Thank you for that positive feedback !
Very cool. And understanding him this way makes him as “modern” as Derrida.
For me the point is of course to explicate or unfold what this “information” is.
Of course we enact our trust in the possibility of communication. How does “meaning” or “information” have something to do with “the real world” ?
From over here, you have answered your own question. For those with the know-how, a base-2 numeral is “just as good” as its equivalent base-10 numeral. For those without the know-how, the base-2 numeral will “malfunction.” Likewise notches on a stick may not be noticed as a numeral at all.
This just-as-good-ness is grounded in our doing things with numerals/numbers. Pure math looks for deep structure without reference to any particular activity.
For instance, group theory intentionally ignores everything about the group except that it is a group. So the results of group theory are “instantly” applicable to all “actual” groups.
It can be anything - a recipe, an instruction, a formula.
Imagine this scenario. There is a sentry in a watchtower, looking through a telescope. The watchtower stands on top of a headland which forms the northern entrance to a harbour. The sentry’s job is to keep a lookout.
When the sentry sees a ship on the horizon, he sends a signal about the impending arrival. The signal is sent via a code - a semaphore, comprising a set of flags.
One flag is for the number of masts the ship has, which provides an indication of the class, and size, of the vessel; another indicates its nationality; and the third indicates its expected time of arrival - before or after noon.
When he has made this identification he hoists his flags, and then tugs on a rope which sounds a steam-horn. The horn alerts the shipping clerk who resides in an office on the dockside about a mile away. He comes out of his office and looks at the flags through his telescope. Then he writes down what they tell him - three-masted ship is on the horizon; Greek; arriving this afternoon.
He goes back inside and transmits this piece of information to the harbourmaster’s cottage via Morse code, where it is written in a log-book by another shipping clerk, under ‘Arrivals’.
In this transaction, a single item of information has been relayed by various means. First, by semaphore; second, by Morse code; and finally, in writing. The physical forms and the nature of the symbolic code is completely different in each step: the flags are visual, the morse code auditory, the log book entry written text. But the same information is represented in each step of the sequence.
In this scenario, what changes are the symbolic forms and means of transmission - flags, Morse code, and written text. What doesn’t change is the information content or meaning - Greek ship, three masted, arriving after noon.
I hope that conveys the point a little better. It’s related to the principle of multiple realisability,
1 Like
I love your use of the different sense organs and the leaping from code to code. “Meaning” is not “caught” in any particular “medium” or “coding.” We agree.
But what makes a code a code ? What makes Morse code “work” ? We enact Morse code. If I know both English and Morse code, then I know which English words are pragmatically equivalent to which sequences of dots dashes and pauses. To someone without the training, it’s just noise. What is it to recognize a paraphrase as such ?
The important thing in the word is not the sound alone but the phonic differences that make it possible to distinguish this word from all others, for differences carry signification.
In addition, it is impossible for sound alone, a material element, to belong to language. It is only a secondary thing, substance to be put to use. All our conventional values have the characteristic of not being confused with the tangible element which supports them. For instance, it is not the metal in a piece of money that fixes its value. A coin nominally worth five francs may contain less than half its worth of silver. Its value will vary according to the amount stamped upon it and according to its use inside or outside a political boundary. This is even more true of the linguistic signifier, which is not phonic but incorporeal — constituted not by its material substance but by the differences that separate its sound-image from all others.
Difference is “incorporeal.” Saussure elsewhere insists on “form not substance.” So for me there is something deeply related to Plato. The way I read Plato, I’d even call myself a Platonist. But “mathematical Platonism” is not for me related to “my” Plato or Plato-for-me. To “project” the forms “away from” all sensory-affective being is to miss their importance as the intelligibility of the world itself. Without enacting the equivalence of tokens, we don’t have types. And therefore no tokens either. Types and tokens are a unity.
Derrida famously emphasized “difference” as a fundamental concept, as something like the possibility of concepts. And his approach put Plato in a different light for me.
If you mean, what does it take to recognize a paraphrase, there’s actually a very straightforward answer: intelligence. The etymology is from ‘inter-legere’, 'to ‘read between’, to ‘discern meaning’ (ref). That is what intelligence does. I understand who Saussure is, one of the founders of semiotics, but I think for the point at issue it’s not necessary to introduce this level of complexity.
Think about it as an analogy for hylomorphism - hyle being matter, morphe being form. The information being conveyed in this analogy is morphē, the ‘form’ of the ‘in-form-ation’; the materials being used to convey the information, is the hyle (matter or raw material), The signal comprises the combination of form and matter. At each stage, the agent recognises the in-form-ation (recognises the idea) by virtue of his/her intellligence. That is what allows the information to be communicated.
