66 ideas
| 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. |
| 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. |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| Full Idea: In a sense, satisfaction is the notion of 'truth in a model', and (as Hodes 1984 elegantly puts it) 'truth in a model' is a model of 'truth'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: So we can say that Tarski doesn't offer a definition of truth itself, but replaces it with a 'model' of truth. |
| 13643 | Aristotelian logic is complete [Shapiro] |
| Full Idea: Aristotelian logic is complete. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5) | |
| A reaction: [He cites Corcoran 1972] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| Full Idea: If, for every b∈d, a∈b entails that a∈d, the d is said to be 'transitive'. In other words, d is transitive if it contains every member of each of its members. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.2) | |
| A reaction: The alternative would be that the members of the set are subsets, but the members of those subsets are not themselves members of the higher-level set. |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| Full Idea: The axiom of choice is essential for proving the downward Löwenheim-Skolem Theorem. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| Full Idea: Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper? | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference. |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| Full Idea: In set theory it is central to the iterative conception that the membership relation is well-founded, ...which means there are no infinite descending chains from any relation. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.4) |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| Full Idea: The argument behind Russell's paradox shows that in set theory there are logical sets (i.e. classes) that are not iterative sets. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: In his preface, Shapiro expresses doubts about the idea of a 'logical set'. Hence the theorists like the iterative hierarchy because it is well-founded and under control, not because it is comprehensive in scope. See all of pp.19-20. |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| Full Idea: Iterative sets do not exhibit a Boolean structure, because the complement of an iterative set is not itself an iterative set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| Full Idea: A 'well-ordering' of a set X is an irreflexive, transitive, and binary relation on X in which every non-empty subset of X has a least element. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.3) | |
| A reaction: So there is a beginning, an ongoing sequence, and no retracing of steps. |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| Full Idea: There is no question of finding the 'correct' or 'true' logic underlying a part of natural language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: One needs the context of Shapiro's defence of second-order logic to see his reasons for this. Call me romantic, but I retain faith that there is one true logic. The Kennedy Assassination problem - can't see the truth because drowning in evidence. |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| Full Idea: A logic can be seen as the ideal of what may be called 'relative justification', the process of coming to know some propositions on the basis of others. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.3.1) | |
| A reaction: This seems to be the modern idea of logic, as opposed to identification of a set of 'logical truths' from which eternal necessities (such as mathematics) can be derived. 'Know' implies that they are true - which conclusions may not be. |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| Full Idea: Bernays (1918) formulated and proved the completeness of propositional logic, the first precise solution as part of the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.1) |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| Full Idea: In 1910 Weyl observed that set theory seemed to presuppose natural numbers, and he regarded numbers as more fundamental than sets, as did Fraenkel. Dedekind had developed set theory independently, and used it to formulate numbers. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2.2) |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| Full Idea: Skolem and Gödel were the main proponents of first-order languages. The higher-order language 'opposition' was championed by Zermelo, Hilbert, and Bernays. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.2) |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| Full Idea: Almost all the systems developed in the first part of the twentieth century are higher-order; first-order logic was an afterthought. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| Full Idea: The 'triumph' of first-order logic may be related to the remnants of failed foundationalist programmes early this century - logicism and the Hilbert programme. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: Being complete must also be one of its attractions, and Quine seems to like it because of its minimal ontological commitment. |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| Full Idea: Tharp (1975) suggested that compactness, semantic effectiveness, and the Löwenheim-Skolem properties are consequences of features one would want a logic to have. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: I like this proposal, though Shapiro is strongly against. We keep extending our logic so that we can prove new things, but why should we assume that we can prove everything? That's just what Gödel suggests that we should give up on. |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| Full Idea: The notion of finitude is explicitly 'built in' to the systems of first-order languages in one way or another. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1) | |
| A reaction: Personally I am inclined to think that they are none the worse for that. No one had even thought of all these lovely infinities before 1870, and now we are supposed to change our logic (our actual logic!) to accommodate them. Cf quantum logic. |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| Full Idea: Shapiro preferred second-order logic to set theory because second-order logic refers only to the relations and operations in a domain, and not to the other things that set-theory brings with it - other domains, higher-order relations, and so forth. | |
