A. Corpuscularianism and Bk's worries

• corpuscularianism:
1. Its main features (e.g. Boyle): matter is a passive substance resolvable in corpuscles endowed with primary qualities, and therefore subject to mathematization
2. Its role in modern science from Descartes to  Newton.
• Bk's worries: The admission of matter leads to:
1. atheism because it removes God too far from nature
2. impossibility to show that God is immaterial
3. scepticism because matter cannot be known directly due to a representationalist theory of perception. As Bayle notes, if secondary qualities are in the mind, why not primary ones? If so, what do we know about matter?

NOTE: these concerns are evident in the full title of the Principles: A Treatise concening the Principles of human knowledge wherein the chief causes of errors and difficulty in the sciences, with the grounds of scepticism, atheism, and irreligion, are inquired into.

The origin and nature of ideas
Ideas come from sensation and reflection (not clear whether in Lk's sense)
NOTE: standard empiricist account. Bk gives little argument for it.
For ideas, to be is to be perceived (esse est percipi).
In perception, the mind is totally passive; there is no act of perception.

C. Attack on the notion of matter.
Bk's arguments vary greatly in quality, in what they try to achieve, and in the premises they use. However, they can be roughly be divided into two groups:
1. Arguments trying to show that the notion of matter either inconsistent or ultimately unintelligible.
2. Arguments trying to show that the notion of matter is redundant.

Here we just look at some.

1. Notion of matter inconsistent or unintelligible.

Perception argument (P4-5)

1. Matter is a sensible object having a natural or real existence distinct from its being perceived by anyone.
2. A sensible object is something that can be perceived.
3. We perceive only our ideas.
4. An idea cannot be separated, even in thought, from its being perceived.
5. Therefore, a sensible object cannot be separated, even in thought, from its being perceived.
6. Therefore, the very notion of matter involves a contradiction.

Qualities argument (P7-9)

1. Matter is an unthinking substance in which extension, figure, motion etc., subsist.
2. Extension, figure, etc., as they subsist in matter, must be either what we are acquainted with under those names, or else something resembling what we are acquainted with under those names.
3. What we are aquainted with as extension, figure, motion etc. are ideas.

NOTE: We perceive only ideas principle
4. An idea can resemble only another idea.

NOTE: Idea-resemble-only-idea principle
5. Therefore, extension, figure etc. can be only ideas.
6. An idea can subsist only in the thinking substance which perceives it.
7. Therefore, it is contradictory to suppose that extension, figure, etc. subsist in an unthinking substance.
8. Therefore, the very notion of matter involves a contradiction.

1. Matter is the substratum of material qualities
2. The notion of substratum is merely metaphorical
3. Therefore, there is no distinct meaning attached to the words "material substance"
4. Therefore, the notion of matter is unintelligible.

2. Notion of matter redundant:

Knowability argument (P18-9).

1. The existence of matter must be known either by sensation or by reason.
2. Sensation only acquaints us with ideas.
3. Therefore, the existence of matter is not known through sensation.
4. We might have all the ideas we have now without any body existing.
5. Therefore, we cannot infer that matter exists from the claim that we have ideas.
6. Therefore, we cannot know with certainty that matter exists.
7. The alleged causal link between material objects and ideas is unknowable in principle, as Representationalists allow.
8. Therefore, we cannot claim that the existence of matter is probable because it is the best explanation for our having ideas.
9. Therefore, we cannot claim that the existence of matter is certain or even probable.
    

D. Bk's system and why he thinks it superior to Descartes' and Locke's.
1. The two systems:
Bk: Minds, ideas (esse est percipi) and God the direct cause of sensation. Objects as collections of ideas: no matter.
Descartes and Locke: Minds, ideas (esse est percipi), matter (cause of sensation and subject in which the qualities representad by ideas of the senses ultimately reside), God.

2)Why Bk thinks his superior:

• Notion of matter inconsistent or unintelligible.
• We cannot know either with certainty or with probability that matter exists (knowability argument)

Problem: these arguments not convincing.
• There is no need matter. This is both:
• Simpler than Descartes and Locke (no need of duplication beyond the veil of perception)
• More pious for it does not assume God uses instruments (material bodies) to produce sensation in us. Use of instruments denote lack in the agent (P60).
• Brings God at the center of our lives. Every time we sense, we know of God's operation on us.(P149)
• It satisfies common sense.

Problem: far from clear (see below). However, Bk might merely mean being able to speak with the vulgar, like the Copernican who says that the sun is rising.
• Removes risks of scepticism by eliminating matter.

E. Problems with Bk's system:
Some alleged problems not serious, e.g, we eat ideas; Swift leaving Bk on the doorstep because he should be able to go as easily thru a closed door as through an open one (denial of matter); Dr. Johnson kicking the stone.
However, some problems having to do with the distinction between dream and reality, the intersubjectivity of objects, and the continuity of unperceived objects are serious.

