Sorry but I won't order food from you. It would take two or three days to get the order.

I understand the concept of "7" denoting seven, but it is not itself a seven.

End of the test. you get 0/10. — Banno

I answered this before, and my answer has been deleted. So here it is again:

It is a poor analogy because a series of 7 can be instantiated (in the sense of the word as I mean it) : 1,2,3,4,5,6,7. whereas an infinite series cannot. I was arguing in good faith.

The answer is that an event doesn’t occur into a vacuum , but into an exquisitely organized referential totality. That is precisely what an event is, a way that this totality of relevance changes itself moment to moment. So there is a tremendously intricate and intimate overall coherence from one event to the next. Each event is a subtle variation on an ongoing theme, and it’s very appearance shifts the sense of this theme without rending its pragmatic consistency. — Joshs

:up:

Another way to make this point, one which is phenomenological, but also resonates with William James's thought (see Taylor, 1996), is to assert the primacy of the personalistic perspective over the naturalistic perspective. By this I mean that our relating to the world, including when we do science, always takes place within a matrix whose fundamental structure is I-You-It (this is reflected in linguistic communication: I am speaking to You about It) (Patocka, 1998, pp. 9–10). The hard problem gives epistemological and ontological precedence to the impersonal, seeing it as the foundation, but this puts an excessive emphasis on the third-person in the primordial structure of I–You–It in human understanding. What this extreme emphasis fails to take into account is that the mind as a scientific object has to be constituted as such from the personalistic perspective in the empathic co-determination of self and other. — Joshs

Nice quote, Josh.

We cannot hold all our current beliefs about the world up against the world and somehow measure the degree of correspondence between the two. It is, in other words, nonsensical to suggest that we should try to peel our perceptions and beliefs off the world, as it were, in order to compare them in some direct way with what they are about (Stroud 2000, 27). This is not to say that our conceptual schemes create the world, but as Putnam writes, they don't just mirror it either (Putnam 1978, 1). — Joshs

This too.

If every thread on the principles of mathematics is allowed to degenerate into a thread about 0.999...<>1 it would become impossible to do any philosophy of maths. — Banno

:up:

In an attempt to put the thread back on track, I'll go back tot he spoons argument.

There are five spoons on the table. How could any paradox, any alternate paraconsistent mathematics, make it the case that there are not five spoons on the table?

In Wittgensteinian terms, arn't these different language games?

And if that works for spoons, why not for bridges? If the mathematics led to the bridge collapsing, wouldn't we say that we made use of the wrong maths?

There are five spoons on the table. How could any paradox, any alternate paraconsistent mathematics, make it the case that there are not five spoons on the table? — Banno

You asked me the question about there being five spoons a few pages back. You said

Presumably the spirit counts the spoons when no one is around in the quad. I hadn't fully understood that you were so close to Berkeley. — Banno

The point that I'm trying to make is that the table that ostensibly exists in the absence of any observers, is still an object of thought. Your imagining that collection in the absence of any observers, is still an imaginative construction on your part. I'm not saying that, therefore, the table or the spoons cease to exist when not observed, but that whatever you say, believe, or think about what exists or doesn't exist, depends on a framework of judgements which is a product of the mind.

Even if you imagine an empty universe before there were any subjects to observe it, that empty universe, even if characterised by scientific and empirical rigour, is still a mental construction, to the extent that you reference it or contemplate it. And if you don't reference it or contemplate it, then there's no subject of discussion. And to that extent, I am in agreement with Berkeley. Where I'm not in agreement with Berkeley, is that he doesn't recognise the role of universals in the ordering of reason. 'The fact is,' says a Thomist, 'that the human intellect grasps, first in a most indeterminate manner, then more and more distinctly, certain sets of intelligible features, which exist in the real as identical with individuals, with Peter or John for instance, but which are universal in the mind and presented to it as universal objects, positively one (within the mind) and common to an infinity of singular things (in the real).'

Number is a class of universal idea. The mind more or less effortlessly calls on it to organise its cognitions due to its innate rational ability. That is the ability that is denied by empiricist philosophy, with the consequence that maths is then treated as a 'useful fiction'.

That's all for now.

If the mathematics led to the bridge collapsing, wouldn't we say that we made use of the wrong maths? — Banno

We'd probably say the math they used was wrong.

Even if you imagine an empty universe before there were any subjects to observe it, that empty universe, even if characterised by scientific and empirical rigour, is still a mental construction, to the extent that you reference it or contemplate it. — Wayfarer

Of course your imagination of an empty universe is a mental construction, that is a tautological truism; but the empty universe itself (if it exists) is not. It puzzles me that you apparently cannot grasp that basic distinction.

According to scientific realism, an ideal scientific theory has the following features:

1. The claims the theory makes are either true or false, depending on whether the entities talked about by the theory exist and are correctly described by the theory. This is the semantic commitment of scientific realism.
2. The entities described by the scientific theory exist objectively and mind-independently. This is the metaphysical commitment of scientific realism.
3. There are reasons to believe some significant portion of what the theory says. This is the epistemological commitment.

It is 2 that I am calling into question. It puzzles me that you apparently cannot grasp that basic distinction.

More to the point, with respect to mathematical realism - I'm arguing that mathematical objects (such as numbers) are real, in that they're the same for all who can count, but that they're not empirical, because they're perceived by reason, not by sensory perception. Scientific realism, on the other hand, argues that sensory objects are real irrespective of any perspective, that is, 'mind-independently'. It seems to me that most of the argument against mathematical realism comes down to this conflict - because mathematical objects are not sensable, then they can't be regarded as real according to scientific realism, and so must be treated as conventions or useful fiction (by for example 'fictionalism'). And I think this says something really important.

It is 2 that I am calling into question. It puzzles me that you apparently cannot grasp that basic distinction. — Wayfarer

We don't know for sure whether the entities that science describes and every day perception encounters are mind-independently real. And it also depends on what you mean by "entity". Are you saying that it is impossible that these entities are mind-independently existent?

So, I can see the basic distinction between the possibility that those entities are mind-independently real and the possibility that they are not. They are (the) two (logical) possibilities, granted. So what distinction is it here you think I am not grasping?

You seemed to be claiming that an empty universe is (or definitely would be, not merely may be) nothing but a mental construction. And I responded saying that obviously our imagination of the empty universe is a mental construction, but that it does not follow that an empty universe must be a mental construction. There might have been an empty (I took you mean empty of life or consciousness, not totally empty) universe prior to the advent of life. In fact it seems that all the evidence points to the conclusion that there was. And if the universe existed prior to the advent of life and consciousness then it could not have been a mental construction, obviously, unless you were to posit a universal mind in which it existed. Personally I think the idea that it simply existed is the more plausible view, but I grant you that could be thought to be a matter of taste.

I do understand your perplexity about this point. Earlier you said:

Do you deny that it seems obvious that there are temporally persistent objects? Is the door always where you expect it to be or somewhere else? Your front steps? Your driveway? Your car? — Janus

It is empirically obvious and furthermore, true, that these are persistent objects. As I've said, I'm not claiming that, outside your or my perception, objects cease to exist. That is their 'imagined non-existence', or you imagining that they go out of existence. Like G E Moore asking if the carriage wheels disappear when all the passengers are boarded.

As I said, we can imagine the universe with no humans in it - which was empirically the case until a couple of hundred thousand years ago. But that doesn't take into consideration the sense in which even such an 'empty universe' is also an intellectual construct. The mind provides the framework, on the deepest level, within which any such idea is comprehensible. But then 'scientific realism' doesn't see the role that the mind plays. It believes the universe just is at is is, and would be this way even if nobody was in it. It 'brackets out' the subject, not seeing that the subject is still intrinsic but by that act, forgotten. (Schopenhauer makes a remark about that exact point*.)

There's methodological naturalism, which is to act as if an object of analysis appears just as it is, without the slightest hint of subjectivity. Which is all well and good and perfectly proper. But when that becomes metaphysical postulate, that the Universe really is just as it is, without there being any observers in it, then it oversteps by taking a methodological postulate as a metaphysical axiom, which it is not.

That is one of the implications of that essay I often refer to, The Blind Spot of Science. BUT, this is a severe digression within Banno's thread, so I will cease and desist.

----------------

All that is objective, extended, active— that is to say, all
that is material — is regarded by materialism as affording
so solid a basis for its explanation, that a reduction of
everything to this can leave nothing to be desired
(especially if in ultimate analysis this reduction should
resolve itself into action and reaction). But we have
shown that all this is given indirectly and in the highest
degree determined, and is therefore merely a relatively
present object, for it has passed through the machinery
and manufacture of the brain, and has thus come under
the forms of space, time and causality, by means of which
it is first presented to us as extended in space and
active in time. From such an indirectly given object,
materialism seeks to explain what is immediately given,
the idea (in which alone the object that materialism
starts with exists), and finally even the will from which all
those fundamental forces, that manifest themselves, under
the guidance of causes, and therefore according to law,
are in truth to be explained. — Schopenhauer, World as Idea 35

I do understand your perplexity about this point. — Wayfarer

I'm not perplexed; I just outlined the possibilities.

As I said, we can imagine the universe with no humans in it - which was empirically the case until a couple of hundred thousand years ago. But that doesn't take into consideration the sense in which even such an 'empty universe' is also an intellectual construct. — Wayfarer

It is you who seem to be perplexed on this point. So you're claiming the universe did not exist prior to consciousness, or you are claiming that it could not have existed? And I'm asking about it actually having existed then, not about our imagining now it having existed then.

BUT, this is a severe digression within Banno's thread, so I will cease and desist. — Wayfarer

I wouldn't worry about that, Banno has himself also derailed this thread. But if you are worried about it, then answer me in the 'realism' thread instead.

Do you deny that it seems obvious that there are temporally persistent objects? Is the door always where you expect it to be or somewhere else? Your front steps? Your driveway? Your car? — Janus

Let’s talk about what we actually experience as we make our way toward that door that we remember being there. As we approach it there is absolutely nothing about the visual scene that reproduces itself
exactly from moment to moment. The lighting, our angle , speed and style of approach and the accompanying perspectival view, howour eyes and neck and body turn in relation to the door, and how we need to move our body to open it and get through it. The classic empirical argument is that it is just the appearances that change, not the object itself. The phenomenological argument , however , is that we make the mistake of grounding the appearances on a notion of the identically self-persisting object which is itself constructed by us out of changing appearances.

So is there really a door there or is it just a subjective and intersubjective construction? The answer is both We dont make up or imagine the door.
We perceptually construct a reliably consistent unity by cobbling together memory, a continuing flow of new sensation, and based on this , expectations of what is to come next. This peceptual cobbling is what we see as this door. As we approach the door , we arrive with a rich web of perceptual expectations of what what we are about to encounter. As we begin to see it, what we see forces our perceptual system to rapidly adjust these expectations to the novelties of the current perspective. We don’t generally notice this adjustment taking place , and instead simply say we are seeing the ‘same’ door. We are indeed seeing something similar , and we only notice the discrepancies if they are pronounced ( under certain lighting conditions it may no longer look like a door ) or with certain brain injuries that interfere with our ability to make perceptual adjustments between expectation and reality. What we can never have , is evidence of temporally self -identical persistence of objects that doesn’t presuppose what it claims to prove.

You could legitimately argue that for all intents and purposes , making the classical empirical claim that objects persist over time as self-identical vs making the phenomenological argument that we construe self-identicality out of self-similarity leads to the same experience of the world and of science. I think this is true at the perceptual level , and with regard to the natural
sciences , but the classical view becomes limiting when we continue to apply it in the social sciences, particularly to psychological phenomena like empathy, affectivity and psychopathology.


“ For Husserl, physical nature makes itself known in what appears perceptually. The very idea of defining the really real reality as the unknown cause of our experience, and to suggest that the investigated object is a mere sign of a distinct hidden object whose real nature must remain unknown and which can never be apprehended according to its own determinations, is for Husserl nothing but a piece of mythologizing (Husserl 1982: 122).

Rather than defining objective reality as what is there in itself, rather than distinguishing how things are for us from how they are simpliciter in order then to insist that
the investigation of the latter is the truly important one, Husserl urges us to face up to the fact that our
access to as well as the very nature of objectivity necessarily involves both subjectivity and
intersubjectivity. Indeed, rather than being the antipode of objectivity, rather than constituting an obstacle and hindrance to scientific knowledge, (inter)subjectivity is for Husserl a necessary enabling condition.”(Dan Zahavi)

Every schoolboy knows, that if he has 6 pairs of pants, then he has a dozen pants.

Banno has spoons on the table. I prefer beans if there are five, or ducks if they are aligned, but spoons will do. A teaspoon, a dessertspoon a soupspoon and a couple of love-spoons. Five spoons. So I pick them up one by one and say to you 'this is a spoon, it is not a number' each time until I have all the spoons back in the drawer, and then I say - 'there is no five on the table, and I have not picked it up, Therefore there is no five and never was. It was empty talk.

I doubt you are convinced. I hope you are not. It's the old stuff and arrangements switcheroo. There is stuff, and stuff is always in some kind of arrangement - the cat is on or off the mat, the spoons are on the table or in the drawer, the ducks are in a row or not, the beans form a hill or do not. This is the reality about which we like to talk and share tales of. Cats and ducks and beans and spoons and arrangements and quantities and relations of them. Things arranged - cat on mat - each word refers to reality - things in relation. The relation is as real as the things. But it is not the stuff. This is conventionally physicalist materialist, but materialists do not deny the reality of structure and mathematics is the study of structure. One counts things, and one does not count nothing. one gets things in a row, or one on another, but not nothings. As they say in schoolboy physics, "state your units". There is no 'on' unless something is on another thing, and there is no 'five' unless there are five spoons, or beans, or schoolboys.

I don't disagree with anything you say there. But it doesn't seem to have any bearing on what I've been arguing. which is that there is something temporally persistent there which is reliably appearing as a door to both animals and humans. Sure animals don't conceive of it in human language, in English for example as a door; but, judging from their behavior, they certainly see it as a kind of affordance, as something like a "to be walked through".

I think we are in agreement, right up until:

And if you don't reference it or contemplate it, then there's no subject of discussion. — Wayfarer

I might read this in either of two ways. Perhaps as the tautology that if we do not talk about it, then it is not the subject of discussion. With that I agree. Alternately, that if we do not talk about it, then it isn't there. With that, I disagree. And indeed you seem to be saying the former, since you also say

I'm not saying that, therefore, the table or the spoons cease to exist when not observed, but that whatever you say, believe, or think about what exists or doesn't exist, depends on a framework of judgements which is a product of the mind. — Wayfarer

As for the universals and so on, one's mind only gets to organise the spoons into fives if there are indeed five. That seems to be 's point. So it isn't just mind that counts.

they're perceived by reason, not by sensory perception. — Wayfarer

But here:

At about age four or five a child stops having to count the dots and sees four.

All that, and yet there is a door.

That is, what exactly is added by the phenomenological analysis? Why wouldn't it 'drop out', like a boxed beetle?

Why wouldn't it 'drop out', like a boxed beetle? — Banno

Because it matters greatly when we get to the higher level of political, ethical, scientific and personal conceptualization. At these levels, ‘dropping out’ the acknowledgement that such frameworks of understanding, like simple perceptions, are not inner representations of pre-existing data but constructions which generate the criteria for the evidence that appears within them leads to political and ethical
violence, interpersonal conflictual and conformity rather than innovation. The important doorways in our lives are not geometric but metaphorical shapes. These are constantly shape-shifting, and we end up being barred from many opportunities to pass through new portals of
understanding because of our assumption that the empirically true is what persists in itself. independent of our conceptions. goals and aims.

Only what is derivative can drop out. Phenomenology is the condition of possibility for such notions as identical self-persistence, so one can bracket off what is empirically real as objectively present and not lose any of what is essential to experience
Boxed beetles drop out precisely because they become meaningless without their connection to contextual use. So what should drop
out isn’t the phenomenological analysis but the classical empirical assumption of self-identical persistence.
Heidegger makes such a point when he says that pointing to a door as simply an objectively present object rather than as part of a contextually relevant activity for us is failing to understand as it any more.

“ When we just stare at something, our just-having-it-before-us lies before us as a failure to understand ­it any more.”(Being and Time)

At about age four or five a child stops having to count the dots and sees four. — Banno

But that is due to the innate ability which is unique to human children. Some animals can recognise up to about 2-3, but I think the point stands. In any case it's a very simple illustration, humans can recognise all manner of complex symbolic relationships, something which to some extent is learned by experience, but unless the innate capability existed, then they would have no chance of learning it. No amount of effort has ever imparted significant language skills to non-human primates.

I think we are in agreement, right up until:
And if you don't reference it or contemplate it, then there's no subject of discussion.
— Wayfarer

I might read this in either of two ways. Perhaps as the tautology that if we do not talk about it, then it is not the subject of discussion. With that I agree. Alternately, that if we do not talk about it, then it isn't there. With that, I disagree. — Banno

As I said to Janus, the principle I'm calling into question is this one:

'The entities described by the scientific theory exist objectively and mind-independently. This is the metaphysical commitment of scientific realism.'

I am questioning that they exist 'objectively and mind-independendently', in other words, I'm questioning the metaphysical commitment to scientific realism.

0ne of our learned contributors made the point so well that I can do no better than reproduce it:

Traditionally, the discipline of Physics charts only the primary qualities of objects, events and processes i.e. their mathematical interrelations, where the relationship of their primary qualities to their secondary qualities (i.e. qualia) is ignored and undetermined. The reason why the secondary qualities are classically ignored by physics is as a consequence of traditional physics treating it's subject matter to be independent of any particular observer, which is itself due partly to convenience and simplification, and due partly as a consequence of the objective of physics to model the causal relationships that hold between action and consequence irrespective of the contextual nuances and discrepancies of any given observer.

Strictly speaking, the propositions of physics are senseless, like an unexecuted computer program, until as and when the propositions are used by an agent and thereby become grounded in the agent's perceptual apparatus in a bespoke fashion, at which point Locke's secondary qualities become temporarily welded to the physical concepts.

Classical physical concepts are therefore by design irreducible to mental concepts; something has been a central feature of physics rather than a bug, at least up until the discovery of special relativity and quantum mechanics, both of which show that even the Lockean primary qualities of objects are relative to perspective. — sime

The key point is the very last one. Indeed this is why I keep arguing, to much general annoyance, that the net effect of early 20th C physics has been to undermine scientific realism (and thereby classical materialism). The role of the observer is inextricably entwined with any statements, even those that are 'true for all observers'. For practical purposes they can be 'bracketed out', but it's when this 'bracketing out' is taken to be a philosophical principle, rather than a methodological step, that 'scientism' enters the picture.

At about age four or five a child stops having to count the dots and sees four.
— Banno

But that is due to the innate ability which is unique to human children. Some animals can recognise up to about 2-3, but I think the point stands. In any case it's a very simple illustration, humans can recognise all manner of complex symbolic relationships, something which to some extent is learned by experience, but unless the innate capability existed, then they would have no chance of learning it. — Wayfarer

Recognizing 4 dots as the number 4 is just pattern recognition , not a mathematical ability. This is no different than recognizing a bunch of lines as a house. The pattern of dots on the dice begin to look like a picture of something , in this case a particular number, when the concept 4 is paired with the pattern of dots enough times. This is not unlike a dog associating the sight of a food dish and the sound of a crinkling package with the image of food.
What is innate is simply synthesizing new levels
of sense on the basis of what appears similar to something else. The similar becomes fused in our mind with what preceded it and we then have a néw unity. Animals do this too, but their synthesizing abilities fall
far short of ours, which is why their language capabilities are so rudimentary.

I like the rest of your post.

there is something temporally persistent there which is reliably appearing as a door to both animals and humans. Sure animals don't conceive of it in human language, in English for example as a door; but, judging from their behavior, they certainly see it as a kind of affordance, as something like a "to be walked through". — Janus

Maybe we can agree that what is
‘temporally persistent’ doesn’t have to mean temporally self-identical in order to give rise to the appearance of enduring objects. But keep in mind that whatever it is that appears immediately before us and other animals in perception is just a small part of what we actually experience as actually present. The rest comes from memory and is fused with that small bit of stimulus that comes to us from outside.

We can see how important this synthesizing filling in becomes when we think about how much of our human environment consists not of simple physical entities but of cultural value objects. In our homes , for instance, chairs , appliances, cupboards , couches , computers , these are all objects for us based on how we use them. A chair is for sitting, a cupboard is for storage, etc. How we look at such things , how we interact with them, even our ability to see them as single, unified objects , is dependent on our understanding of what they are for.
Does a dog see a computer a s a single entity? How could it? A desktop computer is a mouse, maybe a tower , a monitor , maybe a printer. But to a dog they are only objects to the extent it can grab them in it’s teeth and move them around. The same is true of a three dimensional carving of a chinese word symbol. To the dog and to the human. who doesn’t recognize it it is a random pattern of lines and curves. Are they seeing the same thing as the person who can read it ? No, that person has synthesized something more complex. Is the symbol less real than what the animal sees?!Not if we propose that an ‘object’ is a way in which an organism interacts with an aspect of its world. Almost all
of the culture objects in the human world are objects that don’t exist for other animals because their interaction with their world is so much simpler.

Piaget never renounced the notion of the real , but said that human individual and cultural development was a process of embedding the real within more and more differentiated schemes of relation. He said we were always on the way to the object, that objectivity was an asymptotic limit towards which human knowledge progressed. What he meant was that the reliability you associate with persistent objects like rocks and doors , only is really attainable as we create more and more complex schemes of reciprocal
relation to allow us to predict and anticipate the changes in our world in more and more adequate ways.


Persistence and self-identicality don’t add up to meaningfulness , reliability and usefulness if they are meant to pertain to what something supposedly is in itself outside of its role in an organism’s functioning.

Recognizing 4 dots as the number 4 is just pattern recognition , not a mathematical ability. — Joshs

If that were so then the position of the dots would make a difference.

It doesn't.

Subitising is more than just pattern recognition, although that is part of it.

Recognizing 4 dots as the number 4 is just pattern recognition , not a mathematical ability.
— Joshs


If that were so then the position of the dots would make a difference.

It doesn't. — Banno

We can also learn to immediately recognize a patten of 5 or 6 dots as their corresponding numbers. The more dots that are involved , the more important the placement of the dots is. My own experience with dice is certainly that way. I instantly know what ‘5’ looks like because I’m familiar with their placement on the dice. Change that pattern and I guarantee you there will be a slight lag before I process it as 5.

“In playing dominoes, for example, we grasp groups of ten to twelve dots with one glance. Indeed, we even assess their number with total immediacy. It must be observed, however, that in such cases we can speak neither of an actual colligating nor of an actual enumerating. The number name is here directly associated with the characteristic sensuous appearance, and is then recalled on each occasion by means of that appearance without any conceptual mediation. With groups that large, as everyone can test, a direct and authentic collection and enumeration is an impossibility.” (Husserl, Philosophy of Arithmetic)

Meh. There's plenty of academic research out there on the topic. It's an ongoing debate of some pedagogic import. At the very most, it is a combination of pattern recognition and number sense. What you see in a die is irrelevant. As are Husserl's armchair musings.

Same holds for most of what philosophers like to call innate abilities.

Tell me what you think is going on when someone instantly recognizes the number 4 in a pattern of 4 dots. Or for that matter , when a savant reads off pi to 100 decimal places , because the two skills are closely related( Daniel Tennant described how he did it. He visualized the numbers as a landscape.It had nothing to do with a calculative skill )

What you see in a die is irrelevant. As are Husserl's armchair musings. — Banno

Here’s some more armchair musings from Husserl. You’re going to have to refute them with your own arguments. Let the show begin.

In Chapter XI we treated in detail the problem of how immediate appraisal of groups comes about without the actual carrying out of the relevant psychical activities - those of individual appre-hension and collection. A unitary intuition is given to us, and in one glance we judge: a group of balls, coins, and so on. To explain this peculiar fact we referred to the figural Moments of the unitary group intuitions which enter into an association with the name and the symbolic concept of the multiplicity - mediating the reproduction of the latter, and thereby making possible the immediate appraisal of the phenomenon as a group. Immediate number estimation presents a quite similar problem and the means referred to completely suffice for its solution.

The matter stands forth most clearly in examples, as is abundantly illustrated in play at dice, dominos and cards. Each surface of a die possesses a characteristic fixed configuration of dots which enters into an association with the number name (or with the symbolic concept of a certain number named by it). If several dice are thrown simultaneously, then either there occurs a rapid quasi-summation utilizing the tables of addition - in which, of course, the mere number words intervene - or else, given long practice, the number word corresponding to the sum of dots is reproduced immediately by means of the figural character of the total complex phenomenon.

The number of configurations to be impressed upon us for this is in fact only a limited one. The same holds true for play with dominos, and it is well known what a knack experienced players have for instantaneous estimation of numbers. They often can count up to forty dots in one glance. In the examples considered up to now the configurations were of a fixed type, or even more so, were closely related in type. In order to explain the latter case it should be pointed out that a die surface, for example, in each change of position through rota-tion, receives another figural character, and that it therefore must basically be the corresponding generic character that establishes the association [with the number]. This observation makes it clear that the difference between the cases considered and others where wholly arbitrary distributions of objects are estimated as to number is not so great as it might at first appear. However three cleanly separated objects may be distributed in the field of vision, they together form a characteristic configuration -presupposing that they can in general fuse into an intuitively unitary appearance of a group.

The various three-point configurations which arise, depending upon the varying relative positions of the objects, are indeed well-distinguished in intuition. But they possess so much striking analogy that the character common to them all can mediate with certainty the reproduction of the number three (or, more precisely, of the name "three," along with the symbolic concept of a specific number named by it). A some-what more essential difference is exhibited by the figural character only in cases where the three objects come to lie in a straight or approximately straight line: a boundary case whose quite noticeable special character makes possible the association of the number. It is similar with groups of four objects. Here the configuration exhibits either the familiar quadralateral type, or else other characteristic types show up - as when all four or any three of the objects lie in a row, or when one object falls within a triangular figure formed by the three remaining ones. And so on. The more objects the group includes, the greater is the re-spective number of intuitively distinct figural types, and thus it becomes understandable why in reliable number estimation we usually do not get past groups of five members - unless by means of constant, methodical practice. Preyer, who did experiments on this, is of the opinion that in the latter case the attainable limits may lie, on the average, at twenty. Nevertheless, the famous calculator Dahse could instantaneously estimate some thirty arbitrarily distributed objects.”


“…after repeated enumeration of many types of object distributions, the number names enter into fixed associations with their typical figural characters. Moreover, I would hold it to be quite well possible that even someone completely ignorant of enumerating could bring the number names into association with those figural characters, and develop into a skillful domino player, for example.”

Scans appear to show the brain area used in subitizing is the same as used for counting, not for recognising patterns; it's not settled, but it's not simple.

https://www.mathematicalbrain.com/pdf/SUBIT.PDF

...these results do not confirm the existence of a dedicated neural system for subitizing that is not involved in counting. The previous hypothesis that sub- itizing and counting are two qualitatively different mechanisms based on two separate networks does not receive confirmation from the present study.

Notice that pattern recognition played the same role in subitizing and in counting.

You’re going to have to refute them... — Joshs

No, I don't. The science will settle the issue. Subitizing is not just pattern recognition, but involves counting.

Edit: Just to make my point clear, your claim was that subitising is just pattern recognition. In this study it was shown that pattern recognition showed up in groups of four or less, and also in groups of more than four. That is, pattern recognition was found in both subitising and counting. It has a part to play, but is not the whole of the story.

@Isaac?

Same holds for most of what philosophers like to call innate abilities. — Banno

yes well sometimes their absence also makes itself reasonably clear.

There's a true saying, 'you can't fake talent'.

I agree that pattern recognition and counting are different abilities. I thnk too much importance is accorded to the former by a lot of people.