164 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 19250 | 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. |
| 19228 | 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. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 19241 | 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. |
| 19227 | 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. |
| 19218 | 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. |
| 21489 | Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin] |
| Full Idea: In Peirce's system, a super-ordinate discipline provides general laws or principles for subordinate disciplines, which in turn provide concrete examples of those general laws. | |
| From: report of Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 1 'System' | |
| A reaction: Does he really mean that subordinate disciplines have no principles or laws? That can't be right. |
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| Full Idea: Metaphysical systems have not usually rested upon any observed facts, or not in any great degree. They are chiefly adopted because their fundamental propositions seem 'agreeable to reason', which means that which we find ourselves inclined to believe. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.15) | |
| A reaction: This leads to Peirce's key claim - that we should allow our beliefs to be formed by something outside of ourselves. I don't share Peirce's contempt for metaphysics, which I take to be about the most abstract presuppositions of our ordinary beliefs. |
| 14799 | Metaphysics rests on observations, but ones so common we hardly notice them [Peirce] |
| Full Idea: Metaphysics really rests on observations, whether consciously or not. The only reason this is not recognised is that it rests upon kinds of phenomena with which every man's experience is so saturated that he pays no particular attention to them. | |
| From: Charles Sanders Peirce (The Approach to Metaphysics [1898], p.311) | |
| A reaction: I think this is entirely right. I would say that the only thing that distinguishes metaphysical thought is its extreme level of generality, which makes it very hard to substantiate, because it is so remote from its evidential base. |
| 19229 | 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. |
| 19219 | 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! |
| 14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
| Full Idea: The demonstrations of the metaphysicians are all moonshine. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 19231 | 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. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 14764 | I am saturated with the spirit of physical science [Peirce] |
| Full Idea: I am saturated, through and through, with the spirit of the physical sciences. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.1) |
| 14782 | Philosophy is an experimental science, resting on common experience [Peirce] |
| Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], I) | |
| A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree. |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| Full Idea: The object of reasoning is to find out, from the consideration of what we already know, something else which we do not know. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 7) | |
| A reaction: I defy anyone to come up with a better definition of reasoning than that. The emphasis is on knowledge rather than truth, which you would expect from a pragmatist. …Actually the definition doesn't cover conditional reasoning terribly well. |
| 14779 | I reason in order to avoid disappointment and surprise [Peirce] |
| Full Idea: I do not reason for the sake of my delight in reasoning, but solely to avoid disappointment and surprise. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: Hence Peirce places more emphasis on inductive and abductive reasoning than on deductive reasoning. I have to agree with him. Anyone account of why we reason must have an evolutionary framework. What advantage does reason bestow? It concerns the future. |
| 14787 | Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce] |
| Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
| 19247 | 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. |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 7661 | Truth is the opinion fated to be ultimately agreed by all investigators [Peirce] |
| Full Idea: The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.38) | |
| A reaction: At least this affirms that truth is an ideal about which we dream, and is not confined merely to what we can actually know. But it rules out anything beyond the reach of all investigation, which seems a misconception of truth. What could angels know? |
| 19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
| Full Idea: In Peirce's naturalist view of truth, it is a catch-all for the particular local aims of enquiry - empirical adequacy, predictive power, coherence, simplicity, elegance, explanatory power, a reliable guide to action, fruitfulness, great understanding. | |
| From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 1 | |
| A reaction: The aims I cited in my thesis on explanation. One given, for me, is that truth is an ideal, which may or may not be attainable, to varying degrees. It is just what thinking aims at. I suspect, though, that these listed items have one thing in common. |
| 19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
| Full Idea: Peirce was not in the slightest bit tempted by the thought that a belief is true if it is useful. | |