F. God
We know God exists because he must be the cause of some of our ideas.
The Argument:

1. Ideas must have causes
2. some of my ideas are independent of my will and, because of the transparency of the mind, I know are not caused by me.
3. hence, they are caused by other spirit(s).  But given the orderliness and enormous complexity of my sensations, they can be produced only by God.
4. Therefore, God exists, and I can be assured of it as soon as I open my eyes.

Problem: God causes in me certain sets of ideas which constitute objects I sense. Among these is my body. Hence, it would seem that I cannot be the cause of the motions of my body. So, Bk owes us an expalnation of freedom, which he does not give.

G. Empirical science.

Theoretical entities.
Notions such as force, attraction, gravity, imperceptible corpuscles, natural powers are merely theoretical; they are parts of complex theories understood not in terms of realism, but in terms of instrumentalism (prediction of phenomena). Possible equivalence of Copernicus and Ptolemy (Siris, 228).

Attack on Newton's absolute space/time, motion/rest (P110-17) .
Newton took space to be an infinite immovable, indivisible quasi-container, penetrating everything, and an attribute of God.  The existence of absolute space was taken to be experimentally proved by the bucket experiment (whether this was Newton's view is unclear)  Absolute space is to be distinguished from relative space.
Bk's critiques:

• We do not perceive space itself, as N. admits. Hence, absolute space is an abstract idea, i.e. no idea at all.(P116)
• Absolute space takes on divine features, which is impious (P117)
• Bucket experiment invalid.  Motion must be perceivable; consequently, it requires two bodies whose reciprocal distance varies (also, the body moved must have a force applied to it P 114). But when N. claims the water in the bucket has the greatest motion (i.e. when bucket  "moving" as well), it has no motion at all. (P112)

H. Mathematical sciences

Arithmetic and Geometry (P 118-32)
Formalistic view of Arithmetic as a science of signs (P 122), since we have no idea of unity, and hence of numbers, which are but collections of unities. All these are abstract ideas, and hence no ideas at all (P 120)
Originally Bk had a a quasi-empirical view of Geometry (minimum sensibile) and seemed to claim that classical geometry can be reconstructed in that way (P 132).  Notice his critique of infinite divisibility, infinitesimals, and traditional geometrical notions (e.g. line=length w/t breadt) as abstract ideas, and hence absurd. (P 130)
Problem: no incommensurables.
Later, he seems to have adopted a formalist view (De Motu, par. 39)

Calculus (The Analyst, 1734)
Against scientists like Halley, who ridiculed Christian dogmas, e.g., trinity, as absurd, Berkeley produced a very clever critique of calculus.  Here's the gist of it.

Given any straight line TL (see fig.), the ratio between LM and TM (or LR and BR) is the slope of TL.  The slope of a line and a point of the line determine the line. Hence, finding the slope of the tangent TL to a curve at a point B is sufficient to determine TL fully.  Infinitesimal calculus provides an easy way to find the slope. What follows is a specific example of how a Leibnizian would proceed in the case of a parabola of equation x=yy. [I use yy for y squared].
1)x=yy                    (equation of parabola; see fig.)
2)x+dx=(y+dy)(y+dy)         (This means that the point N belongs to the parabola)
3)x+dx=yy+2ydy+dydy  (from (2) by algebra)
4)dx=2ydy+dydy          (from (3) using (1))
5)dx/dy=2y+dy            (from (4) dividing by dy)
6)dx/dy=2y                 (from (5) by omitting dy)
So, 1/2y is the slope of any tangent to the parabola of equation x=yy (notice that for Leibniz dx/dy is a ratio, not a derivative,i.e., a limit).
Notice that dy is different from 0, since (5) was obtained by dividing by dy. So, why can dy be omitted to obtain (6)? Roughly, the reason a Leibnizian would give is that dy is an infinitesimal, i.e. an infinitely small quantity or a quantity which can be made as small as one pleases, in equation (5) in which other quantities are not infinitesimal.  Once dx/dy is known, it is possible to calculate TP (the subtangent to the parabola in B). A Leibnizian would procede thus:
7) TP : y = BR : LR   (similarity of triangles)
8) TP : y = BR : NR   (because dy and dx are infinitesimals, i.e. N is very close to B and hence LN is infinitesimal)
9) TP : y = dx : dy      (from (8))
10) TP = y (dx/dy)     (from (9) by theory of proportions)
11) TP = y (2y)          (from (10) and (6))
12) TP = 2x                (from (11) and (1)).
Notice that (12) is known to be correct from Greek geometry.  Berkeley, quite resonably, attacked the procedures allowing to go from (4) to (6) (the first error) and from (7) to (8) (the second error) as being either inconsistent, or destroying the mathematical claims of absolute precision.  How is it, then, that calculus obtains the correct result? Berkeley's reply is that by a lucky chance, the first and the second error cancel each other out and 'bring forth truth, though...[not] science.' Hence, the correct result would be obtained even without infinitesimals. However, he did not generalize this conclusion. (See The Analyst, secs. 18-23).