roman Catholic. We talked about the fact that she was more surprised than he was about the fact that their connection transcends their difference in metaphysics. He sees himself as a devout Roman Catholic; she sees him as a good human being.
This conversation reminded me of an older thought that’s been swirling around in my head for a few weeks: the disunity of reason.
It is widely held by philosophers (that peculiar sub-species!) that reason is unified: that the ideally rational person is one for whom there are no fissures, breaks, ruptures, or discontinuities anywhere in the inferential relations between semantic contents that comprise his or her cognitive grasp of the world (including himself or herself as part of that world).
This is particularly true when it comes to the distinction between “theoretical reason” and “practical reason”. By “theoretical reason” I mean one’s ability to conceptualize the world-as-experienced as more-or-less systematic, and by “practical reason” I mean one’s ability to act in the world according to judgments that are justified by agent-relative and also agent-indifferent reasons (“prudence” and “morality”, respectively).
The whole philosophical tradition from Plato onward assumes that reason is unified, and especially, that theoretical and practical reason are unified — different exercises of the same basic faculty. Some philosophers think of them as closer together than others — for example, Aristotle distinguishes between episteme (knowledge of general principles in science, mathematics, and metaphysics) and phronesis (knowledge of particular situations in virtuous action). But even Aristotle does not doubt that episteme and phronesis are exercises of a single capacity, reason (nous).
However, as we learn more about how our cognitive system is actually structured, we should consider the possibility that reason is not unified at all. If Horst’s Cognitive Pluralism is right, then we should expect that our minds are more like patchworks of domain-specific modules that can reason quite well within those domains but not so well across them.
To Horst’s model I’d add the further conjecture: that we have pretty good reason to associate our capacity for “theoretical reason” (abstract thinking and long-term planning) with the dorsolateral prefrontal cortex and also pretty good reason to associate our capacity for “practical reason” (self-control and virtuous conduct) with the ventromedial prefrontal cortex (and especially in its dense interconnections with the limbic system).
But if that conjecture is on the right track, then we would expect to find consistency between theoretical reason and practical reason only to the extent that there are reciprocal interconnections between these regions of prefrontal cortex. And of course there are reciprocal interconnections — but (and this is the important point!) to the extent that these regions are also functionally distinct, then to that same extent reason is disunified.
And as a consequence, metaphysics and ethics may have somewhat less to do with each other than previous philosophers have supposed.
So you do not think that there is any such thing as objective knowledge?
Right.
There can be objective facts, but not objective knowledge. It’s the knowing part that cannot be objective.
I didn’t say that pure sense perception was a reality. But the beauty of the human mind is that we can imagine possible scenarios and speculate about what they would be like. A bit like building simplified models of specific aspects of life in order to better understand its workings.
I agree that we are not just passive receivers of our senses and so in reality pure sense impressions never occur. I have given examples of where real life comes closest to the scenario of experiencing a pure sense impression. And it must be admitted that the gaining of sight is to begin with a somewhat chaotic expereince until the mind begins to “make sense” of what is seen.
Given that we cannot have objective knowledge, we cannot have knowledge of objective facts. Therefore these ‘facts’ are objective in name only, and not in any useful or practical sense. There’s not much point in calling them objective.
Flint:
And so paramecia think, as you are using the term.
I am talking about human senses and human thinking.
For you to argue that my scenario involves treating thinking as equivalent in paramecia and in humans then you will have to persuade me that paramecia have equivalent senses to humans.
That does not make sense. You say “Therefore …” but it doesn’t follow from the prior sentence.
I am not talking about mathematics, I am talking about circles. And the ideal circle certainly is connected to the circles we recognize in the world around us, they belong together. I am saying that it is precisely because of our human organization that we first experience physical circles and the ideal circle as separate.
Kantian Naturalist:
To me that is gobbledegook for, “Their first experience of sight was an unrecognisable chaos”.
The optic nerve sends signals to the brain which I would say is the organ which allows us to think. How did you make sense of my words and arrive at the response above? Did you use your thinking power to put those words together or was it just a product of your body?
Numbers aren’t erroneous, the concept of numbers existing on their own without any relation to anything external to them is erroneous.
So you are not interested in aquiring knowledge for its own sake?
Are you sure? There are a certain pair of twins called Mork & Mung :}
Numbers aren’t erroneous, the concept of numbers existing on their own without any relation to anything external to them is erroneous.
So you are not interested in aquiring knowledge for its own sake?
Sure. But now you are talking about counting behaviors rather than about abstract objects.
But only as an abstract object (useful fiction).
I have not had the opportunity to discuss circles with any aliens from Andromeda.
Are you sure? There are a certain pair of twins called Mork & Mung :}
I have a twin?
That seems to either agree with my fictionalism, or to assert that all of pure mathematics is erroneous. I’m not sure which.