| From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2 | |
| A reaction: All students of the pragmatic theory of truth should start with this idea, because it rejects the caricature view of pragmatic truth, a view which is easily rebutted. James seems to have been guilty of this sin. |
| 21494 | If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce] |
| Full Idea: Two related worries about Peirce's account of truth are (from Royce) what are we to make of truth if enquiry never reaches an end, and (from Russell) what are we to make of truth if enquiry ends prematurely? | |
| From: comment on Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 3 'issues' | |
| A reaction: The defence of Peirce must be that the theory is not holistic - referring to the whole Truth about absolutely everything. The discovery of the periodic table seems to me to support Peirce. In many areas basic enquiry has reached an end. |
| 19246 | '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. |
| 15335 | Peirce's theory offers anti-realist verificationism, but surely how things are is independent of us? [Horsten on Peirce] |
| Full Idea: Peirce's anti-realist theory of a truth is a verificationist theory. Truth is judged to be an epistemic notion. But the way things are is independent of the evidence we may be able to obtain for or against a judgement. | |
| From: comment on Charles Sanders Peirce (Pragmatism in Retrospect [1906]) by Leon Horsten - The Tarskian Turn 02.1 | |
| A reaction: This criticism doesn't quite capture the point that Peirce's theory is that truth is an ideal, not the set of opinions that miserable little humans eventually settle for when they get bored. Truth is an aspect of rationality, perhaps. |
| 14796 | Independent truth (if there is any) is the ultimate result of sufficient enquiry [Peirce] |
| Full Idea: I hold that truth's independence of individual opinions is due (so far as there is any 'truth') to its being the predestined result to which sufficient enquiry would ultimately lead. | |
| From: Charles Sanders Peirce (Pragmatism in Retrospect [1906], p.288) |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
| Full Idea: Either J and the judgment 'I say that J is true' are the same for all judgments or for none. But if identical, their denials are identical. These are 'J is not true' and 'I do not say that J is true', which are different. No judgment judges itself true. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: If you are going to espouse the Ramseyan redundancy view of truth, you had better make sure you are not guilty of the error which Peirce identifies here. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
| Full Idea: It is foolish to study logic unless one is persuaded that one's own reasonings are more or less bad. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], II) |
| 19237 | 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. |
| 19256 | 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. |
| 21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
| Full Idea: The pure mathematician deals exclusively with hypotheses. Whether or not there is any corresponding real thing, he does not care. | |
| From: Charles Sanders Peirce (works [1892], CP5.567), quoted by Albert Atkin - Peirce 3 'separation' | |
| A reaction: [Dated 1902] Maybe we should identify a huge branch of human learning as Hyptheticals. Professor of Hypotheticals at Cambridge University. The trouble is it would have to include computer games. So why does maths matter more than games? |
| 14783 | Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce] |
| Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) |
| 19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
| Full Idea: Peirce takes bivalence not to be a law of logic, but a regulative assumption of enquiry. | |
| From: report of Charles Sanders Peirce (works [1892]) by Cheryl Misak - Pragmatism and Deflationism 2 n10 | |
| A reaction: I like this. For most enquiries it's either true or not true, it's either there or it's not there. When you aren't faced with these simple dichotomies (in history, or quantum mechanics) you can relax, and allow truth value gaps etc. |
| 19238 | 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. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 9117 | The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen] |
| Full Idea: Hart argues that the smallest heap consists of four objects: three on the bottom, one on the top. | |
| From: report of William D. Hart (Hat-Tricks and Heaps [1992]) by Roy Sorensen - Vagueness and Contradiction Intro | |
| A reaction: If the objects were rough bolders, you could get away with two on the bottom. He's wrong. No one would accept as a 'heap' four minute grains barely visible to the naked eye. No one would describe such a group of items in a supermarket as a heap. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 14775 | Numbers are just names devised for counting [Peirce] |
| Full Idea: Numbers are merely a system of names devised by men for the purpose of counting. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: This seems a perfectly plausible view prior to the advent of Cantor, set theory and modern mathematical logic. I suppose the modern reply to this is that Peirce may be right about origin, but that men thereby stumbled on an Aladdin's Cave of riches. |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
| Full Idea: To say that 'if' there are two persons and each person has two eyes there 'will be' four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: One eye for each arm of the people is certainly a fact. Frege uses this equivalence to build numbers. I think Peirce is wrong. If it is not a fact that these people have four eyes, I don't know what 'four' means. It's being two pairs is also a fact. |