2 Likes
Yes, so we agree that “something” is “being communicated.” I even agree that it takes “intelligence” to do this.
I also accept something like form and matter. Of course
So the issue is making sense of this “form” and this “matter.” I am extremely fascinated by this issue.
I propose that we can understand form or idea as the temporal unity of “informed matter.”
I propose that “quality” is a good name for matter. Basically quality includes any kind of “sensory-affective presence.” If aliens have strange sense organs, hard for us to grasp, well we will speculate about how the ripe tomato is “there” for them. Perhaps they count themselves as having 27 sense organs.
We would call them “intelligent” if we could have a conversation with them. Now what could convince us that we were indeed communicating ? We are present to one another in terms of
“informed quality” or “empirical reality.” At least I am not assuming something like telepathy. We will have to trade sounds and gestures and pictures and who knows what to establish a sense of “meaning” the same thing by such signs.
As I see it, lifting forms above all instantiation plucks them out of the possibility of meaning. Our Cartesian heritage encourages us to think of our interior monologue as something “outside of” or “above” the world. But even this monologue, for me at least, has the quality of English phonemes, like remembered or imagined conversation in English. Why the persistence of these arbitrary phonemes in a realm beyond the world ?
Let’s get back to this question:
Sets (and other mathematical entities) are abstract objects, lacking any spatio-temporal location. Their existence is not contingent on our existence. They lack causal efficacy. Our question, then, given that we lack sense experience of sets, is how we can justify our beliefs about sets and set theory.
There are a variety of distinct answers to our question. Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.
Do you agree with this apparent incompatability?
I don’t object for the reasons they do. I think the “physical” is often used in a confused and vague manner.
The “genuinely physical” object is only an object “through” the kind of “ideality” that I’ve been defending here. Ideality is a normative concept. It’s not about different kinds of stuff. The concept of self and other are complementary. Language is not something “inside” people. The world is not inside people, and it is already meaningful, suffused with the “ideal.”
So the “ingredient ontology” approach is “blind to the forum.”
The hard problem of the physical. Let people worry about that now and then.
I was looking for a good quote from Curry on platonism, and I found a strangely relevant passage in a paper about Curry’s philosophy of math.
The customary syntactic way of thinking about formal systems views them as systems of character strings, which are classes of equivalent inscriptions, which are already a kind of abstract object (Curry 1963: 15–16). Curry sets aside the nominalistic aims of interpreting these character strings as mereological sums of particular inscriptions, instances of brain activity, etc. The character strings have the smallest components, which are then concatenated. Once one realizes that this concatenation operation needs to be associative, then one has already realized that there is an implicit algebraic structure in how the character strings are built up (Curry 1963: 51–52).
If I learn that 1 + 2 = 3, I am not learning about the decontextualized marks made in pencil on my paper.
The most formalist or computational approaches to math still depend on the irreducible “ideality” of the iterable symbol.
A more mundane example is the letter A. Even if I use the same font, each inscription of the letter A is a singular event or thing in the world. Yet it is also “an A.” Or an “instance” of the letter A.
In some books, you’ll find a variety of vastly different glyphs that are recognizably instances of the letter A.
Early deep learning tackled the famous problem of categorizing the handwritten digits of zip-codes. In our decimal system, there are ten categories. The category of “nine” has “no true face.” Is there a way of writing a 9 that is more “real” than the others ? Some we might find more legible or attractive, sure. But I’m pointing at “categoricity” itself.
This “deep” categoricity is presupposed, even by the formalist. We might say “of course it is,” especially if intelligibility is something like a facility with this ideality.
The context is the formal system, though. You’re not adding apples. You’re exploring the world of math. I agree with Curry. People often believe they have freed themselves from abstract objects by dismissing propositions, but seem not to notice that sentences are abstract also. So are letters. It’s abstract objects all the way down since properties are abstract.
On the other hand, I can imagine a spectrum with pure, unadulterated abstraction on one end, and pure sensory input on the other. The poles are states of meaninglessness. Meaning is only found where the two are interacting, or fused in the way the concept of a tree is fused to my experience of patches of light and dark, green here, black there.
1 Like
Aristotle, in De Anima, argued that thinking in general (which includes knowledge as one kind of thinking) cannot be a property of a body; it cannot, as he put it, ‘be blended with a body’. This is because in thinking, the intelligible object or form is present in the intellect, and thinking itself is the identification of the intellect with this intelligible. Among other things, this means that you could not think if materialism is true… . Thinking is not something that is, in principle, like sensing or perceiving; this is because thinking is a universalising activity. This is what this means: when you think, you see - mentally see - a form which could not, in principle, be identical with a particular - including a particular neurological element, a circuit, or a state of a circuit, or a synapse, and so on. This is so because the object of thinking is universal, or the mind is operating universally.
