Combining Texts

All the ideas for 'Essays on Intellectual Powers: Conception', 'Philosophy of Mathematics' and 'Reasoning and the Logic of Things'

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77 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
Everything interesting should be recorded, with records that can be rearranged [Peirce]
     Full Idea: Everything worth notice is worth recording; and those records should be so made that they can readily be arranged, and particularly so that they can be rearranged.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: Yet another epigraph for my project! Peirce must have had a study piled with labelled notes, and he would have adored this database, at least in its theory.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Sciences concern existence, but philosophy also concerns potential existence [Peirce]
     Full Idea: Philosophy differs from the special sciences in not confining itself to the reality of existence, but also to the reality of potential being.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: One might reply that sciences also concern potential being, if their output is universal generalisations (such as 'laws'). I take disposition and powers to be central to existence, which are hence of interest to sciences.
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
An idea on its own isn't an idea, because they are continuous systems [Peirce]
     Full Idea: There is no such thing as an absolutely detached idea. It would be no idea at all. For an idea is itself a continuous system.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: This is the new anti-epigraph for this database. This idea is part of Peirce's idea that relations are the central feature of our grasp of the world.
1. Philosophy / D. Nature of Philosophy / 6. Hopes for Philosophy
Philosophy is a search for real truth [Peirce]
     Full Idea: Philosophy differs from mathematics in being a search for real truth.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: This is important, coming from the founder of pragmatism, in rejecting the anti-realism which a lot of modern pragmatists seem to like.
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Metaphysics is pointless without exact modern logic [Peirce]
     Full Idea: The metaphysician who is not prepared to grapple with the difficulties of modern exact logic had better put up his shutters and go out of the trade.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: This announcement comes before Russell proclaimed mathematical logic to be the heart of metaphysics (though it is contemporary with Frege's work, of which Peirce was unaware). It places Peirce firmly in the analytic tradition.
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
Metaphysics is the science of both experience, and its general laws and types [Peirce]
     Full Idea: Metaphysics is the science of being, not merely as given in physical experience, but of being in general, its laws and types.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: I agree with this. The question then is whether such a science is possible. Dogmatic empiricists think not. Explanatory empiricists (me) think it is.
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce]
     Full Idea: Metaphysical reasonings, such as they have hitherto been, have been simple enough for the most part. It is the metaphysical concepts which it is difficult to apprehend.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: Peirce is not, of course, saying that it is just conceptual, because for him science comes first. It is the woolly concepts that alienate some people from metaphysics. Metaphysicians should challenge the concepts they use much, much more!
1. Philosophy / F. Analytic Philosophy / 6. Logical Analysis
Metaphysics is turning into logic, and logic is becoming mathematics [Peirce]
     Full Idea: Metaphysics is gradually and surely taking on the character of a logic. And finally seems destined to become more and more converted into mathematics.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: Remarkably prescient for 1898. I don't think Peirce knew of Frege (and certainly not when he wrote this). It shows that the revolution of Frege and Russell was in the air. It's there in Dedekind's writings. Peirce doesn't seem to be a logicist.
2. Reason / D. Definition / 2. Aims of Definition
Definitions should be replaceable by primitives, and should not be creative [Brown,JR]
     Full Idea: The standard requirement of definitions involves 'eliminability' (any defined terms must be replaceable by primitives) and 'non-creativity' (proofs of theorems should not depend on the definition).
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
     A reaction: [He cites Russell and Whitehead as a source for this view] This is the austere view of the mathematician or logician. But almost every abstract concept that we use was actually defined in a creative way.
3. Truth / A. Truth Problems / 6. Verisimilitude
The one unpardonable offence in reasoning is to block the route to further truth [Peirce]
     Full Idea: To set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)
     A reaction: This is Popper's rather dubious objection to essentialism in science. Yet Popper tried to do the same thing with his account of induction.
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
'Holding for true' is either practical commitment, or provisional theory [Peirce]
     Full Idea: Whether or not 'truth' has two meanings, I think 'holding for true' has two kinds. One is practical holding for true which alone is entitled to the name of Belief; the other is the acceptance of a proposition, which in pure science is always provisional.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)
     A reaction: The problem here seems to be that we can act on a proposition without wholly believing it, like walking across thin ice.
