Monday, October 30, 2017

Feser on the argument from indeterminacy

Here.  Please also follow the link to his essay in the American Catholic Philosophical Quarterly.



Atno said...


One could then take it in the direction of McCabe's argument for how humans can carry on an activity that is independent of material organs. Or something similar to David Braine's argument.

I think the same problem would also affect the rules, however. "Everything can be made to accord with the rule". But then we get to Kripke's reading of Wittgenstein, and the "skeptical solution" is a non-starter. To me, something like the scholastic conception of human mind is unavoidable.

(I'm still reading your links. I hope you'll enjoy Braine's book -- I recommended him not as a defense of my view on the argument from mental causation, as I believe Braine would not agree with me either, but because it's an example of a wittgensteinian-aristotelian using language as a sort of "argument from reason" against naturalist views of the human person. So let me know what you think when you get to read it)

Atno said...


I forgot to ask. Related to your What is your view on the possible origins of language? It is curious enough, but this understanding of language -- which seems to me plausible -- seems to lend itself into an argument for God in a manner pretty much analogous to the classical cosmological arguments. Haldane argues the point in "Atheism and Theism", setting it as an argument for a "First Thinker". The general insight, however, goes back to at least Anthony Kenny, who, despite not setting it as any argument for theism, presented it as a mystery: language cannot be explained through evolutionary means, much like we can't say golf was created because golf players had an evolutionary advantage against non-players; it is conventional, and so must be purposefully created. However, it is impossible that someone who did not have language could have conceived of a purpose for language and then created it for that purpose. But neither is it possible that language could have been created by accident, as if someone could just accidentally follow and keep following rules of language.

As a theist, I wouldn't have any problem with the conclusion that language must originate from a divine "First Thinker". But I am not necessarily endorsing this line of argument, either, just putting it there because I find it interesting and have yet to see many other wittgensteinians adress it, besides Kenny for instance.

David Brightly said...

For those like me without an ACPQ subscriptionJames Ross's Immaterial Aspects of Thought can be found here and Ed Feser's Kripke, Ross, ... here.

David Brightly said...

Oops, Feser is here.

Joseph Hinman (Metacrock) said...

Good there are places like this site and Feser's and the Secular Outpost where the level of discourse can rise above the simple name calling that passes for arguments on so many other sites.

I try to make my log such a place, although doesn't always make it. today it does,on Metacrock's blog

Occam, Fine tuning, Best evidence

StardustyPsyche said...

Joe Hinman said...

" Good there are places like this site and Feser's and the Secular Outpost where the level of discourse can rise above the simple name calling that passes for arguments on so many other sites."
--Feser is himself a name caller and is quite content with idiot moron stupid homo troll on his site.

Joseph Hinman (Metacrock) said...

I am guilty, i try but...

David Brightly said...

Ross's second premise is that physical processes are indeterminate. Indeterminate with respect to what? Kripke's argument inclines us to think that words are indeterminate as to meaning. If all we have to go on is our answers to a series of addition examples with arguments less than 57 then we don't seem to have much evidence that 'add' meant plus to us rather than quus. Ross applies the same line of thought to an adding machine. If all we have to go on is a log of inputs (each less than 57) and outputs then it appears the machine is indeterminate as to the function it implements. Is it plus or is it quus? But Ross goes further. Feser says,

To reinforce the claim that material processes cannot in any case determine meaning, Ross, again following Kripke, notes that there are no physical features of an adding machine, calculator, or computer that can determine whether it is carrying out addition or quaddition, no matter how far we extend its outputs. KRIAT, p16.