…the fact that in thinking, your mind is identical with the form that it thinks, means (for Aristotle and for all Platonists) that since the form ‘thought’ is detached from matter, ‘mind’ is immaterial too.
Lloyd Gerson, Platonism vs Naturalism.
Methodological platonism is uncontroversial, for mathematics is de dicto an abstract science. The same is true of linguistics and computer science. Yet all subjects have an abstract component.
Controversy starts upon the reification of abstract rules and objects to the status of objectivity. But what do self-described “metaphysical platonists” mean when they speak of being committed to the independent existence of abstract objects?
In my view, the metaphysical platonist is taking abstract rules and entities as being explanatorily primal, and that this attitude is dogmatic and the mark of rote learning and subject misunderstanding.
Not to put too fine a point on it, but the metaphysical platonist isn’t reifying anything. The abstract object is accepted because something has been identified as being neither mental nor physical. The methodological platonist is going to church regularly, but remains agnostic.
You’re kind of saying Godel showed the marks of rote learning and subject misunderstanding. I think he just reflects a particular worldview.
It’s not like the other side of the issue is free of conundrums. You just pick your poison, unless you just remain agnostic.
Methdological platonism isn’t a widely used term. But lets say that the methodology amounts to representing a system at multiple levels of description, where each level of description employs its own language and set of concepts that are semantically closed, self-contained and make no reference to the other levels of description, nor to the concepts used at the other levels.
These levels and their separate languages aren’t intended to be interpreted as having ontological independence from one another, but only as having semantic independence from one another.
The seven-layer OSI model of computer networks is a reasonable exemplar:
Physical → Data Link → Network → Transport → Session → Presentation → Application.
-
The semantics of each layer are independent: a description as to how one level is implemented is intended to say nothing about how the other levels are implemented.
-
Nonetheless, every network engineer knows that there aren’t seven substances involved; just because the layers are de dicto independent doesn’t imply that the layers are de facto independent.
Likewise, we can interpret Frege’s three realms (the physical, the psychological, the mathematical) as a de dicto distinction rather than a de facto distinction , where these realms can be reconciled through e.g, a Peircian semiotic analysis, so as to avoid metaphysical platonism which explains nothing.
Kurt Godel’s continual evolution of thought on this subject is historically interesting, but he was primarily a logician rather than a philsopher, and he evidently didn’t manage to resolve the logical difficulties of his “Platonism” that he was well aware of.
1 Like
I see what you’re going for, it’s just that I can tell you exactly how the physical, say sound waves, is transformed into an analog electrical signal via a microphone. I can tell you how the analog signal is converted to digital in the A/D converter, how the digital signal is multiplexed for transmission, etc. I can tell you what kind of device was used to burn the firmware and how the machine code is manipulated by higher level languages.
Abstract objects aren’t like this. They’re aspects of thought. We can’t think without them. What a materialist aims to show is that they aren’t real. They’re illusions. Since showing that is problematic, since we can’t think without them, a materialist will take caution back from the wind and suggest that there’s some solution out there, we just haven’t found it yet. The solution has to be there because: worldview.
At base level, this is a worldview issue.
1 Like
Alex Rosenberg, among others, actually does bite the bullet on this. It is perhaps easier to maintain this position when one is already a determinist and an incompatibalist, and especially if one is an epiphenomenalist. In that case, there is already no real room left for reason(s) to do anything, even if it were somehow an “authority.” I’m not sure how far away teleosemantics, etc. actually get from this.
Anyhow, I would think that the key assumption making this difficulty hard to escape would be mechanism. The rest of the broadly naturalist paradigm doesn’t seem obviously at odds with the normativity of reason here. However, with mechanism, the order of reasons has to be extrinsic to the (more fundamentally causal) order of mechanism, or reducible to it.
Whereas making the “space of reason” merely an alternative descriptive realm (a position perhaps aligned with weak emergence) has the problem that reason seems ultimately irrelevant for explaining reasoning in action (in practice). In this case, the “authority” of reason ends up a bit strained, because whether a person obeys it or not comes down to mechanism. This is going to be problematic for anyone holding to “ought implies can,” and yet “ought implies can” is a pretty standard commitment among those who reject teleology (which would seem to be definitive of modern naturalism). And, if one accepts that “oughts” are primarily about obligation, then it does indeed seem odd that one would be obligated to do what is impossible for one to do. Similarly, under the solution where “ought” is always hypothetical and instrumental (i.e., do x if you want to accomplish y), then normative reasoning turns out to be merely descriptive in the end—i.e. it merely describes the way different means mechanistically produce different ends.