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR]
     Full Idea: The set-theory account of infinity doesn't just say that we can keep on counting, but that the natural numbers are an actual infinite set. This is necessary to make sense of the powerset of ω, as the set of all its subsets, and thus even bigger.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: I don't personally find this to be sufficient reason to commit myself to the existence of actual infinities. In fact I have growing doubts about the whole role of set theory in philosophy of mathematics. Shows how much I know.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory assumed that there is a set for every condition [Brown,JR]
     Full Idea: In the early versions of set theory ('naïve' set theory), the axiom of comprehension assumed that for any condition there is a set of objects satisfying that condition (so P(x)↔x∈{x:P(x)}), but this led directly to Russell's Paradox.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: How rarely any philosophers state this problem clearly (as Brown does here). This is incredibly important for our understanding of how we classify the world. I'm tempted to just ignore Russell, and treat sets in a natural and sensible way.
Nowadays conditions are only defined on existing sets [Brown,JR]
     Full Idea: In current set theory Russell's Paradox is avoided by saying that a condition can only be defined on already existing sets.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: A response to Idea 9613. This leaves us with no account of how sets are created, so we have the modern notion that absolutely any grouping of daft things is a perfectly good set. The logicians seem to have hijacked common sense.
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
The 'iterative' view says sets start with the empty set and build up [Brown,JR]
     Full Idea: The modern 'iterative' concept of a set starts with the empty set φ (or unsetted individuals), then uses set-forming operations (characterized by the axioms) to build up ever more complex sets.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: The only sets in our system will be those we can construct, rather than anything accepted intuitively. It is more about building an elaborate machine that works than about giving a good model of reality.
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
A flock of birds is not a set, because a set cannot go anywhere [Brown,JR]
     Full Idea: Neither a flock of birds nor a pack of wolves is strictly a set, since a flock can fly south, and a pack can be on the prowl, whereas sets go nowhere and menace no one.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
     A reaction: To say that the pack menaced you would presumably be to commit the fallacy of composition. Doesn't the number 64 have properties which its set-theoretic elements (whatever we decide they are) will lack?
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce]
     Full Idea: The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds.
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Our research always hopes that reality embodies the logic we are employing [Peirce]
     Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII)
     A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
If a proposition is false, then its negation is true [Brown,JR]
     Full Idea: The law of excluded middle says if a proposition is false, then its negation is true
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1)
     A reaction: Surely that is the best statement of the law? How do you write that down? ¬(P)→¬P? No, because it is a semantic claim, not a syntactic claim, so a truth table captures it. Semantic claims are bigger than syntactic claims.
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce]
     Full Idea: In the place of the class ...the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: Peirce's logic of relations might support the purely structural view of reality defended by Ladyman and Ross. Modern logic standardly expresses its semantics in terms of set theory. Peirce pioneered relations in logic.
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR]
     Full Idea: The three views one could adopt concerning axioms are that they are self-evident truths, or that they are arbitrary stipulations, or that they are fallible attempts to describe how things are.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10)
     A reaction: Presumably modern platonists like the third version, with others choosing the second, and hardly anyone now having the confidence to embrace the first.
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox
Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR]
     Full Idea: Berry's Paradox refers to 'the least integer not namable in fewer than nineteen syllables' - a paradox because it has just been named in eighteen syllables.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: Apparently George Boolos used this quirky idea as a basis for a new and more streamlined proof of Gödel's Theorem. Don't tell me you don't find that impressive.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematics is the only place where we are sure we are right [Brown,JR]
     Full Idea: Mathematics seems to be the one and only place where we humans can be absolutely sure that we got it right.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1)
     A reaction: Apart from death and taxes, that is. Personally I am more certain of the keyboard I am typing on than I am of Pythagoras's Theorem, but the experts seem pretty confident about the number stuff.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR]
     Full Idea: 'There are two apples' can be recast as 'x is an apple and y is an apple, and x isn't y, and if z is an apple it is the same as x or y', which makes no appeal at all to mathematics.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: He cites this as the basis of Hartry Field's claim that science can be done without numbers. The logic is ∃x∃y∀z(Ax&Ay&(x¬=y)&(Az→z=x∨z=y)).