You seem to imply that would not be useful. I wonder why you think that.
I did think of making a similar remark but then I worried that some folk might not get the joke and might see it as offensive.
For me, calling something an “attractor” is alluding to a DST mathematics. I am not sure if that math can be made compatible with the Bayesian probability (or information theory) formalization underling Clark’s ideas.
I also don’t see the explanatory value of calling something an “attractor”. On its own, it’s simply a term in a formal language; it does not have a content without a model and the model’s justification, as you yourself say in other posts about math.
I’ll be interested to see where you go with these ideas if you have time to post further about them as they develop.
No quadruped (or any other biped or noped for that matter) has demonstrated any conceptualization of 2+2 or any other mathematical equation. So regardless of what has ever roamed this world, mathematical concepts exist only with humans as far as the evidence shows.
Yes. Not only do I understand it, I know it has never changed.
Yes, I am familiar with Hericlitus. What of his writing do you feel supports your position?
I think I am experiencing the real world. The key is that I find no reason to presume that what I sense is merely some illusionary reflection of the “real” since I can’t experience anything regarding said alleged illusion. And, presuming there is no indication of any illusion – that is, presuming that if there is an illusionary “real”, it is so well hidden from our senses that all we can experience is the world around us, then that world that we can experience IS all of reality for all intents and purposes.
So, yes, when I gaze upon the natural world, I am 100% certain it is the ONLY real world rather than a reflection of something else.
I will unhappily confess that I don’t have the background to assess this problem. I would need to team up with a neuroscientist. (Fortunately I know a few.)
The gist of my idea was that perhaps one could appeal to Freeman’s work on modeling neurodynamics as attractors in order to give us a theory of how neurons coordinate their activity so as to give us large-scale assemblages that can in turn function as action-guiding representations.
But perhaps the mathematics simply doesn’t work here.
The appeal of talking about attractors when talking about neurodynamics — about what large groups of neurons do — is that it gives us a way of talking about representations without falling afoul of the standard epistemological picture according to which a representation must be static.
Or, as Churchland put it in his criticism of DST, the DST folks aren’t justified in their anti-representationalism because it never occurred to them that perhaps dynamical systems are representations!
Sorry I messed up my last post. I rushed away without checking it after hitting the send button.
A duality conceived in the heavens.
Numbers are particularly abstract enitities, but it wasn’t always so. Look at Roman numerals, how “I” represents a finger and “V” represents a hand with the angle made between four fingers together and the thumb. We have concepts such as unity, duality and other small values, and in the world around us we can peceive many things that match these concepts. But when it comes to large amounts such as £1000000 or $1000000 we don’t conceive of 1000000 separate units, we conceive of this amount as a unity, one “million”. And if we had this amount to spend then we would decide how we could divide up this unity on the items we desired.
And discovering the beauty of mathematics can bring joy. Its one thing being able to apply the Pythagorean theorem without really knowing it but its another when you first work through the proof for yourself and understanding lights up in your consciousness.
The Theorum of Pythagoras is a mathematical truth.
Just because no prehistoric quadruped had a conception of 2+2=4, does not alter the fact that they possessed 2 forelimbs and 2 hindlimbs making a total of 4 limbs. Our concept of 2+2=4 is aligned with reality in its application in all quadrupeds.
If it has never changed then this must mean that it was always on the screen of your device, and that the device you have displayed it on has alway existed. Even considering the short term and you are talking about change since the said circle came into being it would mean that your screen hasn’t been changed since you first displayed it. I’m still not sure if you are being serious.
Support of my position is irrelevant. You claimed that the Greeks didn’t think that the territory changed. Heraclitus refutes that claim.
So that makes you a naive realist which is a fair enough position to hold as long as you can justify it. But I suspect that by holding this position you would be in a very small minority here.
Okay. But you are missing the distinction usually made between numbers and numerals.
A few times here I’ve mentioned Benacerraf’s Dilemma. Here’s the basic idea, omitting some details:
(1) Suppose there are abstract entities: entities that have no spatial or temporal properties.
(2) Our basic understanding of knowledge involves causal relations — we know what we are looking at because of the underlying causal relations between perceptible objects, perceptual conditions, our sensory systems, and our cognitive systems.
(3) Objects that have no spatial or temporal properties cannot be assigned any causal relations.
(4) Therefore, if there are abstract entities, then we cannot know that there are.
The Platonist is going to deny (2), but then she needs to give us an alternative epistemology to account for our knowledge of abstract entities. This cannot involve merely asserting that we have a “faculty” for knowing abstract entities; she needs to show us that we do indeed have such a faculty.
And this cannot be done by merely asserting that “the intellect” is such a faculty. For one can indeed allow that we have a capacity for judging what is available to our senses without embracing the further idea that the intellect allows us to know things that have no causal relations with our senses at all.
