A Defense of Berkelean Idealism: How Size is not Objective

Introduction:

Berkeley's idealism is a response to epistemological theories of the mind proposed by contemporary philosophers David Hume and John Locke, who propose the mind operates on an imagistic model, meaning the mind works off of perceptions more than anything else. His work was primarily concerned with criticizing indirect realism, which defends there is a truly independent and objective world which our imperfect perceptions cannot fully apprehend so thus our perceptual world, the one we live in, is an interpretation or representation of the truly objective. He does this by adopting a theory of idealism debunking the notion of an objective world and instead advancing that our perceptual world is actually wholly dependent on the mind. This article will outline a criticism toward's Berkeley's account of shape, where he argues shape is not an objective quality of objects because an object's size is dependent on the perspective it's seen from. I outline how this point is inefficient in defending Berkeley's theory, and provide a counter-argument which aims to challenge a conventional understanding of size while maintaining Berkeley's theory. I explain how size depends on the scale of measurement and why measurements cannot provide evidence of true size; thereby maintaining the mind-dependence of shape by eliminating the notion that it is objective in any way.

In A Treatise Concerning the Principles of Human Knowledge (1710), and Three Dialogues between Hylas and Philonous (1713), referred to as Three Dialogues from here on, Berkeley approaches each of the qualities which objects are known to have and poses arguments for how they don't inhere within the objects themselves but rather in the mind of the observer. These qualities were detailed by John Locke in his An Essay Concerning Human Understanding (1690), where each object is given primary qualities, which inhere within the object itself, and secondary qualities, which depend on the situation of the observer. The primary qualities including size, shape, and weight; while the secondary qualities include colour, taste, and smell. Berkeley's goal is to show how each of the primary qualities depends on the mind, rather in these objects, so he can advance his own idealism. 

Confusing Apparent and Actual Size:

If you look up toward a visible moon you could fit the moon, in its apparent entirety, between your fingers and thumb, yet we know that's not representative of the moon's actual size (1737.1 kilometres in radius). The average human hand is 7.2 inches in length, much too small to contain the true size of the moon between its fingers. This occurs because of the distance between the moon and your hand, making the apparent size of the moon from your perspective small enough to fit between your fingers.

Berkeley uses this fact to argue that size is not objective since an objects size depends on the position from which you observe it. This can be found in Three Dialogues (p.13), where the protagonist Philonous exposes, what he believes to be, a contradiction in Hylas' judgement that the true size of an insect's foot is the size which the insect sees, a human sees and what every animal would see despite those sizes all appearing different due to their differing physical perspectives. If the sizes do indeed appear different, and they are all the true size of the insect's foot, he argues; then it can't possibly be the case that the insect's foot has a fixed, inherent size. Berkeley has written the character of Hylas to be an advocate of the physicalist theories he argues against and Philonous is the expositor of his own ideas. This exchange seeks to shows the absurdity of the physicalist's claim that an object has a fixed size, yet it would appear Philonous is conflating actual and apparent size with each other.

This mix-up is later addressed in the same text when Hylas has the following to say: "... Granted that large and small consist merely in the relation other extended things have to the parts of our own bodies, and so aren’t really in the substances themselves; still, we don’t have to say the same about absolute extendedness, which is something abstracted from large and small, from this or that particular size and shape..." (p.15). This part of the text touches upon a different key aspect of Berkeley's theory. Philonous retorts to Hylas that "everything which exists is particular" (p.16), so if absolute extendedness (size) exists it must be particular and have qualities, but since absolute extendedness is removed from any such qualities it can't be reasoned to exist. Thus, notions of an objects actual size are to be discredited under false premises. Berkeley appears to have multiple answers to this single point (a characteristic of his works as a whole) and I aim to show how this point specifically does not falter despite this apparent flaw.

The difficulty in Philonous' explanation about the insect's foot arises when we consider principle of measurements. It can very easily be criticized by stating that the size of the insect's foot is still indeed fixed, and it is rather the difference in distance of the perceiver that's causing the apparent discrepancy in size, just like the earlier example of the moon. The apparent size and the actual size is different. While the apparent size can change, the foot does have an actual size which is a fixed value. Thus, in this moment, Philonous appears to be confused about this distinction, citing the apparent size of the foot to be evidence that it doesn't an actual fixed size.

I will now propose a counter argument to show how this doesn't threaten the argument made by Philonous.