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / n. Pi
π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR]
     Full Idea: The number π is not only irrational, but it is also (unlike √2) a 'transcendental' number, because it is not the solution of an algebraic equation.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10)
     A reaction: So is that a superficial property, or a profound one? Answers on a post card.
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
Mathematics represents the world through structurally similar models. [Brown,JR]
     Full Idea: Mathematics hooks onto the world by providing representations in the form of structurally similar models.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: This is Brown's conclusion. It needs notions of mapping, one-to-one correspondence, and similarity. I like the idea of a 'model', as used in both logic and mathematics, and children's hobbies. The mind is a model-making machine.
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
There is no limit to how many ways something can be proved in mathematics [Brown,JR]
     Full Idea: I'm tempted to say that mathematics is so rich that there are indefinitely many ways to prove anything - verbal/symbolic derivations and pictures are just two.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 9)
     A reaction: Brown has been defending pictures as a form of proof. I wonder how long his list would be, if we challenged him to give more details? Some people have very low standards of proof.
Computers played an essential role in proving the four-colour theorem of maps [Brown,JR]
     Full Idea: The celebrity of the famous proof in 1976 of the four-colour theorem of maps is that a computer played an essential role in the proof.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch.10)
     A reaction: The problem concerns the reliability of the computers, but then all the people who check a traditional proof might also be unreliable. Quis custodet custodies?
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
Set theory may represent all of mathematics, without actually being mathematics [Brown,JR]
     Full Idea: Maybe all of mathematics can be represented in set theory, but we should not think that mathematics is set theory. Functions can be represented as order pairs, but perhaps that is not what functions really are.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
     A reaction: This seems to me to be the correct view of the situation. If 2 is represented as {φ,{φ}}, why is that asymmetrical? The first digit seems to be the senior and original partner, but how could the digits of 2 differ from one another?
When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR]
     Full Idea: The basic definition of a graph can be given in set-theoretic terms,...but then what could an unlabelled graph be?
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 7)
     A reaction: An unlabelled graph will at least need a verbal description for it to have any significance at all. My daily mood-swings look like this....
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
To see a structure in something, we must already have the idea of the structure [Brown,JR]
     Full Idea: Epistemology is a big worry for structuralists. ..To conjecture that something has a particular structure, we must already have conceived of the idea of the structure itself; we cannot be discovering structures by conjecturing them.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: This has to be a crucial area of discussion. Do we have our heads full of abstract structures before we look out of the window? Externalism about the mind is important here; mind and world are not utterly distinct things.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR]
     Full Idea: Set theory is at the very heart of mathematics; it may even be all there is to mathematics. The notion of set, however, seems quite contrary to the spirit of structuralism.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: So much the worse for sets, I say. You can, for example, define ordinality in terms of sets, but that is no good if ordinality is basic to the nature of numbers, rather than a later addition.
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
The irrationality of root-2 was achieved by intellect, not experience [Brown,JR]
     Full Idea: We could not discover irrational numbers by physical measurement. The discovery of the irrationality of the square root of two was an intellectual achievement, not at all connected to sense experience.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 1)
     A reaction: Brown declares himself a platonist, and this is clearly a key argument for him, and rather a good one. Hm. I'll get back to you on this one...
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
There is an infinity of mathematical objects, so they can't be physical [Brown,JR]
     Full Idea: A simple argument makes it clear that all mathematical arguments are abstract: there are infinitely many numbers, but only a finite number of physical entities, so most mathematical objects are non-physical. The best assumption is that they all are.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: This, it seems to me, is where constructivists score well (cf. Idea 9608). I don't have an infinity of bricks to build an infinity of houses, but I can imagine that the bricks just keep coming if I need them. Imagination is what is unbounded.