To an engineer this is absurd. One simply takes the machine apart to see how it works. Not something we can do with people, note. This is one of Dillard's objections that Feser treats on p21:

Dillard says that there is a determinate difference between an and-gate, an or-gate, and other logic gates, which falsifies Ross’s claim that physical phenomena are inherently indeterminate. But this simply ignores Kripke’s point that whether a machine has certain computational properties—in this case, whether a given electrical circuit really instantiates an and-gate or is instead malfunctioning—is not something that can be read off from the physical properties of the circuit itself, but depends on the intentions of the designer. [and once we are back with a human designer Kripke's argument against determinate meaning kicks in]

But this rebuttal from malfunctioning carries no weight. The circuit may well not be doing what the designer intended but it nevertheless is doing something determinate. Suppose the and-gate has its first input accidentally disconnected so that it 'floats' up to TRUE. Then the broken and-gate delivers the identity function on its second input. The effect of the faulty gate on the larger circuit will depend on how it is embedded in it, but it will be a determinate effect.

Kripke's thought experiment may well make us sceptical about meaning. After all, the nature of meaning remains a philosophical puzzle, and an eliminativist response may be plausible. But to Ross's we can give a 'straight' answer. We are comfortable enough in our science and engineering to reject it outright.

Atno said...


This does not answer the problem. The issue is not that the effect of the faulty gate will be a determinate effect, but that it will not be determinate with regards to meaning. Besides, the issue is completely general and not limited to a calculator -- which is just an illustration --, since we are dealing with determinate meaning, you wouldn't even be able to make sense of the idea of a faulty gate.

The issue is very simple, really: there is nothing intrinsic in any material being that could lead us to a determinate meaning. A sign can be taken to mean absolutely anything, and even if you scale down possible interpretations (which already requires us to employ determinate concepts) there will always be different equally possible interpretations contained in anything. But if that's the case, we can't get off the ground. But we DO get off the ground and understand determinate meanings and concepts, but that's only because our thoughts are not themselves wholly material; there are immaterial, determinate aspects of thought.

Whatever is material is indeterminate towards meaning, and that is precisely why we can arbitrarily create signs and even make such things as calculators and computers whose outputs convey something *we* have determined as a meaning.

David Brightly said...

Hello Miguel. I think we can all agree on the arbitrariness and conventionality of the meanings we attach to external physical symbols. That isn’t controversial. If the matter is really as simple as this, why do you think that Ross goes to the length of invoking a difficult, heavyweight argument, one of the ‘jewels of analytic philosophy’ [KRIAT, p2], to make his case?

Atno said...

Because this jewel of analytic philosophy illustrates the problem of semantic indeterminacy quite well, because it applies it to mathematics and reasoning in general. The problem, however, is very general and goes back at least to Saint Augustine. In one of his dialogues, Augustine and his son discuss how a person can come to know what exactly "running" is if they only ever have access to indeterminate particular instances, which can be interpreted in a multiplicity of different ways. Wittgenstein makes the point when discussing the problem of ostensive definitions, and so does Quine and, of course, Kripke. Ross uses Kripke's argument because it is already formulated as a skeptical challenge: Kripke shows how the indeterminacy of the material can have catastrophic results for reasoning and science.

If we can both agree on the arbitrariness and conventionality of meanings we attach to external physical symbols, then you're already on your way to become the target of Kripke's skeptic. Whatever is material is indeterminate for meaning. + can stand for plus. Or it can stand for "quus". And the interpretations you make of a "faulty gate" in the calculator can be perfectly consistent with infinite specific definitions of quaddition.

Of course we know what addition is. But that's because we have a determinate understanding of it as a determinate, immaterial concept, that can admit of no other interpretations. Our thoughts have immaterial aspects; they are unlike a painting or a "mental picture" which, particular and material as it is, admits of semantic indeterminacy (everything material includes accidental aspects such as spatio-temporality, dimensions, accidental relations etc which play no role in a definition, and indeed must be abstracted away from any definitions).

bmiller said...

Tell your wife *Happy Birthday* and many returns.

David Brightly said...

Miguel, You say,

The issue is not that the effect of the faulty gate will be a determinate effect, but that it will not be determinate with regards to meaning.

My take on this is rather different. Kripke's argument is about meaning but Ross's argument, though clearly inspired by Kripke, seems to be about function, where this term is understood in the mathematical sense as the relation between 'inputs', in some sense, and 'outputs', in some sense. Ross's premises are (1) that when we are doing an addition sum the relation between the inputs and outputs is perfectly determinate, but that (2) when it's a machine doing the sum the relationship is indeterminate. The Kripke-inspired argument is intended to back up (2). Do you agree thus far, or have I misread Ross/Feser?

bmiller said...