The problem of normativity then is in many ways similar to the problem of “strong emergence” or the other “hard problems” of qualia and intentionality.
Now, of course, there is surely the objection that people can be “non-reductive physicalists.” However, if the solution here involves “strong emergence,” it simply runs into all the problems associated with that position. Whereas if the solution involves abandoning mechanism so that strong emergence is no longer required, I’d wonder if it even ought to be called naturalism anymore. For it seems to be that no supposition of modern naturalism is more definitive than its mechanistic conceptualization of causality (from which its position against teleology, and for cosmic homogenity, the univocity of being, and mathematization all flow).
At any rate, the relevance here is that Benacerraf’s Problem is, as far as I am aware, the paradigmatic case against mathematical platonism (even if elements of the epistemic horn long predate it). But Benacerraf’s Problem presupposes a mechanistic model of causality or something like it. And evolutionary extensions of Benacerraf also work by assuming mechanism. So, that to me looks like the primary place of friction.
Of course, it’s not 1970 anymore, and physicists like Max Tegmark don’t seem to have had their naturalist card revoked for positing that the cosmos is just a mathematical object. But then, if an infinite multiverse of all possibilities, eternally actualized (including, for instance, a timeline where quantum flux is “just so” as to result in the resurrection of Jesus of Nazareth, etc.) is comfortably “naturalist” because it is ultimately grounded in mechanistic principles, but Aristotle or natural law theory remain “non-naturalist,” I’m not sure how “naturalism” doesn’t start to look principally vibes based (which is a point Charles Taylor makes, although he more tactfully calls it “aesthetic preference.”)
Yes, and also the supernatural wasn’t ruled out, so retaining elements that might be associated with it posed no significant problem for one’s credibility. I think the separate magisteria actually remain immensely influential as an escape route from the problems associated with naturalism, it’s just that few people want to defend it explicitly today. It is preformed rather than defended.
Yet I, for one, am not convinced that appeals to the ways in which language, culture, history, etc. all shape science can be used to screen naturalism away from the problems of mechanism, except maybe as a sort of smoke screen. I think you can see this in the mainstream naturalist reaction to guys like Latour. At the end of the day, either scientific anti-realism is embraced, and mechanism is just a story we tell, our it reveals something deep about the cosmos. Attempts to split the difference often strike me as arbitrary, merely means to having one’s cake and eating it too.
1 Like
Exactly. This is how I read Plato’s unwritten doctrine. One pole is “ineffable sensation” and the other is an “idea without content,” or “empty unity.”
1 Like
There’s something faintly oxymoronic about this isn’t there? 
Notice the caveat in the original post:
As regards ‘independence’, I believe there’s something not often commented about the independence of mathematical & ideas. They’re not dependent on nor arrived at by consensus, but are rather derived by necessity from mathematical principles. That is the sense in which they’re independent. But at the same time, they are only accessible through the intellect. Empiricism, on the other hand, seems to rest a great deal on the notion of the mind-independent nature of sensible objects; when, as Kant has shown, the way that objects appear to us is determined by our own sensory and cognitive apparatus. At the same time, however, empiricism is inclined to deny actual reality to mathematical principles ideas, save for them being a ‘product of the mind’ or even as ‘useful fictions’. That, I think, is at the basis of this whole debate: that empiricism gets the nature of understanding precisely backwards.
Yes, and the same is true when you describe your use of an abstact object.
In order for you to use, understand or prove a mathematics theorem, you must first interpret that theorem physically and psychologically in a bespoke fashion in terms of your local and private context. And yet, you have no translation rules to appeal to in that regard.
Likewise, you have no translation rules for mapping a design specification with respect to one ISO network layer into a design specification in an earlier layer, due to their semantic independence.
The so-called “hard problem” is another example of similar misunderstandings on both sides of the debate. For Optical redness is de dicto semantically independent of experiential redness, but they are not de facto independent, for if they were then optical redness would be empirically meaningless.
Those who deny that there is a hard problem, e.g Daniel Dennett, fail to comprehend the independence of physical concepts and phenomenological concepts. Yet on the other side, those who believe in a hard problem fail to understand that the nature of this independence is semantic and indispensible, as opposed to metaphysical and problematic.
1 Like
Yes. We basically just have training, and then even a “faith” in the general if imperfect intelligibly of what we say to others.
I agree with you, and I’ve been making this point in other threads.
Perhaps you overlook the transformation of the hard problem of consciousness into the hard problem of being or the hard problem of the physical. As I see it, we need not start from dualism. I’m not sure where your own starting point may be.