| 14788 | Mathematics is close to logic, but is even more abstract [Peirce] |
| Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV) | |
| A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities. |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 19226 | 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. |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 21492 | Realism is basic to the scientific method [Peirce] |
| Full Idea: The fundamental hypothesis of the method of science is this: There are real things, whose characters are entirely independent of our opinion of them. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Albert Atkin - Peirce 3 'method' | |
| A reaction: He admits later that this is only a commitment and not a fact. It seems to me that when you combine this idea with the huge success of science, the denial of realism is crazy. Philosophy has a lot to answer for. |
| 19240 | 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. |
| 19239 | 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. |
| 10352 | The real is the idea in which the community ultimately settles down [Peirce] |
| Full Idea: The real is the idea in which the community ultimately settles down. | |
| From: Charles Sanders Peirce (works [1892]), quoted by Martin Kusch - Knowledge by Agreement Ch.16 | |
| A reaction: If this is anti-realism, then I don't like it. If it is realist, then it is probably a bit on the optimistic side (if you think about cultures that are into witchcraft and voodoo). |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| Full Idea: Nobody can really doubt that there are Reals, for, if he did, doubt would not be a source of dissatisfaction. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.19) | |
| A reaction: This rests on Peirce's view that all that really matters is a sense of genuine dissatisfaction, rather than a theoretical idea. So even at the end of Meditation One, Descartes isn't actually worried about whether his furniture exists. |
| 14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |
| Full Idea: Facts are hard things which do not consist in my thinking so and so, but stand unmoved by whatever you or I or any man or generations of men may opine about them. | |
| From: Charles Sanders Peirce (Criterion of Validity in Reasoning [1903], I) | |
| A reaction: This is my view of facts, with which I am perfectly happy, for all the difficulties involved in individuating facts, and in disentangling them from our own modes of thought and expression. Let us try to establish the facts. |
| 13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
| Full Idea: It was Peirce and Schröder in the nineteenth century who began a systematic taxonomy of relations. | |
| From: report of Charles Sanders Peirce (works [1892], 4) by William D. Hart - The Evolution of Logic 4 |
| 21491 | Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin] |
| Full Idea: The realism about possibilities, generalities, tendencies and habits that we find in Peirce's later maxim is something that the logical positivists would have been uncomfortable with. | |
| From: report of Charles Sanders Peirce (works [1892]) by Albert Atkin - Peirce 2 'Concl' | |
| A reaction: Atkin examines the various later statements of the earlier maxim, given here in Idea 21490. Ryle and Quine express the empiricist and logical positivist approach to dispositions. |
| 14798 | All communication is vague, and is outside the principle of non-contradiction [Peirce] |
| Full Idea: The 'vague' might be defined as that to which the principle of contradiction does not apply. For it is false neither that an animal (in a vague sense) is male, nor that an animal is female. No communication between persons can be entirely non-vague. | |
| From: Charles Sanders Peirce (Critical Common-Sensism [1905], I) | |
| A reaction: Note that he makes vagueness largely a matter of the way we talk, which is David Lewis's approach, and looks right to me. |
| 14797 | Vagueness is a neglected but important part of mathematical thought [Peirce] |
| Full Idea: Logicians have too much neglected the study of vagueness, not suspecting the important part it plays in mathematical thought. It is the antithetical analogue of generality. | |
| From: Charles Sanders Peirce (Critical Common-Sensism [1905], I) |
| 14786 | Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce] |
| Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient). | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) |
| 14804 | Is chance just unknown laws? But the laws operate the same, whatever chance occurs [Peirce] |
| Full Idea: Chance is the name for some law that is unknown to us? If you say 'each die moves under the influence of precise mechanical laws', it seems to me it is not these laws which made the tie turn up sixes, for the laws act the same when other throws come up. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.333) |
| 19252 | 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) |
| 14303 | Truth-functional conditionals have a simple falsification, when A is true and B is false [Peirce] |
| Full Idea: The utility of [truth-functional conditionals] is that it puts us in possession of a rule...[namely] The hypothetical proposition may be ...falsified by a single state of things, but only by one in which A [antecedent] is true and B [consequent] is false. | |