Numbers are not abstracted from particulars, because each number is a particular [Brown,JR]
     Full Idea: Numbers are not 'abstract' (in the old sense, of universals abstracted from particulars), since each of the integers is a unique individual, a particular, not a universal.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: An interesting observation which I have not seen directly stated before. Compare Idea 645. I suspect that numbers should be thought of as higher-order abstractions, which don't behave like normal universals (i.e. they're not distributed).
6. Mathematics / C. Sources of Mathematics / 5. Numbers as Adjectival
Empiricists base numbers on objects, Platonists base them on properties [Brown,JR]
     Full Idea: Perhaps, instead of objects, numbers are associated with properties of objects. Basing them on objects is strongly empiricist and uses first-order logic, whereas the latter view is somewhat Platonistic, and uses second-order logic.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
     A reaction: I don't seem to have a view on this. You can count tomatoes, or you can count red objects, or even 'instances of red'. Numbers refer to whatever can be individuated. No individuation, no arithmetic. (It's also Hume v Armstrong on laws on nature).
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Does some mathematics depend entirely on notation? [Brown,JR]
     Full Idea: Are there mathematical properties which can only be discovered using a particular notation?
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6)
     A reaction: If so, this would seem to be a serious difficulty for platonists. Brown has just been exploring the mathematical theory of knots.
For nomalists there are no numbers, only numerals [Brown,JR]
     Full Idea: For the instinctive nominalist in mathematics, there are no numbers, only numerals.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: Maybe. A numeral is a specific sign, sometimes in a specific natural language, so this seems to miss the fact that cardinality etc are features of reality, not just conventions.
The most brilliant formalist was Hilbert [Brown,JR]
     Full Idea: In mathematics, the most brilliant formalist of all was Hilbert
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: He seems to have developed his fully formalist views later in his career. See Mathematics|Basis of Mathematic|Formalism in our thematic section. Kreisel denies that Hilbert was a true formalist.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
There are no constructions for many highly desirable results in mathematics [Brown,JR]
     Full Idea: Constuctivists link truth with constructive proof, but necessarily lack constructions for many highly desirable results of classical mathematics, making their account of mathematical truth rather implausible.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: The tricky word here is 'desirable', which is an odd criterion for mathematical truth. Nevertheless this sounds like a good objection. How flexible might the concept of a 'construction' be?
Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR]
     Full Idea: If we define p as '3 if Goldbach's Conjecture is true' and '5 if Goldbach's Conjecture is false', it seems that p must be a prime number, but, amazingly, constructivists would not accept this without a proof of Goldbach's Conjecture.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 8)
     A reaction: A very similar argument structure to Schrödinger's Cat. This seems (as Brown implies) to be a devastating knock-down argument, but I'll keep an open mind for now.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
We now know that mathematics only studies hypotheses, not facts [Peirce]
     Full Idea: It did not become clear to mathematicians before modern times that they study nothing but hypotheses without as pure mathematicians caring at all how the actual facts may be.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: 'Modern' here is 1898. As a logical principle this would seem to qualify as 'if-thenism' (see alphabetical themes). It's modern descendant might be modal structuralism (see Geoffrey Hellman). It take maths to be hypotheses abstracted from experience.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
David's 'Napoleon' is about something concrete and something abstract [Brown,JR]
     Full Idea: David's painting of Napoleon (on a white horse) is a 'picture' of Napoleon, and a 'symbol' of leadership, courage, adventure. It manages to be about something concrete and something abstract.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 3)
     A reaction: This strikes me as the germ of an extremely important idea - that abstraction is involved in our perception of the concrete, so that they are not two entirely separate realms. Seeing 'as' involves abstraction.
7. Existence / D. Theories of Reality / 2. Realism
Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce]
     Full Idea: If there is any reality, then it consists of this: that there is in the being of things something which corresponds to the process of reasoning.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: A nice definition of realism, a little different from usual. I belief that the normal logic of daily thought corresponds (in its rules and connectives) to the way the world is. We evaluate success in logic by truth-preservation.