Ross's premises are (1) that when we are doing an addition sum the relation between the inputs and outputs is perfectly determinate, but that (2) when it's a machine doing the sum the relationship is indeterminate.

I don't think the point is that we can take a machine apart and see that it works in a particular way. It's that we can equally suppose it has multiple various purposes.

When we do addition we know precisely what we are trying to do. When we come across a physical artifact with no background information there is no way to tell exactly what it supposed to be doing.

It is draining a battery. It is heating the air. It is changing voltage levels. But without some additional information we don't know exactly which of them it is supposed to be doing. We can't know if, in series of 4 interconnected AND gates, and one of them always outputs "1" regardless of the inputs if it does that by accident or design.

David Brightly said...

Hello BM. I agree with you that we cannot read off the purpose of an artefact or the intent of its designer from its physical structure. For this we need to interrogate the designer not the artefact. But again, this is not what Ross's argument is about. The words 'purpose' and 'intention' do not appear in KRIAT.

bmiller said...

Hi David,

Nice to chat with you again.

The words 'purpose' and 'intention' do not appear in KRIAT.

Yes, but the word judgment does appear in Ross's paper which is the background of Feser's article.

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process. If all thinking, all judgment, is determinate in that way, no physical process can be (the whole of) any judgment at all. Furthermore, "functions" among physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be neither wholly physical processes nor wholly functions among physical processes.

By judgement Ross means the ability to distinguish between truth and effect understanding.

There is a larger and bolder project of epistemology naturalized, namely, to explain human thought in terms available to physical science, particularly the aspects of thought that carry truth values, and have formal features, like validity or mathematical form. That project seems to have hit a stone wall, a difficulty so grave that philosophers dismiss the underlying argument, or adopt a cavalier certainty that our judgments only simulate certain pure forms and never are real cases of, e.g., conjunction, modus ponens, adding, or genuine validity. The difficulty is that, in principle, such truth-carrying thoughts2 cannot be wholly physical (though they might have a physical medium),3 because they have features that no physical thing or process can have at all.

So the question is an AND gate judging the truth or falsity of of something when it's inputs change? Then that would depend on the intent of the designer or programmer.

David Brightly said...

Those paragraphs are from the introduction where Ross gives us a summary of his argument. He's saying that he's going to show us that no physical process can be sufficiently determinate to constitute a judgement. So if you accept that the physical process going on in an and-gate is indeterminate then it cannot be making judgements. But he has to demonstrate this lack of determinateness. And that's where I say his case falls down. And it fails because, in the case of artefacts, unlike with ourselves, the Kripkean argument from observation histories is not all that we have to go on in pinning down the function that's being performed. We can look inside and use our scientific understanding of the behaviour of matter to capture what goes on.

bmiller said...

We can look inside and use our scientific understanding of the behaviour of matter to capture what goes on.

We don't even have to look inside the gate to observe *that* the voltage levels change according to some pattern. But those physical states could be judged to represent a part of any number of different functions. CPUs are made up of many of those gates and sometimes those gates are running a word processing document, sometimes they are doing speech recognition sometimes they are running a spreadsheet and so on. Merely observing the states change do not tell us what is truly going on.

How do you think an AND gates carry truth values in the absence of human thought?

Atno said...


The problem is the indeterminateness of the physical in relation to meaning. The problem is not that we can't see what a machine is doing, but that we can't, from that alone, interpret how exactly we should understand the meaning (or purpose) of these operations. You'd have to ask the programmer, but he, too, would have to have a determinate idea of what the operations were for, and what they meant. It ultimately goes back to the human mind, but the human mind cannot itself appeal just to purely physical signs if it is to know the determinate meaning in question.

We can see that the mechanism follows some kind of pattern; it "follows a rule", in a way. But the problem, as Kripke puts it, is that anything can be made to conform with the rule. Quaddition is a case in point.

