A. Corpuscularianism and Bk's worries

• corpuscularianism:
1. Its main features (e.g. Boyle): matter is a substance resolvable in corpuscles endowed with primary qualities, and therefore subject to mathematization
2. Its role in modern science from Descartes to  Newton.
3. Lk's basic acceptance of it.
• 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 (representationalism). 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.
NOTE: Compare with Lk (sensation and the dark room) and contrast with Spinoza.
Bk. seems to take it for granted that ideas are images.
NOTE: contrast with Descartes and Spinoza

The critique of abstract ideas:

i) A Lockean account of abstract ideas:
general terms (dog) refer to individual dogs through the mediation of the abstract idea of dog, which picks out a set of properties which all dogs share.

ii) Bk's critique: abstract ideas are: 1) impossible; 2) not needed; 3) originate from the abuse of language(P21)

1. Why abstract ideas impossible:

all ideas are ideas of particulars (imagistic view of ideas entails this). Lk's idea of triangle is one of a triangle which is neither right nor oblique; neither equilateral, nor scalenon, but all and none of these (P13). But  such a triangle is impossible.
Problems:
• Bk. misreads Lk, who probably doesn't hold all ideas are of particulars (issue of whether he has imagistic view or not). "being triangular" is not the full description of any particular, and as such it neither includes, nor excludes being right or oblique.
• if an idea of X lacks the representation of a feature F, then it needn't be the idea of an X which lacks F, i.e. of an X which has not-F.
 
2. Why abstract ideas not needed.

Ideas don't become abstract, but general by selective attention: in the proof of triangle's property, the idea used is of a particular triangle, but only those features of it which are general are used. (P15-16)  In other words, an idea becomes general not by acquiring or losing particular features, but by being used in a certain way.
Problem:
How do I know Bk's general idea of triangle represents all triangles without an abstract idea of triangle?
 
3. Why abstract ideas originate in the abuse of language.

The supporters of abstract ideas assume (P 18) that every general term (e.g. the term 'dog') has a precise immediate signification , i.e., a reference (the abstract idea of dog), and that through this idea the term indirectly refers to things (dogs).
This false because:
• terms refer on the basis of how they're used (e.g. general idea of triangle)
• not all terms need signify something; at times we use language to reach emotive results (instrumentalist view of language)
• terms refer directly to things (because, as we'll see, for Bk things are collections of ideas)

NOTE: For Bk both the Schools and Lk fall prey of the abuse of language.  Hence, the need to consider ideas per se, apart from language (P21-4).

1. Notion of matter inconsistent or unintelligible.

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 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.

1. Matter is an unthinking substance which causes ideas in us.
2. In order to be a cause, something must be active.
3. All our ideas, including extension,figure etc., are visibly inactive.

NOTE: transparency-of-ideas principle
4. Our only conception (i.e. notion, not idea: more on this later) of activity comes from the consideration of the will of a thinking substance.
5. Therefore, we have no consistent notion of an active unthinking substance.
6. Therefore, matter cannot exist.

1. Matter is a substance which has a real existence independently of the mind.
2. But it is impossible to conceive of a substance existing unconceived without ipso facto conceiving it.
3. Therefore, we have no consistent notion of matter.
4. Therefore, matter cannot exist.

Problems with the argument:
• At most proves that matter cannot exist unconceived, not unperceived.
• Proves too much, if anything: If sound, then what is not thought by me cannot exist, for if I try to conceive of it, it is ipso facto conceived by me.
• fails to show that the proposition P ="there are bodies nobody has thought of" is inconsistent, even if one concedes that the thinking of P makes it false (Compare with "I do not exist").
• Moreover, one needn't conceive that the thinking of P makes P false: 'there is a tree which I conceive of as unconceived' is self-refuting because "being conceived" is attributed to the unconceived tree.  However, 'I conceive that there is a tree which exists unconceived' is not self-refuting because "being conceived" is attributes to a proposition, not to a tree.

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.

Problem:
The argument assumes a notion of substratum which is Lockean and would be rejected by the Rationalists exactly on Bk's grounds.

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.

We perceive only our ideas
Accepted by Representationalists like Lk and not really discussed in the Principles.  Bk's arguments are in the Dialogues (1st). Three basic arguments:

1. Pleasure/pain argument.

An intense degree of heat is pain because one experiences not heat and then pain, but a simple uniform sensation. But pain is an idea. Hence, heat is an idea.
Problems:
• Why is heat pain?
• Bk sems to confuse heat with the feeling of heat.
2. Relativity of perception argument.

Color of an object changes if viewed from far, close, or under a microscope (e.g., clouds, blood). But since the object doesn't change, the color must be an idea.
Problem: Confusion of how things are with how they appear?
3. Causation of perception argument.