| From: Charles Sanders Peirce (On the Algebra of Logic [1895], p.218), quoted by Stephen Mumford - Dispositions | |
| A reaction: Personally I am rather more interested in verifying conditionals than in falsifying them. I certainly don't accept them until they are falsified, unless they have massive support from surrounding facts. |
| 19232 | 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. |
| 16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
| Full Idea: The possible is necessarily general…..It is only actuality, the force of existence, which bursts the fluidity of the general and produces a discrete unit. | |
| From: Charles Sanders Peirce (works [1892]), quoted by François Recanati - Mental Files 13.1 | |
| A reaction: [Papers 4 1967:147] This was quoted by Prior, and is often cited. Recanati is interested in the notion of a singular thought being tied to actuality, by generating a mental file. |
| 19089 | Our whole conception of an object is its possible practical consequences [Peirce] |
| Full Idea: Consider what effects, which might conceivably have practical bearings, we conceive the objects of our conceptions to have. Then, our conception of these effects is the whole of our conception of the object. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], EP i.132), quoted by Albert Atkin - Peirce 2 'early' | |
| A reaction: This is his 1878 version, which was fine-tuned later in life. He seems to have extended his principle to include possibilities, as well as the mere objects. That is, he moved beyond mere nominalism. |
| 7660 | We are aware of beliefs, they appease our doubts, and they are rules of action, or habits [Peirce] |
| Full Idea: A belief has just three properties: first, it is something that we are aware of; second, it appeases the irritation of doubt; and, third, it involves the establishment in our nature of a rule of action, or, say for short, a habit. | |
| From: Charles Sanders Peirce (How to Make our Ideas Clear [1878], p.28) | |
| A reaction: Peirce probably believed that Bismarck breathed oxygen, but was unaware of his belief, and no one ever dreamed of acting on such a belief, unless Bismarck was gasping for air. |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| Full Idea: The feeling of believing is a more or less sure indication of there being established in our nature some habit which will determine our actions. Doubt never has such an effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
| A reaction: It is one thing to assert this fairly accurate observation, and another to assert that this is the essence or definition of a belief. Perhaps it is the purpose of belief, without being the phenomenological essence of it. We act in states of uncertainty. |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| Full Idea: As soon as a firm belief is reached we are entirely satisfied, whether the belief be true or false. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.10) | |
| A reaction: This does not deny that the truth or falsehood of a belief is independent of whether we are satisfied with it. It is making a fair point, though, about why we believe things, and it can't be because of truth, because we don't know how to ensure that. |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| Full Idea: We seek for a belief that we shall think to be true; but we think each one of our beliefs to be true, and, indeed, it is mere tautology to say so. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: If, as I do, you like to define belief as 'commitment to truth', Peirce makes a rather startling observation. You are rendered unable to ask whether your beliefs are true, because you have defined them as true. Nice point… |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| Full Idea: The mere putting of a proposition into the interrogative form does not stimulate the mind to any struggle after belief; there must be a real and living doubt. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: This the attractive aspect of Peirce's pragmatism, that he is always focusing on real life rather than abstract theory or pure logic. |
| 14781 | A 'belief' is a habit which determines how our imagination and actions proceed [Peirce] |
| Full Idea: A cerebral habit of the highest kind, which will determine what we do in fancy as well as what we do in action, is called a 'belief'. | |
| From: Charles Sanders Peirce (What is a Leading Principle? [1880], I) |
| 19223 | 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. |
| 19107 | Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce] |
| Full Idea: Inquiry is not standing upon a bedrock of fact. It is walking up a bog, and can only say, this ground seems to hold for the present. Here I will stay until it begins to give way. | |
| From: Charles Sanders Peirce (works [1892], CP 5.589), quoted by Gottfried Leibniz - Letter to Newton 4 | |
| A reaction: [I don't know which article this lovely quote comes from] |
| 14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
| Full Idea: All positive reasoning is judging the proportion of something in a whole collection by the proportion found in a sample. Hence we can never hope to attain absolute certainty, absolute exactitude, absolute universality. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) | |
| A reaction: This is the basis of Peirce's fallibilism - that all 'positive' reasoning (whatever that it?) is based on statistical induction. I'm all in favour of fallibilism, but find Peirce's claim to be a bit too narrow. He was too mesmerised by physical science. |
| 14768 | Infallibility in science is just a joke [Peirce] |