The medievals knew that we grasped determinate concepts, from our own experience, and that the meanings of the words we use were determinate ones that belong not to us, but to the language, which is public. They also knew that nothing physical could ever be a determinate concept, or limit itself to a determinate meaning. There are immaterial aspects of human thought.

What Ross does in his argument is show that the denial of such a fact not only goes against what we find out by experience, but also that it would completely undermine reason and science, and is self-defeating.

A computer does not actually "play chess". That's just how we read its carefully programmed movements, because we know what chess is, how to play it, what its rules are. But if we only had access to the physical operations of the computer, these same operations could be compatible not only with what we call "chess", but with an indefinite number of alternative games and meanings. We'd have to ask the programmer about it, but he'd only be able to answer it if at the time he had determinate knowledge of chess. The computer's physical actions (which are all that he has) do not secure meaning by themselves, they are not determinate in relation to concepts. Material beings are never determinate in this sense. But human thinking is determinate (hence immaterial), and if it were not, the way would be open for Kripkenstein's skeptic to destroy reason and science.

David Brightly said...

BM, We have to look inside the device for at least two reasons. First, to convince ourselves that the relation between inputs and outputs is independent of time (subject to certain operational constraints like not clocking the circuit too quickly or letting it get too hot). Second, in the case of the adder, making sure that there are no critical values for the inputs, like 57 and above in Kripke's quus, at which the device departs from the observed pattern. What is really going on is that the and-gate instantiates the function (high, high)-->high, (high, low)-->low, (low, high)-->low, (low, low)-->low. The circuit carries merely voltages not truth values, but its function is isomorphic to the truth table for logical &.

Miguel, As I indicated at the beginning, I am happy to allow that the operations of the adder are indeterminate as to meaning. Indeed, not being elements within some linguistic system, they are not candidates for having meaning in the first place. But Ross's claim is that they are indeterminate as to function. The word 'function' occurs dozens of times in IAT; the word 'meaning' not once. For all I know what you say about human thought may well be true. My position is that Ross's argument doesn't demonstrate it, and I'm focused quite narrowly on that.

bmiller said...


What is really going on is that the and-gate instantiates the function (high, high)-->high, (high, low)-->low, (low, high)-->low, (low, low)-->low.

OK, that is what you think it is doing, until the output stays high regardless of the inputs for a time, and then starts back to what looks like an and-gate instantiation. Then the question is whether the gate was doing an and-gate function at all or some other function entirely.

Now you may argue that you inspected it and can tell how it is physically supposed to operate, but unless you know what function it is supposed to do maybe what looks like a marginal trace leading to intermittent operation was part of the planned function. Remember, we can't suppose we know that it's supposed to be an and-gate in the first place.

David Brightly said...

Yes we can. Ross's claim is that no physical process is determinate. So for a counter-example I can pick any device. I choose one designed to be an and-gate.

bmiller said...

I afraid I'm a little lost.

If you already know specifically that *you* are exercising an AND gate that physically operates the way *you* want, then of course *you* have made the function seem to be determinate. But I challenge the idea that the AND gate itself is making the determination. I could witness the same set of inputs and outputs and consider it a NAND gate since I consider +3V a "0" and 0V a "1". The exact same physical device operating in exactly the same way is instantiating a AND function for you and a NAND function for me.

David Brightly said...

Sure. If we label high as F and low as T the operation table becomes (F, F)-->F, (F, T)-->T, (T, F)-->T, (T, T)-->T, which we might more naturally call 'or'. But the way the circuit acts on voltages remains the same. We might call this phenomenon the 'indeterminacy of interpretation or representation'. It's what Miguel was bringing up and it's trivially always with us. It's very much like choosing a coordinate system in which to describe a physical situation. Different observers assign a point or an event different coordinates but the point or event is determinate and unchanged---and there's no one 'right' coordinate system.

Atno said...