There may be no reality; it's just our one desperate hope of knowing anything [Peirce]
     Full Idea: What is reality? Perhaps there isn't any such thing at all. It is but a working hypothesis which we try, our one desperate forlorn hope of knowing anything.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: I'm not quite sure why the hope is 'forlorn'. We have no current reason to doubt that the hypothesis is working out extremely well. Lovely idea, though.
9. Objects / D. Essence of Objects / 4. Essence as Definition
Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid]
     Full Idea: Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition.
     From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1)
     A reaction: Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition.
10. Modality / B. Possibility / 7. Chance
Objective chance is the property of a distribution [Peirce]
     Full Idea: Chance, as an objective phenomenon, is a property of a distribution. ...In order to have any meaning, it must refer to some definite arrangement of all the things.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VI)
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
In ordinary language a conditional statement assumes that the antecedent is true [Peirce]
     Full Idea: In our ordinary use of language we always understand the range of possibility in such a sense that in some possible case the antecedent shall be true.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Peirce is discussing Diodorus, and proposes the view nowadays defended by Edgington, though in the end Peirce defends the standard material conditional as simpler. I suspect that this discussion by Peirce is not well known.
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
     Full Idea: Reid pointed out how easily conceivable mathematical and geometric impossibilities are.
     From: report of Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], IV.III) by George Molnar - Powers 11.3
     A reaction: The defence would be that you have to really really conceive them, and the only way the impossible can be conceived is by blurring it at the crucial point, or by claiming to conceive more than you actually can
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce]
     Full Idea: 'Full belief' is willingness to upon a proposition in vital crises, 'opinion' is willingness to act on it in relatively insignificant affairs. But pure science has nothing at all to do with action.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: A nice clear statement of the pragmatic view of beliefs. It is not much help in distinguishing full belief about the solar system from mere opinion about remote galaxies. Ditto for historical events.
12. Knowledge Sources / D. Empiricism / 2. Associationism
We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce]
     Full Idea: Allying certain ideas like 'crimson' and 'scarlet' is called 'association by resemblance'. The name is not a good one, since it implies that resemblance causes association, while in point of fact it is the association which constitutes the resemblance.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII)
     A reaction: I take it that Hume would have agreed with this. It is an answer to Russell's claim that 'resemblance' must itself be a universal.
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
Scientists will give up any conclusion, if experience opposes it [Peirce]
     Full Idea: The scientific man is not in the least wedded to his conclusions. He risks nothing upon them. He stands ready to abandon one or all as experience opposes them.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: In the age of massive speculative research grants, the idea that 'he risks nothing upon them' is no longer true. Ditto for building aircraft and bridges, which are full of theoretical science. Notoriously, many scientists don't live up to Peirce's idea.
14. Science / A. Basis of Science / 2. Demonstration
If each inference slightly reduced our certainty, science would soon be in trouble [Peirce]
     Full Idea: Were every probable inference less certain than its premises, science, which piles inference upon inference, often quite deeply, would soon be in a bad way.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)
     A reaction: This seems to endorse Aristotle's picture of demonstration about scientific and practical things as being a form of precise logic, rather than progressive probabilities. Our generalisations may be more certain than the particulars they rely on.
14. Science / B. Scientific Theories / 1. Scientific Theory
I classify science by level of abstraction; principles derive from above, and data from below [Peirce]
     Full Idea: I classify the sciences on Comte's general principles, in order of the abstractness of their objects, so that each science may largely rest for its principles upon those above it in the scale, while drawing its data in part from those below it.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: He places mathematics at the peak of abstraction. I assume physics is more abstract than biology. So chemistry draws principles from physics and data from biology. Not sure about this. Probably need to read Comte on it.
14. Science / C. Induction / 2. Aims of Induction
'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce]
     Full Idea: The word 'inductio' is Cicero's imitation of Aristotle's term 'epagoge'. It fails to convey the full significance of the Greek word, which implies the examples are arrayed and brought forward in a mass. 'The assault upon the generals by the singulars'.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Interesting, thought I don't think there is enough evidence in Aristotle to get the Greek idea fully clear.