| Full Idea: Infallibility in scientific matters seems to me irresistibly comical. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.3) |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
| Full Idea: It seems to me there is the most historic proof that innate truths are particularly uncertain and mixed up with error, and therefore a fortiori not without exception. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 14789 | Experience is indeed our only source of knowledge, provided we include inner experience [Peirce] |
| Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898]) | |
| A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience. |
| 19253 | 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. |
| 14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
| Full Idea: The doctrine of the association of ideas is, to my thinking, the finest piece of philosophical work of the prescientific ages. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 14794 | Instead of seeking Truth, we should seek belief that is beyond doubt [Peirce] |
| Full Idea: Your problems would be greatly simplified, if, instead of saying that you want to know the Truth, you were simply to say that you want to attain a state of belief unassailable beyond doubt. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
| A reaction: This is not the same as saying that belief beyond doubt IS truth. He is merely offering a strategy for scientists to side-step the sort of scepticism raised by Descartes and radical empiricists. |
| 14795 | Pragmatism is a way of establishing meanings, not a theory of metaphysics or a set of truths [Peirce] |
| Full Idea: Pragmatism is no doctrine of metaphysics, no attempt to determine the truth of things. It is merely a method of ascertaining the meanings of hard words and of abstract concepts. | |
| From: Charles Sanders Peirce (Pragmatism in Retrospect [1906], p.271) | |
| A reaction: Suddenly I recognise a prominent strand of modern philosophy of language (especially in America) for what it is. |
| 14785 | The world is one of experience, but experiences are always located among our ideas [Peirce] |
| Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], III) | |
| A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered. |
| 14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
| Full Idea: A truth which rests on the authority of inspiration only is of a somewhat incomprehensible nature; and we can never be sure that we rightly comprehend it. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
| Full Idea: Even if we decide that an idea really is inspired, we cannot be sure, or nearly sure, that the statement is true. We know one of the commandments of the Bible was printed without a 'not' in it. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
| Full Idea: We never can be absolutely certain that any given deliverance [of revelation] really is inspired; for that can only be established by reasoning. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II) |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| Full Idea: It is necessary that a method should be found by which our beliefs be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.5 | |
| A reaction: This very sensible and interesting remark hovers somewhere between empiricism and pragmatism. Fogelin very persuasively builds his account of knowledge on it. The key point is that we hardly ever choose what to believe. See Idea 2454. |
| 19224 | 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. |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| Full Idea: It is a common idea that demonstration must rest on indubitable propositions, either first principles of a general nature, or first sensations; but actual demonstration is completely satisfactory if it starts from propositions free from all actual doubt. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: Another nice example of Peirce focusing on the practical business of thinking, rather than abstract theory. I agree with this approach, that explanation and proof do not aim at perfection and indubitability, but at what satisfies a critical mind. |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| Full Idea: To satisfy our doubts it is necessary that a method should be found by which our beliefs may be determined by nothing human, but by some external permanency - by something upon which our thinking has no effect. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.18) | |
| A reaction: This may be the single most important idea in pragmatism and in the philosophy of science. See Fodor on experiments (Idea 2455). Put the question to nature. The essential aim is to be passive in our beliefs - just let reality form them. |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| Full Idea: Some people seem to love to argue a point after all the world is fully convinced of it. But no further advance can be made. When doubt ceases, mental action on the subject comes to an end; and, if it did go on, it would be without purpose. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.11) | |
| A reaction: This is the way Peirce's pragmatism, which deals with how real thinking actually works (rather than abstract logic), deals with scepticism. However, there is a borderline where almost everyone is satisfied, but the very wise person remains sceptical. |
| 19243 | 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. |
| 14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
| Full Idea: The works of Duns Scotus have strongly influenced me. …His logic and metaphysics, torn away from its medievalism, …will go far toward supplying the philosophy which is best to harmonize with physical science. | |