Someone can learn how to play chess by observing it, sure, but that is because humans have the capacity to grasp universal and determinate concepts. Our experience of the world is interwoven with meaning and proper language. I am not denying that we can learn through observation; the point is that what is purely physical can never be determinate with regards to meaning, what is physical can never be a universal and determinate concept. But we *do* understand determinate meanings, we do grasp universal and determinate concepts, but the implication of this is that our thinking is not physical, it is determinate and hence immaterial. Saint Augustine, when discussing semantic indeterminacy, also made the point that " intelligent person would be able to understand" what is being taught (e.g. what is running based on different examples of people running), but that's because of intelligence. It's what is implied by it. I'd recommend you to read this post on Feser's blog:

If, however, materialism were true, and we had no immaterial active intellect, then we would never be able to understand and make use of determinate concepts. We'd be limited to physical representations and physical associations which, by themselves, can never lead us to any determinate and universal concepts. And thus Kripkenstein's challenge would emerge.

The thomistic understanding of the intellect is a very subtle and sophisticated one. The soul is not actually a substance; properly speaking, the human being is the substance in question, the soul is the substantial form of the human being. However, the human soul is a subsistent immaterial form because it carries out an operation that is intrinsically (not extrinsically) independent of any bodily organs (the intellection, which is to say, our grasp of universal and determinate concepts), hence why it is immortal. It can be a bit tricky, but there are different articles and books to explain it in different ways. Feser gives a handy account of it in "Aquinas" and in some blog posts of his. Gyula Klima has an article named "Aquinas on the materiality of the human soul and the immateriality of the human intellect" in which he spells out the idea in a logical and semantic manner.

Also, the brain cannot be the proper "vehicle" for human thought because, being material, it could not have the power for the immaterial. Thinking is determinate and immaterial, and to say that the brain is somehow its "vehicle" would seem to me to fall to similar interaction problems that plague Cartesian views of the mind. It would end up like some kind of property dualism, but that will not do to make sense of thinking.

Besides, if the brain were the vehicle or locus of thought, then thought would not actually be immaterial, because since the brain is material, it would not be able to "encode" information as universal forms (which have no particularity, and hence no materiality), because the information in question would be "contaminated" by the brain's spatio-temporal features (which are affected by the known or perceived sensible objects) much like how phantasms have spatio-temporal features by virtue of being produced by our (spatio-temporal) senses. Klima's article explains this in more depth.

Atno said...

I don't think I understand your point about the phantasms, however. If you refer to their privateness, they are just sensible forms stored in our imagination, and we can understand them determinately because of our intellectual capacity. Anyway, here are some quotes by Herbet McCabe on the phantasms and thought. Thought it could be of interest. They're taken from the book "On Aquinas":

"To the argument that you can interfere with somebody's ability to entertain meanings by damaging his body, especially his brain, Aquinas replies that this is because for us, at least in this life, understanding has always to be accompanied by some kind of bodily activity of the imaginatio, or as he often says, some phantasmata. This is most clearly the case when your thinking is accompanied by an imaginary conversation with yourself-imagining what it would be like to speak bodily; but it is also often the case that we think in pictures or with imaginary or constructed diagrams. But, in any case, Aquinas would and did ( I think rightly) argue that thinking itself could not be any such operation of a sensitive bodily power (as we should say, an operation of the brain), which for him is what imaginatio is."

"to say that understanding is not an operation of the brain, of the imaginatio, a phantasma, but nonetheless has to be accompanied by some such physical operations, phantasmata, is not unlike saying that the meaning of a word is not a physical property of a word, like its sound or length, but nonetheless the meaning needs some word or other in some language with some sound or length for it to be the meaning of that word. In other words the problem is very much the same whether we see it in terms of the physical, individual, material brain and its relation to the concept or in terms of the physical, individual, material word and its relation to its meaning. (Remember, once more, that I am using 'word' to mean any conventional sign: a flag or a symbolic road-sign is a word in this sense."

And this is a quote by Aquinas himself about phantasms and sense perception:

The intelligible species is to the intellect what the sensible image is to the sense. But the sensible image is not what is perceived, but rather that by which sense perceives. Therefore the intelligible species is not what is actually understood, but that by which the intellect understands. (ST I. 85.2)

David Brightly said...