| From: report of Stewart Shapiro (Foundations without Foundationalism [1991]) by Shaughan Lavine - Understanding the Infinite VII.4 |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| Full Idea: Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: [my summary] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
|
Full Idea:
In 'Henkin' semantics, in a given model |
|
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| Full Idea: In the standard semantics of second-order logic, by fixing a domain one thereby fixes the range of both the first-order variables and the second-order variables. There is no further 'interpreting' to be done. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 3.3) | |
| A reaction: This contrasts with 'Henkin' semantics (Idea 13650), or first-order semantics, which involve more than one domain of quantification. |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| Full Idea: The counterparts of Completeness, Compactness and the Löwenheim-Skolem theorems all fail for second-order languages with standard semantics, but hold for Henkin or first-order semantics. Hence such logics are much like first-order logic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: Shapiro votes for the standard semantics, because he wants the greater expressive power, especially for the characterization of infinite structures. |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| Full Idea: It follows from Gödel's incompleteness theorem that the semantic consequence relation of second-order logic is not effective. For example, the set of logical truths of any second-order logic is not recursively enumerable. It is not even arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I don't fully understand this, but it sounds rather major, and a good reason to avoid second-order logic (despite Shapiro's proselytising). See Peter Smith on 'effectively enumerable'. |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| Full Idea: Second-order logic is inherently incomplete, so its semantic consequence relation is not effective. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| Full Idea: It is sometimes difficult to find a formula that is a suitable counterpart of a particular sentence of natural language, and there is no acclaimed criterion for what counts as a good, or even acceptable, 'translation'. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| Full Idea: The main role of substitutional semantics is to reduce ontology. As an alternative to model-theoretic semantics for formal languages, the idea is to replace the 'satisfaction' relation of formulas (by objects) with the 'truth' of sentences (using terms). | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: I find this very appealing, and Ruth Barcan Marcus is the person to look at. My intuition is that logic should have no ontology at all, as it is just about how inference works, not about how things are. Shapiro offers a compromise. |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| Full Idea: The 'satisfaction' relation may be thought of as a function from models, assignments, and formulas to the truth values {true,false}. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: This at least makes clear that satisfaction is not the same as truth. Now you have to understand how Tarski can define truth in terms of satisfaction. |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| Full Idea: Typically, model-theoretic semantics is formulated in set theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.5.1) |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| Full Idea: An axiomatization is 'categorical' if all its models are isomorphic to one another; ..hence it has 'essentially only one' interpretation [Veblen 1904]. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.2.1) |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| Full Idea: Categoricity cannot be attained in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.3) |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| Full Idea: A language has the Downward Löwenheim-Skolem property if each satisfiable countable set of sentences has a model whose domain is at most countable. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't employ an infinite model to represent a fact about a countable set. |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| Full Idea: A language has the Upward Löwenheim-Skolem property if for each set of sentences whose model has an infinite domain, then it has a model at least as big as each infinite cardinal. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) | |
| A reaction: This means you can't have a countable model to represent a fact about infinite sets. |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| Full Idea: The Löwenheim-Skolem theorems mean that no first-order theory with an infinite model is categorical. If Γ has an infinite model, then it has a model of every infinite cardinality. So first-order languages cannot characterize infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: So much of the debate about different logics hinges on characterizing 'infinite structures' - whatever they are! Shapiro is a leading structuralist in mathematics, so he wants second-order logic to help with his project. |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| Full Idea: The Upward Löwenheim-Skolem theorem fails (trivially) with substitutional semantics. If there are only countably many terms of the language, then there are no uncountable substitution models. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) | |
| A reaction: Better and better. See Idea 13674. Why postulate more objects than you can possibly name? I'm even suspicious of all real numbers, because you can't properly define them in finite terms. Shapiro objects that the uncountable can't be characterized. |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| Full Idea: A logic is 'weakly sound' if every theorem is a logical truth, and 'strongly sound', or simply 'sound', if every deduction from Γ is a semantic consequence of Γ. Soundness indicates that the deductive system is faithful to the semantics. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.1) | |
| A reaction: Similarly, 'weakly complete' is when every logical truth is a theorem. |
| 13628 | We can live well without completeness in logic [Shapiro] |