And this is precisely what is at issue — the Platonist asserts, without any further argument or evidence, that the intellect has powers far beyond what needs to be ascribed to it in order to explain our judgments about empirical objects.
In short, the Platonist cannot win the argument against the Kantian merely by asserting what the Kantian denies; she must provide us with a theory of the intellect which demonstrates that the intellect has powers that the Kantian fails to acknowledge.
You – a human – holds the knowledge of quadrupeds having four legs. Heck…the human-given name even denotes such. We humans can count, even things from the past. But at the time those quadrupeds roamed when there were no men to count their legs (or ribs or toes or any other body parts) they had no given number of limbs. They weren’t even “quadrupeds” back then; ‘cuz there ain’t no one for to give [them] no pain…err…name.
Oh for goodness sake…Are you telling me that you believe that when something moves, it changes? If I toss a Frisbee across my yard, is a completely different Frisbee every millimeter it moves? Or are you implying it’s a visual thing (or lack there of) that causes this change? Like, do my walls change at night when it’s dark and the lights are out?
C’mon…seriously?
I don’t think Heraclitus’ perspective on change (of life in particular) reflected the majority Greek perspective on nature in general. But be that as it may, I’ll grant you that he appears to hold that the territory changed. I’m not sure how this supports your point though.
Well I can use my sloppy use of language to make my point.
We use numerals such as two, brace, II, deux, pair, zwei, 2, duo, couple and so on, to represent the concept of duality. We perceive two entities such as a pair of shoes, or two tones of a siren, or night and day, and we attach to these the concept of duality. All people who are thinking correctly will have this same concept for these various entities. It is only because of our human organization that the percept and the concept, which belong together, were seen as apart in the first place. Our thinking is the process by which we re-attach what we have at the beginning torn apart.
It is like the blind person gaining sight. They only slowly make sense of the separate shapes and colours, as their thinking makes the connections necessary to view reality. Another example which demonstrates this is by looking at a pencil semi-submerged in water. Our senses alone tell us that the pencil is bent but when we have learned through thinking the concept of refraction we can re-attach this concept to what we see and then understand the reality of the situation. Without the concept we will believe that the pencil is bent, with it we know the real situation.
Now for small quantities we can unify our percepts while still retaining the constituent numbers. We have the concepts solo, duo, trio, quartet and so on in cases where we can perceive the group as a whole and we can also easily determine the individual numbers involved. On the other hand we have concepts such as forest, flock of starlings or shoal of fish when we are focusing on a group which is seen as a whole. Our concept unifies the multiplicity.
I don’t much care for the term “percept”. There are no such things. Perception is a process, not a bunch of thingies.
At least as I look at it, counting is a process or behavior. Numerals are what we write down to keep track of our counting. Numbers are imaginary ideal objects that we use when theorizing about the counting process. When doing mathematics, it is useful to pretend that numbers actually exist — hence my fictionalism. And it is useful to pretend that numerals are representations of numbers.
The above propositions make several presuppositions. If we wish to understand knowledge we must be careful to make our starting point as free from suppositions as possible. This is why Rudolf Steiner in his book The Philosophy of Spiritual Activity later known as The Philosophy of Freedom begins from the starting point of “the given” and the process of thinking.
He says
Thinking must precede subject and object because it is only through thinking that we arrive at these concepts. At this stage the given cannot be considered under the classification of subject or object, cause or effect, appearance or reality, representation or thing-in-itself; as these terms are the product of thinking.
The whole of the given is abstract before thinking is applied to it. The relation of the ideal circle to physically perceivable circles is not a caual one. For our organisation there are two sides separated which really belong together. The ideal circle which is really the idea of a circle belongs to every physical representation of a circle, they are a unity and we cannot say that one causes the other.
Anyone whothinks that there is nothing but movement just borrows this concept from their sense experience and then applies it in an abstract way.
And these are the sort of conclusions which naturally follow from treating numbers as isolated abstract entities.
I consider what you quoted from Steiner to be pure unadulterated nonsense.
Michael Wilson explains what Steiner meant by percept here
In describing the percept (see Chapter 4), Steiner mentions the ambiguity of current speech. The German word Wahrnehmung, like the English “perception”, can mean either the process of perceiving or the object perceived as an element of observation. Steiner uses the word in the latter sense, and the word “percept”, though not perhaps in common use, does avoid the ambiguity. The word does not refer to an actual concrete object that is being observed, for this would only be recognized as such after the appropriate concept had been attached to it, but to the content of observation devoid of any conceptual element. This includes not only sensations of color, sound, pressure, warmth, taste, smell, and so on, but feelings of pleasure and pain and even thoughts, once the thinking is done. Modern science has come to the conclusion that one cannot deal with a sensation devoid of any conceptual element, and uses the term “perception” to include the whole response to a stimulus, in other words, to mean the result of perceiving. But even if one cannot communicate the nature of an experience of pure percept to another person, one must still be able to deal with it as an essential part of the analysis of the process of knowledge. Using the word “percept” for this element of the analysis, we are free to keep the word “perception” for the process of perceiving.