Hello Hal, I'd like to concentrate on Ross's argument for his second premise, and as I've said above, I don't think this is about meaning, despite its provenance in Kripke. Perhaps you can persuade me otherwise?

David Brightly said...

Morning Hal. A reply to yours of 6:04 PM. Anyone arguing for Ross's conclusion, that thought lies beyond the merely physical, has to find some criterion or hallmark of thought that demonstrably exceeds the physical. Rule-following, as opposed to rule-accordancy, probably won't do because any argument that rule-following exceeds the physical is likely to come back to thought itself and thus beg the question. But Ross thinks he has found his non-question-begging hallmark in determinacy of function. I really must insist that the argument is about function. The word appears on every page of fifteen bar two for a total of more than one hundred occurrences. 'Rule', and 'mean or 'meaning' appear not at all or only in footnotes. We have to get to grips with what he means here, say, on p141:

Whatever the discriminable features of a physical process may be,
there will always be a pair of incompatible predicates, each as empir-
ically adequate as the other, to name a function the exhibited data
or process "satisfies." That condition holds for any finite actual
"outputs," no matter how many. That is a feature of physical pro-
cess itself, of change. There is nothing about a physical process, or
any repetitions of it, to block it from being a case of incompossible
forms ("functions"), if it could be a case of any pure form at all.
That is because the differentiating point, the point where the behav-
ioral outputs diverge to manifest different functions, can lie beyond
the actual, even if the actual should be infinite; e.g., it could lie in
what the thing would have done, had things been otherwise in
certain ways. For instance, if the function is x(*)y = (x + y, if
y < 10**40 years, = x + y + 1, otherwise), the differentiating output
would lie beyond the conjectured life of the universe.

David Brightly said...

Hello Hal. You have highlighted 'predicate' and 'name' here. Can I ask what you think Ross means by these terms, and how a predicate can be said to name something?

David Brightly said...

Right. So if the predicate is the function---and I agree that this must be what Ross means---then in what sense can it name a function? I think this is an example of Ross's infelicitous style of writing that brings one up short and makes reading him a struggle. I guess that by 'name a function' he means identify a function---a thing identifies itself, I suppose, in a trivial kind of way. But let's be charitable. Can we then agree that despite the terms 'predicate' and 'name' that he uses here, he's not talking about linguistic entities? In particular, not about things that have meanings? He's just talking about functions, abstractions of a mathematical nature. And his claim is just that there is no fact of the matter as to what function relates the inputs and outputs.

David Brightly said...

Ross must be conflating a relation with the English or mathematical sentence that defines it. Consider the function defined by f(x)=2x+1. The RHS specifies the relation between an input x and the corresponding output f(x). We might put this in English as 'double the input and add one'. Or 'double _ and add one', where we understand that we substitute an expression for an input in the place where '_' occurs to get an expression for the output. This gappy sentence starts to look like a predicate---a sentence with the subject left out. And such a predicate uniquely defines or, if you are Ross, 'names' a function. Note that a function can be defined by distinct predicates: 'multiply _ by two' and 'add _ to _' define the same function. So the predicate of a function is indeterminate. But I don't think Ross means this.

David Brightly said...

Seems to me that we need to know the meanings of addition, multiplication, division, etc. in order to perform a mathematical function.
OK. I'm using 'function' here in the technical sense with which it's used in mathematics as outlined here, see especially the section Introduction and Examples. When we talk of performing a math function we tend to mean following a procedure or algorithm that takes a representation of an input number, say, and produces a representation of the corresponding output number. So plus(123, 456)=579 is a bit of information about the abstract function plus. Addition is a procedure that takes, say, the concrete symbol lists ['1', '2', '3'] and ['4', '5', '6] and mechanically produces the symbol list ['5', '7', '9']. We learned how to do this with pencil and paper in early days at school. Or we could count 123 marbles into a bag, and then another 456 marbles into the bag, and then count them all out again. Or we could use rotating gear wheels as in an adding machine or electronic circuits in a computer to manipulate concrete representations of abstract numbers. It's not clear to me how meaning figures in this. Ross wants to say that the computer isn't 'really' doing addition, but then he doesn't tell us what addition 'really' is. Obviously, if I hadn't learned the procedure for addition, you could write out the rules I had to follow in order to do it and I'd have to understand your instructions. But a computer follows the instructions in its program without understanding them in the same sense of 'understand'. It's as if it were a physical embodiment of their meanings itself. The instruction says 'Do this' and it does this.