14. Science / C. Induction / 3. Limits of Induction
How does induction get started? [Peirce]
     Full Idea: Induction can never make a first suggestion.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: This seems to lead to the general modern problem of the 'theory-laden' nature of observation. You don't see anything at all without some idea of what you are looking for. How do you spot the 'next instance'. Instance of what? Nice.
Induction can never prove that laws have no exceptions [Peirce]
     Full Idea: Induction can never afford the slightest reason to think that a law is without an exception.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Part of the general Humean doubts about induction, but very precisely stated, and undeniable. You can then give up on universal laws, or look for deeper reasons to justify your conviction that there are no exceptions. E.g. observe mass, or Higgs Boson.
The worst fallacy in induction is generalising one recondite property from a sample [Peirce]
     Full Idea: The most dangerous fallacy of inductive reasoning consists in examining a sample, finding some recondite property in it, and concluding at once that it belongs to the whole collection.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: The point, I take it, is not that you infer that the whole collection has all the properties of the sample, but that some 'recondite' or unusual property is sufficiently unusual to be treated as general.
14. Science / D. Explanation / 4. Explanation Doubts / b. Rejecting explanation
Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce]
     Full Idea: Men many times fancy that they act from reason, when the reasons they attribute to themselves are nothing but excuses which unconscious instinct invents to satisfy the teasing 'whys' of the ego.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: A strikely modern thought, supported by a lot of modern neuro-science and psychology. It is crucial to realise that we don't have to accept the best explanation we can think of.
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
We may think animals reason very little, but they hardly ever make mistakes! [Peirce]
     Full Idea: Those whom we are so fond of referring to as the 'lower animals' reason very little. Now I beg you to observe that those beings very rarely commit a mistake, while we ---- !
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: We might take this as pessimism about reason, but I would take it as inviting a much broader view of rationality. I think nearly all animal behaviour is highly rational. Are animals 'sensible' in what they do? Their rationality is unadventurous.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Generalisation is the great law of mind [Peirce]
     Full Idea: The generalising tendency is the great law of mind.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII)
     A reaction: How else could a small and compact mind get a grip on a vast and diverse reality? This must even apply to inarticulate higher animals.
Generalization is the true end of life [Peirce]
     Full Idea: Generalization, the spelling out of continuous systems, in thought, in sentiment, in deed, is the true end of life.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III)
     A reaction: I take understanding to be the true aim of life, and full grasp of particulars (e.g. of particular people) is as necessary as generalisation. This is still a very nice bold idea.
16. Persons / C. Self-Awareness / 2. Knowing the Self
'Know yourself' is not introspection; it is grasping how others see you [Peirce]
     Full Idea: 'Know thyself' does not mean instrospect your soul. It means see yourself as others would see you if they were intimate enough with you.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: When it comes to anger management, I would have thought that introspection had some use. You can see a tantrum coming before even your intimates can. Nice disagreement with Sartre! (Idea 7123)
17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism
Whatever is First must be sentient [Peirce]
     Full Idea: I think that what is First is ipso facto sentient.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII)
     A reaction: He doesn't mention Leibniz's monads, but that looks like the ancestor of Peirce's idea. He doesn't make clear (here) how far he would take the idea. I would just say that whatever is 'First' must be active rather than passive.
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
Reasoning involves observation, experiment, and habituation [Peirce]
     Full Idea: The mental operations concerning in reasoning are three. The first is Observation; the second is Experimentation; and the third is Habituation.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V)
     A reaction: I like the breadth of this. Even those who think scientific reasoning has priority over logic (as I do, thinking of it as the evaluation of evidence, with Sherlock Holmes as its role model) will be surprised to finding observation and habituation there.
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Everybody overrates their own reasoning, so it is clearly superficial [Peirce]
     Full Idea: The very fact that everybody so ridiculously overrates his own reasoning, is sufficient to show how superficial the faculty is.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: A nice remark. The obvious counter-thought is that the collective reasoning of mankind really has been rather impressive, even though people haven't yet figured out how to live at peace with one another.
18. Thought / E. Abstraction / 1. Abstract Thought
'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR]
     Full Idea: The current usage of 'abstract' simply means outside space and time, not concrete, not physical.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: This is in contrast to Idea 9609 (the older notion of being abstracted). It seems odd that our ancestors had a theory about where such ideas came from, but modern thinkers have no theory at all. Blame Frege for that.