But everyone must have the same concept of such things as the number 4 or we could not share our mathematical workings or our scientific quantative knowledge with each other. So I don’t see how the use of pure mathematics can be called a fiction. Better to call it a non material fact. 2+2=4 is a non material fact. A quadruped by possessing 2 forelimbs and 2 hindlimbs is a material fact. The former is pure mathematics the latter applied mathematics.
I disagree.
We need some common behaviors. We don’t need the same concept.
I didn’t call that a fiction. I use “fiction” for objects (such as numbers), not for the use of those objects.
The idea that a quadruped is doing applied mathematics, by virtue of having 2 fore limbs and 2 hind limbs — frankly that idea is absurd.
Can you explain in what way is your concept of “4” different to mine or anybody elses?
But a quadruped wasn’t applying the mathematics, I was.
Do you believe it to be fact or fiction that a diplodocus was a quadruped?
Concepts are subjective, so we can’t actually compare them between people.
Are we talking about the numeral “4” or the number 4? Are we talking about the integer 4, the rational number 4, the real number 4, or the complex number 4. Or are we talking about the number 4 in modular arithmetic (with a modulous greater than 4? Or are we talking about the p-adic number 4?
Those are all aspects of my concept of 4. Most of them were not part of my concept of 4, back when I was in elementary school.
I’m glad you cleared that up.
I’m am talking about the pure concept for which 4 is a symbol. You have taken the pure concept and attached further concepts which are extraneous to its essence. You introduce the categories such as “intergers” and “real numbers”. These are unified groups and so you have introduced the concept of unity.
So you have included the concept of unity, the concept of categories, the concept of opposites, the concept of continuous variability and other concepts within the concept of 4. I would say that these concepts cannot be included in the concept 4, but the concept 4 can be included in these concepts.
You will have to explain what you mean by “pure concept”, because I’m inclined to doubt that there are such things.
To me, part of what constitutes a concept is how you use it. If you remove that (presumably to purify it), then all you have is a name. And why would you then need a symbol for something that is only a name?
I should have added that you have just made an excellent argument that your concept 4 is different from mine. So you have inadvertently refuted your claim that concepts are the same for everybody.
Neither; it is a human description. From said description, we humans can make statements about diplodocus that are factual, but none of those “facts” exist without human perspective understanding.
I’m totally convinced you’ve never spent any time with any children. If you asked some group of 7 y.o. about the “pure concept of with 4 is a symbol”, you’d get about a thousand responses and none of them would have anything to do with any “pure concept” of anything.
Yes, exactly right.
That seems equivalent to saying that “diplodocus was a genus of extinct sauropod dinosaur” would be neither true nor false if no sapient beings had ever evolved to make that claim. That is at odds with what we ordinarily take science to be doing: making assertions about how things are independent of our taking them to be such.
The fact that our knowledge of the world has conditions of possibility in contingent facts about human sentience and sapience doesn’t mean that we aren’t also entitled in regarding our assertions about the world to be claims about how the world is, including assertions about objects and event far removed from us in space or in time. It would be one thing if we were somehow “imprisoned” within our subjectivity, consciousness, or language. But we aren’t. We are organisms of a certain kind, bound up with our environments, having a contingent natural history, and neither more nor less “imprisoned” than a duck or a racoon. All sorts of animals know things about their environments, and so do we. The difference that sapience makes, and especially that peculiar form of sapience called “science,” is that we can catch glimpses of the hidden causal structures that comprise the world’s real contribution to the affordances and solicitations that constitute our perceptual-practical awareness of the world.
I don’t have anything useful to add; popping in to congratulate y’all on remembering there are other things to discuss than “burden tennis”. 🙂
Carry on!
I don’t agree.
When we say “diplodocus was a genus of extinct sauropod dinosaur,” we are projecting our own understanding of the world backward in time. We can do that projecting, even if there were no humans at that earlier time.
Likewise, if we say that an alien from Andromeda would see that Mt Everest is the highest mountain, we are projecting our way of understanding the world onto that alien.
The expression “how the world is” has no meaning apart from “how we perceive or experience the world”.
We are imprisoned in our own system of categories, and our statements are limited to what can be said in terms of those categories. Yes, our system of categories is not rigidly fixed. However, there uncountably infinite possible ways that the world could be categorized, and humans will never use more than finitely many of those systems of categories. That alien from Andromeda might categorize the world in a completely different way which does not share any of our categories.