At the end of the neural chain, there is a mental perception, i.e. an idea of sense.
Problem: seems like an ignoratio elenchi.

1. The qualities of things which resemble ideas are either perceivable or not.
2. If the qualities of things which resemble ideas are perceivable, then they are ideas;
3. If they are not perceivable, then they cannot be colors or figures etc.; for, how can a color be not perceivable, i.e., invisible etc.?
4. A color can resemble only another color; a figure only another figure.
5. Hence, ideas can resemble only ideas, and not the alleged non-ideal qualities in things

Ideas are transparent.
This seems to be taken for granted.  Bk concludes that ideas are inactive, presumably because he fails to perceive (understand?) the causal link among them.
NOTE: Compare to Malebranche or Hume
Moreover, for Bk the mind itself is transparent: there are no unconscious mental acts, states, event, process or whatever.
NOTE: Link with Descartes and Locke; contrast with Leibniz
 

D. Bk's system and why he thinks it superior to Lk'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.
Lk's: 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 LK (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).

Problem: A Leibnizian rejoinder: the more being, the better.
• 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.

Dream/reality problem:
Ideas of sense are caused in us by God. How can Bk distinguish ideas of sense from those of imagination (e.g. dreams)?
Here there are really two problems, an epistemological problem and an ontological one:
Reply to the epistemological problem:
Three basic ways for the distinction:

1. Ideas of sense more lively (P30)
2. Ideas of sense independent of the will (P28-9)
3. Ideas of sense display order and coherence (P30)

NOTE: Compare with Descartes' reply (Med 6) or Lk's.

Intersubjective objects problem:
Each spirit has its own ideas. How can two spirits perceive the numerically same object?
Reply:
All is needed is that the two collections of ideas be qualitatively similar. Asking for more is trifling (3DIII)
Problems:

• It 'solves' the problem by qualifying it a trifling.
• Certainly not commonsensical.

1. God or some other spirit perceive them constantly.

Problem: Not clear any spirit but God will do, and God cannot perceive, since perception, as taken by Bk, requires passivity.
2. God has ideas of them (the archetypes he uses to produce sensations in us)

Problem: Divine archetypes are eternal, objects are not.
3. Phenomenalism: If I were there, I'd perceive them, i.e., God would give me the appropriate ideas. Bk's example of the table and the motion of the earth. (P3,58)  If Bk accepts this, then an object is a collection of actual and/or possible ideas, i.e. a permanent possibility of sensation. However, at 3D Philonous claims against Hylas's phenomenalist suggestion that only ideas are perceivable and they exist iff actually perceived.

The Nature of Spirits
Bk's early view of the moind seems to have been very similar to Hume's: since we have no idea of the mind, it must a bundle of perceptions. However, Bk abandoned this view, adopting the following:  the mind is an active immaterial (hence naturally immortal), unextended substance whose essence is to perceive ideas, will, and reason about ideas. (P27;139)  Moreover, it always perceives and/or wills (reasoning reducible to these).
Problem: Since perception is pasive, and the mind is essentially active, Bk seems committed to the view that it always wills, which seems just false, especially in the light of the transaprencey of the mind.
If the soul always perceives and wills, then  one must face Lk's critique of Descartes' idea that the soul always thinks.  There seem to be three possible solutions:

1. No temporal continuity of spirits.
2. Unconscious ideas (Lz's solution)

NOTE: Bk's rejects this  because for him, the mind is transparent.
3. Solipsistic view of time

E. 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.

F. Empirical science.

Causality.(P25-33;51-53;60-66)
Ideas have no power. Consequently, no causal connection among them, but merely concomitance. Hence, our error in considering the sun the cause of heat just because the two are concomitant and their link independent of our will.
Problems:
If ideas are inefficacious,

1. why do they come in constant groups (e.g. fire near my finger-pain?)

Reply:
The connection of ideas is one of 'mark or sign with the thing signified'. The fire I see is not the cause of pain, but a forewarning of it.
2. why are the mechanisms of a clock needed to have the pointers move?

Reply:
ideas formed into machines, i.e., artificial and regular combinations, as letters formed into words.  A few original ideas by being connected by rules may signify many things in a regular way. That complex mechanisms are followed is a proof of God's wisdom.
NOTE: The task of the scientist is to investigate God's language by discovering its rules (the laws of nature), i.e., the regularities in nature. (P105)

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)

G. 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=y2 ( a Newtonian would proceed somewhat analogously).
1)x=y2                    (equation of parabola; see fig.)
2)x+dx=(y+dy)2         (This means that the point N belongs to the parabola)
3)x+dx=y2+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=y2 (notice that for Leibniz dx/dy is a ratio, not a derivative,i.e., a limit).
Notice that dy*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).