| Full Idea: We can live without completeness in logic, and live well. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: This is the kind of heady suggestion that American philosophers love to make. Sounds OK to me, though. Our ability to draw good inferences should be expected to outrun our ability to actually prove them. Completeness is for wimps. |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| Full Idea: It is sometimes said that non-compactness is a defect of second-order logic, but it is a consequence of a crucial strength - its ability to give categorical characterisations of infinite structures. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: The dispute between fans of first- and second-order may hinge on their attitude to the infinite. I note that Skolem, who was not keen on the infinite, stuck to first-order. Should we launch a new Skolemite Crusade? |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| Full Idea: Compactness is a corollary of soundness and completeness. If Γ is not satisfiable, then, by completeness, Γ is not consistent. But the deductions contain only finite premises. So a finite subset shows the inconsistency. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 4.1) | |
| A reaction: [this is abbreviated, but a proof of compactness] Since all worthwhile logics are sound, this effectively means that completeness entails compactness. |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| Full Idea: A logical language is 'semantically effective' if the collection of logically true sentences is a recursively enumerable set of strings. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 6.5) |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| Full Idea: 'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 2.1) | |
| A reaction: On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before. |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| Full Idea: The main problem of characterizing the natural numbers is to state, somehow, that 0,1,2,.... are all the numbers that there are. We have seen that this can be accomplished with a higher-order language, but not in a first-order language. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.1.4) |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| Full Idea: By convention, the natural numbers are the finite ordinals, the integers are certain equivalence classes of pairs of finite ordinals, etc. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 9.3) |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| Full Idea: The 'continuum' is the cardinality of the powerset of a denumerably infinite set. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.1.2) |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| Full Idea: Few theorists consider first-order arithmetic to be an adequate representation of even basic number theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5 n28) | |
| A reaction: This will be because of Idea 13656. Even 'basic' number theory will include all sorts of vast infinities, and that seems to be where the trouble is. |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| Full Idea: There are sets of natural numbers definable in set-theory but not in arithmetic. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 5.3.3) |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| Full Idea: It is claimed that aiming at a universal language for all contexts, and the thesis that logic does not involve a process of abstraction, separates the logicists from algebraists and mathematicians, and also from modern model theory. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I am intuitively drawn to the idea that logic is essentially the result of a series of abstractions, so this gives me a further reason not to be a logicist. Shapiro cites Goldfarb 1979 and van Heijenoort 1967. Logicists reduce abstraction to logic. |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| Full Idea: I extend Quinean holism to logic itself; there is no sharp border between mathematics and logic, especially the logic of mathematics. One cannot expect to do logic without incorporating some mathematics and accepting at least some of its ontology. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], Pref) | |
| A reaction: I have strong sales resistance to this proposal. Mathematics may have hijacked logic and warped it for its own evil purposes, but if logic is just the study of inferences then it must be more general than to apply specifically to mathematics. |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| Full Idea: Some authors (Poincaré and Russell, for example) were disposed to reject properties that are not definable, or are definable only impredicatively. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 7.1) | |
| A reaction: I take Quine to be the culmination of this line of thought, with his general rejection of 'attributes' in logic and in metaphysics. |
| 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. |
| 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. |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| Full Idea: Properties are often taken to be intensional; equiangular and equilateral are thought to be different properties of triangles, even though any triangle is equilateral if and only if it is equiangular. | |
| From: Stewart Shapiro (Foundations without Foundationalism [1991], 1.3) | |
| A reaction: Many logicians seem to want to treat properties as sets of objects (red being just the set of red things), but this looks like a desperate desire to say everything in first-order logic, where only objects are available to quantify over. |
| 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. |
| 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. |
| 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. |
| 22100 | Experienced time means no two mental moments are ever alike [Bergson] |
| Full Idea: If duration [experienced time] is what we say, deep-seated psychic states are radically heterogeneous to each other, and it is impossible that any two of them should be quite alike, since they are two different moments in a life-story. | |
| From: Henri Bergson (Time and Free Will [1889], p.220), quoted by Pete A.Y. Gunter - Bergson p.174 | |
| A reaction: This implies that we are intrinsically unpredictable, and there certainly can't be a regularity account of mental causation. The sense of time is said to make the self radically different from the rest of reality. Bergson later rejected dualism. |
| 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. |
| 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. |
| 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. |