| From: Charles Sanders Peirce (Concerning the Author [1897], p.2) |
| 19225 | 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. |
| 19234 | '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. |
| 19235 | 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. |
| 19236 | 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. |
| 19251 | 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. |
| 14790 | 'Abduction' is beginning a hypothesis, particularly if it includes preference of one explanation over others [Peirce] |
| Full Idea: The first starting of a hypothesis and the entertaining of it …is an inferential step which I propose to call 'abduction'. This will include a preference for any one hypothesis over others which would equally explain the facts. | |
| From: Charles Sanders Peirce (Abduction and Induction [1901], I) | |
| A reaction: I take there to be no more important function within human thought than the procedure by which we give preference to one particular explanation. It only makes sense, I think, if we take it as part of a coherence theory of justification. |
| 14791 | Abduction involves original suggestions, and not just the testing involved in induction [Peirce] |
| Full Idea: It is of the nature of abduction to involve an original suggestion; while typical induction has no originality in it, but only tests a suggestion already made. | |
| From: Charles Sanders Peirce (Abduction and Induction [1901], I) | |
| A reaction: Peirce's 'abduction' is not, then, just the choice of a best explanation. He came up with the idea because he was keen to capture the creative and imaginative character of rational thought. |
| 19222 | 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. |
| 19220 | 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. |
| 14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
| Full Idea: We can stare stupidly at phenomena; but in the absence of imagination they will not connect themselves together in any rational way. | |
| From: Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], I) | |
| A reaction: The importance of this is its connection between imagination and 'rational' understanding. This is an important corrective to a crude traditional picture of the role of imagination. I would connect imagination with counterfactuals and best explanation. |
| 19255 | 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. |
| 19242 | 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. |
| 19249 | '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) |
| 14802 | Physical and psychical laws of mind are either independent, or derived in one or other direction [Peirce] |
| Full Idea: The question about minds is whether 1) physical and psychical laws are independent (monism, my neutralism), 2) the psychical laws derived and physical laws primordial (materialism), 3) physical law is derived, psychical law primordial (idealism). | |
| From: Charles Sanders Peirce (The Architecture of Theories [1891], p.321) | |
| A reaction: I think you are already in trouble when you start proposing that there are two quite distinct sets of laws, and then worry about how they are related. Assume unity, and only separate them when the science forces you to (which it won't). |
| 19257 | 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. |
| 19248 | 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. |
| 19221 | 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. |
| 14792 | A 'conception', the rational implication of a word, lies in its bearing upon the conduct of life [Peirce] |
| Full Idea: The present writer framed the theory that a 'conception', that is, the rational purport of a word or other expression, lies exclusively in its conceivable bearing upon the conduct of life. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 14793 | The definition of a concept is just its experimental implications [Peirce] |
| Full Idea: If one can define accurately all the conceivable experimental phenomena which the affirmation or denial of a concept could imply, one will have therein a complete definition of the concept, and there is absolutely nothing more in it. | |
| From: Charles Sanders Peirce (Essentials of Pragmatism [1905], I) | |
| A reaction: Strictly, I would have thought you could only affirm or deny a complete proposition, rather than a concept. What should I do with the concept of a 'unicorn'? Note that all theories, such as empiricism or pragmatism, begin with an account of our concepts. |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 14906 | Non-positivist verificationism says only take a hypothesis seriously if it is scientifically based and testable [Ladyman/Ross on Peirce] |
| Full Idea: With Peirce, we endorse a non-positivist version of verificationism - no hypothesis should be taken seriously if apparently beyond our capacity to investigate, and serious metaphysics must concern at least two plausible scientific hypotheses. | |
| From: comment on Charles Sanders Peirce (How to Make our Ideas Clear [1878]) by J Ladyman / D Ross - Every Thing Must Go 1.3 | |
| A reaction: [compressed] They say this is NOT a theory about meaning, as 'The Big Bang was caused by Elvis' is perfectly meaningful. Verificationism always seems to rule out bold speculation. Don't say 'take string theory seriously', if we can't test it? |
| 7634 | Icons resemble their subject, an index is a natural sign, and symbols are conventional [Peirce, by Maund] |