David Brightly said...

Morning Hal.

I think we have gone full circle and arrived back at my initial criticism of the argument at November 03, 2017 4:27 AM. I agree with your summary of Ross and your remarks about signs and about computers not understanding the rules in accordance with which they act.

This is all well and good. My criticism is that Ross completely ignores the possibility that we apply our knowledge of physics, electronics, chip manufacturing, etc, etc, everything I summarise as 'looking inside' the device. When we do this it's obvious that the device is producing representations of sums from representations of summands. In other words, acting in accordance with the abstract pattern we call the function plus. We can't do this 'looking inside' with ourselves. This is where Kripke's sceptical scenario gets its traction and makes us queasy about the existence of meaning. For when we introspect and ask ourselves what we mean by 'plus' all we ever get back is more sentences! It's an interesting observation about the phenomenology of consciousness. The realm of words, as it were, floats above the world like a dictionary in a foreign language, with no apparent connection to the world. Yet if I say to my workmate, 'Pass the hammer', I get what I want. Weird and wonderful!

David Brightly said...

Hal, I'm not sure I understand what you mean by the designer 'representing' the function. Here is a description of an 'adder' circuit. There is no representation of the function plus here---the circuit just pluses! The 'signs' for the inputs and output are just voltages on electrical terminals. Likewise, an old-fashioned mechanical adding machine works by cumulative rotation of gear wheels---plus some linkage to do carries. No representation of plus here either, unless you want to say that the whole device manifests or embodies plus---which is more something I rather than you might be inclined to say (when waxing poetic)!

David Brightly said...

I don't say the circuit qua interconnected system of transistors, or the machine as mechanical system of gears is a representation. But for the purpose of describing what the device does we can associate input voltage patterns or wheel positions with numbers. So the patterns or positions represent numbers. Ross doesn't object to doing this. Indeed he has to accept this to get his argument going at all. He allows that the inputs and outputs of physical devices can be numbers---he just says that the functional relation between inputs and outputs is indeterminate.

In this example I imagine a 3-bit adder circuit equipped with sets of LEDs to signal the inputs and output. Each input/output has to be one of eight patterns: off-off-off, off-off-on, ..., on-on-on which I randomly label a, b, c,..., i. I show how the pattern characteristic of plus is implicitly present.

If the design changes then we have a different machine.

David Brightly said...

Hello Hal, and thanks for sticking at this.

Yes, I certainly agree about Ross's style. He did teach me the word 'compossible', but I doubt I'll ever use it.

In any case, I have been reviewing what you have been posting on this thread and it looks to me like one of the things you are asserting is that it is possible for an engineer to design a machine that can act in accordance with the rule of addition.

I would prefer to say 'design a machine whose operation---more exactly, its initial and final states---can be described using the abstract function we call 'plus''. I also say things like 'its operation instantiates the function plus', by which I mean the same thing.

I think Ross would agree. You also appear to me to be claiming that if we can understand how the engineer designed the adding machine then we can determine the rule it is acting in accordance with.

Again, I would say determine the function it instantiates, which just means find the relation between its initial and final states. Also, I don't say understanding the designer's thinking is necessary for this. In the case of the mechanical adding machine we can just take it apart and everything we need to know is laid bare. Granted, with an electronic chip we need to know the microstructure. I don't know if it's feasible to reverse-engineer chips to the extent that they can be copied. I suspect it is, but I don't think it affects my position if we are obliged to understand the chip manufacturing process from schematics through masks to the silicon foundry. We just have to know that they are reliable, and it seems that they are.