The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR]
     Full Idea: The older sense of 'abstract' applies to universals, where a universal like 'redness' is abstracted from red particulars; it is the one associated with the many. In mathematics, the notion of 'group' or 'vector space' perhaps fits this pattern.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 2)
     A reaction: I am currently investigating whether this 'older' concept is in fact dead. It seems to me that it is needed, as part of cognitive science, and as the crucial link between a materialist metaphysic and the world of ideas.
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR]
     Full Idea: In addition to the sense and reference of term, there is the 'computational' role. The name '2' has a sense (successor of 1) and a reference (the number 2). But the word 'two' has little computational power, Roman 'II' is better, and '2' is a marvel.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 6)
     A reaction: Very interesting, and the point might transfer to natural languages. Synonymous terms carry with them not just different expressive powers, but the capacity to play different roles (e.g. slang and formal terms, gob and mouth).
19. Language / B. Reference / 1. Reference theories
Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid]
     Full Idea: An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description.
     From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1)
     A reaction: [compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade.
19. Language / B. Reference / 3. Direct Reference / c. Social reference
A word's meaning is the thing conceived, as fixed by linguistic experts [Reid]
     Full Idea: The meaning of a word (such as 'felony') is the thing conceived; and that meaning is the conception affixed to it by those who best understand the language.
     From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1)
     A reaction: He means legal experts. This is precisely that same as Putnam's account of the meaning of 'elm tree'. His discussion here of reference is the earliest I have encountered, and it is good common sense (for which Reid is famous).
19. Language / C. Assigning Meanings / 9. Indexical Semantics
Indexicals are unusual words, because they stimulate the hearer to look around [Peirce]
     Full Idea: Words like 'this', 'that', 'I', 'you', enable us to convey meanings which words alone are incompetent to express; they stimulate the hearer to look about him.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II)
     A reaction: Peirce was once of the first to notice the interest of indexicals, and this is a very nice comment on them. A word like 'Look!' isn't like the normal flow of verbiage, and may be the key to indexicals.
23. Ethics / D. Deontological Ethics / 2. Duty
People should follow what lies before them, and is within their power [Peirce]
     Full Idea: Each person ought to select some definite duty that clearly lies before him and is well within his power as the special task of his life.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I)
     A reaction: I like that. Note especially that it should be 'well' within his power. Note also that this is a 'duty', and not just a friendly suggestion. Not sure what the basis of the duty is.
25. Social Practice / E. Policies / 5. Education / b. Education principles
We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce]
     Full Idea: It is not the man who thinks he knows it all, that can bring other men to feel their need for learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR]
     Full Idea: There seem to be no actual infinites in the physical realm. Given the correctness of atomism, there are no infinitely small things, no infinite divisibility. And General Relativity says that the universe is only finitely large.
     From: James Robert Brown (Philosophy of Mathematics [1999], Ch. 5)
     A reaction: If time was infinite, you could travel round in a circle forever. An atom has size, so it has a left, middle and right to it. Etc. They seem to be physical, so we will count those too.
26. Natural Theory / B. Natural Kinds / 1. Natural Kinds
Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce]
     Full Idea: The chemist contents himself with a single experiment to establish any qualitative fact, because he knows there is such a uniformity in the behavior of chemical bodies that another experiment would be a mere repetition of the first in every respect.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV)
     A reaction: I take it this endorses my 'Upanishads' view of natural kinds - that for each strict natural kind, if you've seen one you've them all. This seems to fit atoms and molecules, but only roughly fits tigers.
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Our laws of nature may be the result of evolution [Peirce]
     Full Idea: We may suppose that the laws of nature are results of an evolutionary process. ...But this evolution must proceed according to some principle: and this principle will itself be of the nature of a law.
     From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII)
     A reaction: Maybe I've missed something, but this seems a rather startling idea that doesn't figure much in modern discussions of laws of nature. Lee Smolin's account of evolving universes comes to mind.