The Matter of Scale and the Lack of Evidence of Absolute Size:

The actual size of any object, moon or insect foot, is very difficult if not impossible to obtain. Scientific methods of measurement use standard units which can all be converted between each other. 1 kilometre is 1,000 metres and each metre is 3.28084 feet, making 1 kilometre 3280.84 metres in magnitude. Despite the different units used they each represent the same total space. We can get more accurate results by increasing the number of decimal places, though its generally unnecessary to do so without cause. By convention, we round to a number found to be most relevant to the style of measurement, some examples of which include: counting decimal places, rounding to the nearest whole number, or establishing a relevant number of significant digits to use. The difference between 1 centimetre and 1.0002 centimetres is too insignificant of a change, so, by convention, we would simply use 1cm instead. But, if we are using the most precise measuring instruments, 1.0002cm would be the more accurate measurement in an ideal world where margins of error don't exist (which we can assume is the case of the truly objective world, proposed by indirect realism). We must acknowledge that the two values listed above are indeed two different numbers, but due to convention the practical notation of "1cm" would imply a margin of error between the measurement of "1cm" and the next unit on the measuring tool, such as 1 millimetre (mm) used on conventional school-grade rulers. We can develop this point by considering even smaller units of measurement, getting more precise with smaller units to get a more accurate account of any object's size. It's theoretically possible to continue this ad infinitum, though this is practically impossible. Thus, the actual size of any object cannot be known in this manner and we have no real evidence objects have an "actual size".

An alternate method which some might argue would be to count the number of atoms and the space between them to get the most accurate representation of an object's true size. This would involve measurements on the quantum level, wherein the locations of subatomic particles become probabilities due to the wave-particle effect where any particle can be described either as a particle or wave. Waves themselves are spread out across many points in space and cannot be singled out to any one specific point. This suggests, on a small enough scale, the precise location of particles become a probability rather than determinate, thus the exact locations cannot be determined on scales this small. This doesn't provide any evidence that objects have truly objective and fixed sizes and are thus still dependent on something other than an independent objective reality. Heisenberg's Uncertainty Principle, detailed in a paper titled Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik (1927:1977), translated to The Actual Content Of Quantum Theoretical Kinematics And Mechanics, states that it is not possible to know both the exact location of a particle alongside it's momentum due to the limitations of the precision of measurements. This limitation, I believe, supports the claim that there is no evidence objects have fixed sizes.

A possible counter-point to my argument is to consider an objects size at an individual moment of time rather than across the length of time taken to perform the measurement. If we eliminate change, then it would be possible to get an exact account of the location of every particle, and the distance between, within an object, and thus get an accurate size of it in that one "snapshot" taken out of time. I would argue that in this "snapshot", on a quantum level the particles involved would still exhibit wave-like behavior and thus still have no fixed position, therefore the object itself would still have no fixed size.

Conclusion:

With my counter argument out of the way, I must state that, while I have studied physics at university level, including modules on quantum mechanics, I am not well versed or comfortable in my knowledge of the topic to provide more precise details of the wave-particle duality or Heisenberg's Uncertainty Principle, so my scientific accounts are lacking in detail. However from a philosophical perspective I feel I have represented my current thoughts well enough to satisfy its purpose for this article.

I believe this resolves the issue Berkeley wrote into Philonous' account of size by showing that, even if Berkeley did confuse actual and apparent size with each other (which, as established, wouldn't actually discredit his overall theory), his conclusion in the Three Dialogues still holds on the basis that an object's actual size doesn't depend on a possible objective counterpart as objects have no fixed sizes because of the sheer impossibility of measuring it, and we have no evidence to believe actual size even exists externally of the mind.

References & Bibliography:

Berkeley, G. Three Dialogues between Hylas and Philonous (1713), in the version presented at www.earlymodernexts.com [Accessible at: https://www.earlymoderntexts.com/assets/pdfs/berkeley1713.pdf] [last Accessed: 16:44 09/05/2020]
Berkeley, G. The Principles of Human Knowledge (1710), in the version presented at www.earlymoderntexts.com [Accessible at: https://www.earlymoderntexts.com/assets/pdfs/berkeley1710.pdf] [Last Accessed: 16:46 09/05/2020]

Heisenberg, W., The Actual Content Of Quantum Theoretical Kinematics And Mechanics (1983). Washington, D.C.: National Aeronautics and Space Administration. Translated into English from Z. fuer Phys. (West Germany), v. 43, no. 3-4, 1927 p 172-198

Locke, J. Essay Concerning Human Understanding (1690), in the version presented at www.earlymoderntexts.com [Accessible at: https://www.earlymoderntexts.com/assets/pdfs/locke1690book2.pdf] [Last Accessed: 16:48 09/05/2020]