We can look at the schematics that were posted on the Wiki page you linked to, and we can see how the conversion of the binary notation can be implemented in converting to a decimal notation, etc. But unless one were an engineer I don’t see how one could determine the rules being implemented in the adder.

I think you are being misled by thinking in terms of rules. What sort of rule is implemented in a simple mechanical adding machine? I'm not sure the question makes any sense. But we can ask what mechanical principles govern its working. Stuff about ratios of teeth, angles of rotation, rigidity of metal wheels, and so on. And we can see that the outputs are fixed by its inputs, regardless of its history of (proper) use.

And that, it seems to me, amounts to the same thing as asking the engineer what his intent was in designing the machine and what rules he followed in order ensure that the machine was working properly. If that is the case, you would simply be begging the question, as Feser noted in this quote from his article that you posted above (on November 03, 2017 4:27 AM):

Go back to the mechanical adding machine. Suppose we are given all the conditions under which the machine is to be operated: ambient temperature, lubrication, atmospheric dust levels, limits on turns of the handle before the teeth wear out, etc. We can say that if these conditions are met, then the physics of the machine guarantee that its behaviour instantiates plus. If we couldn't make such a claim the thing would hardly be a reliable adding machine, surely? We can say the same of the electronic adder, but it's a much more complicated story because we can't immediately see all its parts.

David Brightly said...

But I fail to see how this addresses the question of how one can determine the mathematical rule being used to generate the outcome from the input only by the physical properties of the machine. You are still relying on the prior knowledge of the rules engineers follow in designing such a device.

But there is no such 'mathematical rule' being so-used! Try not to think in terms of rules. In any single operation cycle of the machine the final state follows from the initial state because of the way the physical world works, just as a rock released at the top of a mountain rolls to the bottom. With suitable interpretations of the states as numbers, we can describe the relation between the initial and final states as the plus function.

I followed your link to the charts that you posted on your blog, but I have to admit that I couldn’t make much sense of them. I don’t understand why you think it would support the claim that mere physical properties can determine something like a mathematical rule.. Sorry.:-(

Perhaps you are looking for something deep in this---a mathematical rule? What's one of those? :-)---that isn't there. My claim is really rather superficial. Is it acceptable to say that the initial state of the machine can be given by a pair of labels drawn from the symbols a,b,...,i? which label the illumination patterns on the two rows of LEDs that show the inputs? Likewise that the pattern on the output LEDs can be labelled? If we can also accept that each cycle of the device produces the same output for the same input---we can know this from its structure and physics---then we can draw up an operation table showing just what output we get for each possible input. That's my first table. Doesn't look at all like the table for plus, right? But it is plus, or rather a well-defined subset of plus, as the sequence of reorderings and relabellings I go through reveals.

David Brightly said...

Hello Hal,

With suitable interpretations of the states as numbers... I agree that we can question this. But Ross takes it for granted that such interpretations are possible. His beef is that the numbers we thus get are in no determinate relation. I, with my understanding of 'determinate', which may differ from Ross's, demur.

Why did you organize the operations table the way that you did? Well, of course I started with my final table and worked backwards! But is it inconceivable that a device could exist with an operation table like the initial one, once we have agreed what counts as an input or output, and how to label them? Again, Ross's argument seems to assume that this is possible, though he thinks there is a possibility that in the future it may diverge from what we take it to be now, and that this invalidates there being a determinate relationship between inputs and outputs. My position is that the determinate relation changes. I guess that's an impasse.

But then we are back to the questions of how are such rules determined... Again, legitimate questions but not ones that Ross asks. He doesn't talk about rules at all---it's all about function.

Once again, thanks for engaging with this. A final thought: My feeling is that if for other reasons one is comfortable with Ross's conclusion then it's easy to overlook the flaws in his argument, firstly because it's tricky deciphering exactly what the argument is, given his rather opaque style, and secondly as he appears to invoke the weighty authority of Kripke. It pays not to be overawed by the Big K.