| Full Idea: For Peirce there are three different kinds of sign, which are different kinds of representation, built on different relationships: an 'icon' represents what it resembles, an 'index' is a natural sign, and a 'symbol' is a conventional sign. | |
| From: report of Charles Sanders Peirce (Logic as Semiotic: Theory of Signs [1897]) by Barry Maund - Perception Ch.4 | |
| A reaction: Maund makes use of natural signs (like footprints) to explain representative perception. Peirce's distinctions seem useful in philosophy of mind generally, if the brain somehow represents what it experiences. How subjective are signs? |
| 19233 | 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. |
| 14784 | Ethics is the science of aims [Peirce] |
| Full Idea: Ethics is the science of aims. | |
| From: Charles Sanders Peirce (The Nature of Mathematics [1898], II) | |
| A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea. |
| 14805 | Is there any such thing as death among the lower organisms? [Peirce] |
| Full Idea: Among some of the lower organisms, it is a moot point with biologists whether there be anything which ought to be called death. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.334) | |
| A reaction: The point, presumably, is that one phase of an organisms moves into another, and the 'individuals' are not distinct enough for their 'death' to be a significant transition. A nicely mind-expanding thought. |
| 19230 | 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. |
| 19245 | 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) |
| 19244 | 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. |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| Full Idea: The guiding principle is that what is true of one piece of copper is true of another; such a guiding principle with regard to copper would be much safer than with regard to many other substances - brass, for example. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
| A reaction: Peirce is so beautifully simple and sensible. This gives the essential notion of a natural kind, and is a key notion in our whole understanding of physical reality. |
| 14800 | The world is full of variety, but laws seem to produce uniformity [Peirce] |
| Full Idea: Exact law obviously never can produce heterogeneity out of homogeneity; and arbitrary heterogeneity is the feature of the universe the most manifest and characteristic. | |
| From: Charles Sanders Peirce (The Architecture of Theories [1891], p.319) | |
| A reaction: This is the view of laws of nature now associated with Nancy Cartwright, but presumably you can explain the apparent chaos in terms of the intersection of vast numbers of 'laws'. Or, better, there aren't any laws. |
| 19254 | 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. |
| 14806 | If the world is just mechanical, its whole specification has no more explanation than mere chance [Peirce] |
| Full Idea: The mechanical philosopher leaves the whole specification of the world utterly unaccounted for, which is pretty nearly as bad as to baldly attribute it to chance. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.337) | |
| A reaction: If now complete is even remotely available, then that doesn't seem to matter too much, but if there is one message modern physics teaches philosophy, it is that we should not give up on trying to answer the deeper questions. |
| 14803 | The more precise the observations, the less reliable appear to be the laws of nature [Peirce] |
| Full Idea: Try to verify any law of nature, and you will find that the more precise your observations, the more certain they will be to show irregular departures from the law. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.331) | |
| A reaction: This nicely encapsulates modern doubts about whether the so-called 'laws' of nature actually capture what is going on in the real world. |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| Full Idea: It is probably of more advantage to an animal to have his mind filled with pleasing and encouraging visions, independently of their truth; and thus, upon unpractical subjects, natural selection might occasion a fallacious tendency of thought. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p. 8) | |
| A reaction: Note that this is a pragmatist saying that a set of beliefs might work fine but be untrue. So Peirce does not have the highly relativistic notion of truth of some later pragmatists. Good for him. Note the early date to be thinking about Darwin. |
| 14801 | Darwinian evolution is chance, with the destruction of bad results [Peirce] |
| Full Idea: Darwinian evolution is evolution by the operation of chance, and the destruction of bad results. | |
| From: Charles Sanders Peirce (The Architecture of Theories [1891], p.320) | |
| A reaction: The 'destruction of bad results' is a much better slogan for Darwin that Spencer's 'survival of the fittest'. It is, of course, a rather unattractive God who makes progress by endlessly destroying huge quantities of failed (but living) experiments. |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
| Full Idea: If death is annihilation, then the man who believes that he will certainly go straight to heaven when he dies, provided he have fulfilled certain simple observances in this life, has a cheap pleasure which will not be followed by the least disappointment. | |
| From: Charles Sanders Peirce (The Fixation of Belief [1877], p.12) | |
| A reaction: This is a nicely wicked summary of one side of Pascal's options. All the problems of the argument are built into Peirce's word "cheap". Peirce goes on to talk about ostriches burying their heads. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |