The unsupportability of realism about abstract objects

@TuringEquivalent,

TuringEquivalent wrote:

Any physical model in physics are mathematical in nature. It describes an abstract object.

Only if abstract objects exist, which is what you still haven't given any argument for.

TuringEquivalent wrote:

When the physical theory is good, the abstract object in question is a good model for the real world.

If abstract objects can be false of the actual world, how can they be essential for physics? How can they be true of the phenomenal world other than by coincidence? And, again, how do they make statements true?

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@ughaibu,

As I never understand anything you say, I might as well fire away at random in the hope that I might hit something.

I don't think there are any such thing as 'abstract objects' (any more than 'spiritual substance' or 'a being called God'). Numbers, (and forms, and ratios) are not objects at all, but are attributes of the way everything is related. Ratio does not exist, but it is real. Matter exists, but is real only insofar as it is 'given form' (i.e. made rational). Things are only rational insofar as they instantiate the forms and relationships that we are able to represent by way of mathematics and logic. They are only real insofar as they are realizable, and they are only realizable if they are intelligible. So matter itself, although it exists, is the least real level of existence. The only reason anything exists as an object, and the only reason we are able to scrutinize it, is because it has been given form, and we have been given (=evolved) reason. In itself, matter causes nothing and does nothing. It is completely inert and only intelligible because of the emanation of the formless mind that literally 'informs' all of existence (although 'formless mind' should never be mistaken for something or re-ified. All we will ever know are the ratios, not the source of the order.)

Now I guess that nobody accept this is because we are all materialists nowadays, and I really don't know if it is true. But it makes sense, whether it is true or not. According to this view, we think that the least real type of thing is the only reality. This is why nothing makes sense. But this philosophy proposes that the solution to all of it is completely obvious, and that is, that matter is unreal.

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@jeeprs,

jeeprs wrote:

I don't think there are any such thing as 'abstract objects' (any more than 'spiritual substance' or 'a being called God'). Numbers, (and forms, and ratios) are not objects at all, but are attributes of the way everything is related.

That seems uncontroversial, to me.

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@ughaibu,

well that is encouraging, at least.

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@ughaibu,

How are abstract objects supportable without realism? How is it even possible to form abstract objects without it?

Abstract...
Realism...
T

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@ughaibu,

I'm struggling with this thread which appears to be the epitome of what Wittgenstein called "language on holiday".

Lets take "realism". My take on this is that it is about a consensual views of what constitutes "reality", and these are essentially concepts which inform our actions. So whether we relate to such concepts "physically", "emotionally" or "intellectually", they can be termed "real"...they have functional import..[/b]

As for "abstract objects", like "the USA", "a dollar", the "cube root of 10" or "my ambition" they are merely concepts which we cannot directly describe with reference to the concept of our perceptual apparatus. Note that this implies that atoms and sub-atomic particles should be deemed "abstract".

As far as "mathematical entities" are concerned like "the negative roots of an equation", they may or may not give rise to investigative action with respect to predictions of "data collection". During the process of investigation they remain "real", but if no data are forthcoming their status becomes "irrelevant" not "abstract". This is not to say that this status cannot change at a later time.

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@fresco,

Rephrase of last paragraph

As far as "mathematical entities" (which by my definition are abstract) ..as far as they are concerned like "the negative roots of an equation", they may or may not give rise to investigative action with respect to predictions of "data collection", or purely intellectual activity. During the process of investigation they therefore remain "real", but if no data are forthcoming their status becomes "irrelevant" . This is not to say that this status cannot change at a later time.

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@fresco,

I think the whole difficulty with this argument is always determining the meaning of the word 'exist' with regards to the nature of abstract objects. Basically it is a question of ontology. It is probably impossible to reach any kind of consensus view as this has been disputed since Parmenides. I think there is an answer or solution to it, but not within the confines of analytical philosophy. The answer must involve some concept of the hierarchical nature of reality which comprises a number of layers; in other words a hierarchical ontology. I think scholasticism and Platonism provide an hierarchical ontology, but nominalism and science deny it. Therefore the accepted view (which is nominalist/scientific) is that a thing either exists or it doesn't and this applies in the same sense to material and abstract objects. 'Existence' is univocal. We have thrashed this out a number of times in the recent past. 'Six', 'salmon' and 'irony' all exist. They don't exist 'in different ways'. There are no 'ways' in which something exists - either it exists or it doesn't.

In an hierarchical ontology, different classes of thing have different degrees of reality. Typical of this type of ontology are Aristotle's four levels of causality - material, efficient, formal, and final. As far as this outlook is concerned, modern philosophy is trying to account for everything on the same level.

I don't have a reference for a really useful, up-to-date presentation of such an ontology - it is something I would like to get hold of. But the point of it is that there are different types of organizing principles at work at each level. The mathematical relationships belong to the formal level, whereas the 'creative act' arises from the causal level.

At the same time the traditional understanding of the heirarchical nature of being must be updated in light of the discovery of relativity and evolution. So it needs to be re-interpreted, but not simply discarded.

Probably the only source of any of this is Ken Wilber although for some reason I don't want to go there.

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@jeeprs,

I agree.
"Existence" is the basic issue and where a stand is taken between "realism" and "nominalism". I clearly take the latter end, following the adage:
........man is the measure of all things.......
the first level of measurement being "the nominal".

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@jeeprs,

jeeprs wrote:

I think the whole difficulty with this argument is always determining the meaning of the word 'exist' with regards to the nature of abstract objects.

Realists make a specific claim, and that claim is either contentious or it's trivial. Under the principle of charity, one assumes that their claim is contentious, so their claim cannot be addressed by interpreting terms in such a way as to render it trivial. As far as I can tell, neither you nor Fresco are supporting non-trivial realism, but as you're posting on this thread, presumably you both have something relevant to say, but it's not clear what that is.

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@ughaibu,

Are you referring to modern realists, or to scholastic/platonic realists, because their beliefs are diametrically opposed.

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@jeeprs,

jeeprs wrote:

Are you referring to modern realists, or to scholastic/platonic realists, because their beliefs are diametrically opposed.

The opening post, written by me and referring, states

ughaibu wrote:

realism about abstract objects.

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@ughaibu,

The Stanford article about 'abstract objects' states that

Quote:

The contemporary distinction between abstract and concrete is not an ancient distinction. Indeed, there is a strong case for the view that despite occasional anticipations, it plays no significant role in philosophy before the 20th century. The modern distinction bears some resemblance to Plato's distinction between Forms and Sensibles. But Plato's Forms were supposed to be causes par excellence, whereas abstract objects are normally supposed to be causally inert in every sense.

The article further states that

Quote:

Frege concludes that numbers are neither external ‘concrete’ things nor mental entities of any sort...He says that they belong to a "third realm" distinct both from the sensible external world and from the internal world of consciousness.

This is close to what I think about it (note to self: must read up on Frege.) But perhaps this 'third realm' is actually 'reality' - neither 'the sensible external world' nor 'the internal world of consciousness' but that which includes but transcends both. That's why nobody can work out where it is. Perhaps, then, abstract objects are actually objects not within the empirical realm, nor within the individual mind, but intrinsic to the nature of reality. Now, of course, neo-platonists would have no problem thinking like this, but empirical realists cannot. So it is 'off-limits' to current philosophy, even if it appears to be true. But I think as an idea, it presents the solution we are looking for.

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@jeeprs,

jeeprs wrote:

This is close to what I think about it (note to self: must read up on Frege.) But perhaps this 'third realm' is actually 'reality' - neither 'the sensible external world' nor 'the internal world of consciousness' but that which includes but transcends both.

In that case, it appears that you are a realist. Can you meet the arguments in the opening post?

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I quit trying to keep up here. This has gone over my head.

This thread has become too crunchy of granola for me, and I don't eat meat, so that says a lot. This hippie, can't swim that deep. I'm to utilitarian perhaps?

A
R
T

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@ughaibu,

Well I am working on it, but it is a difficult argument. I do appreciate the opportunity to discuss it. There is another piece of supporting material I would like to introduce first, from the Cambridge Companion to Augustine

It is very interesting that almost all of the things he attributes to 'intelligible objects' can also be attributed to 'number'. And I think the other type of thing that we still recognize in the modern world is scientific or natural law (particularly in regards to 3).

Quote:

1. Intelligible objects must be independent of particular minds because they are common to all who think. In coming to grasp them, an individual mind does not alter them in any way; it cannot convert them into its exclusive possessions or transform them into parts of itself. Moreover, the mind discovers them rather than forming or constructing them, and its grasp of them can be more or less adequate. Augustine concludes from these observations that intelligible objects cannot be part of reason's own nature or be produced by reason out of itself. They must exist independently of individual human minds.

2. Intelligible objects must be incorporeal (see below) because they are eternal and immutable. By contrast, all corporeal objects, which we perceive by means of the bodily senses, are contingent and mutable. Moreover, certain intelligible objects - for example, the indivisible mathematical unit - clearly cannot be found in the corporeal world (since all bodies are extended, and hence divisible.) These intelligible objects cannot therefore be perceived by means of the senses; they must be incorporeal and perceptible by reason alone.

3. Intelligible objects must be higher than reason because they judge reason. Augustine means by this that these intelligible objects constitute a normative standard against which our minds are measured. We refer to mathematical objects and truths to judge whether or not, and to what extent, our minds understand mathematics. We consult the rules of wisdom to judge whether or not, and to what extent, a person is wise. In light of these standards, we can judge whether our minds are as they should be. It makes no sense, however, to ask whether these normative intelligible objects are as they should be; they simply are and are normative for other things. In virtue of their normative relation to reason, Augustine argues that these intelligible objects must be higher than it, as a judge is higher than what it judges. Moreover, he believes that apart from the special sort of relation they bear to reason, the intrinsic nature of these objects shows them to be higher than it. These sorts of intelligible objects are eternal and immutable; by contrast, the human mind is clearly mutable. Augustine holds that since it is evident to all who consider it that the immutable is clearly superior to the mutable (it is among the rules of wisdom he identifies), it follows that these objects are higher than reason.

I will have another look at the questions you have set out shortly.

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@jeeprs,

jeeprs wrote:

It is very interesting that almost all of the things he attributes to 'intelligible objects' can also be attributed to 'number'.

Quote:
1. Intelligible objects must be independent of particular minds because they are common to all who think.

Take the case of a square, this is something which exists physically, mentally and is assumed by realists to exist abstractly. Two independent minds can arbitrarily assign units to measure the edge of that square, one mind measures the edge as 1 and the other measures it as 2, this means that for mind number one the area of the square has a number equal to its edge, but this is not true for mind number two. So, I reject the claim that numbers exist independent of particular minds.

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@ughaibu,

Quote:

supernatural solutions are not satisfactory and realism about them shouldn't be adopted for its psychological advantages
f) unless we can demonstrate that explanatory completeness is available to humans, we have no reason to suppose all problems have solutions, and as explanatory completeness appears to be impossible for humans, we should not adopt beliefs that assume the truth of explanatory completeness.

This is an abuse of skepticism, which cannot determine a prior whether a solution might be natural or supernatural. It is after all strictly speaking impossible to specify the extent of nature, and so, what might be 'super' to it. it is apparent that our knowledge of nature is full of holes, yet this declares that it is only here that we can look. Philosophical skepticism does not advocate making such a judgment; it is, rather, the suspension of judgment ('epoche') about what we believe to be true. So this is not skepticism, as such, but rather an a priori philosophical commitment to the types of ideas that will or won't be entertained, masquerading as skepticism, which is what 'modern skepticism' usually is.

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@ughaibu,

your objection only addresses the symbol, not the measure.

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@jeeprs,

jeeprs wrote:

This is an abuse of skepticism, which cannot determine a prior whether a solution might be natural or supernatural.

I dont think that's relevant, because abstract objects are defined as external to the natural world. If this is not the case, then realists lose their recourse for denial of the existence of unicorns.

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The unsupportability of realism about abstract objects

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