38 ideas
| 7454 | Gassendi is the first great empiricist philosopher [Hacking] |
| Full Idea: Gassendi is the first in the great line of empiricist philosophers that gradually came to dominate European thought. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.5) | |
| A reaction: Epicurus, of course, was clearly an empiricist. British readers should note that Gassendi was not British. |
| 4643 | The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations [Baggini /Fosl] |
| Full Idea: The Principle of Sufficient Reason does not presuppose that all explanations will be causal explanations. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.28) | |
| A reaction: This sounds a reasonable note of caution, but doesn't carry much weight unless some type of non-causal reason can be envisaged. God's free will? Our free will? The laws of causation? |
| 4633 | You cannot rationally deny the principle of non-contradiction, because all reasoning requires it [Baggini /Fosl] |
| Full Idea: Anyone who denies the principle of non-contradiction simultaneously affirms it; it cannot be rationally criticised, because it is presupposed by all rationality. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.12) | |
| A reaction: Nietzsche certainly wasn't afraid to ask why we should reject something because it is a contradiction. The 'logic of personal advantage' might allow logical contradictions. |
| 4635 | Dialectic aims at unified truth, unlike analysis, which divides into parts [Baggini /Fosl] |
| Full Idea: Dialectic can be said to aim at wholeness or unity, while 'analytic' thinking divides that with which it deals into parts. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §2.03) | |
| A reaction: I don't accept this division (linked here to Hegel). I am a fan of analysis, as practised by Aristotle, but it is like dismantling an engine to identify and clean the parts, before reassembling it more efficiently. |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| Full Idea: Today we expect that anything worth calling a definition should imply a semantics. | |
| From: Ian Hacking (What is Logic? [1979], §10) | |
| A reaction: He compares this with Gentzen 1935, who was attempting purely syntactic definitions of the logical connectives. |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| Full Idea: 'Dilution' (or 'Thinning') provides an essential contrast between deductive and inductive reasoning; for the introduction of new premises may spoil an inductive inference. | |
| From: Ian Hacking (What is Logic? [1979], §06.2) | |
| A reaction: That is, inductive logic (if there is such a thing) is clearly non-monotonic, whereas classical inductive logic is monotonic. |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| Full Idea: If A |- B and B |- C, then A |- C. This generalises to: If Γ|-A,Θ and Γ,A |- Θ, then Γ |- Θ. Gentzen called this 'cut'. It is the transitivity of a deduction. | |
| From: Ian Hacking (What is Logic? [1979], §06.3) | |
| A reaction: I read the generalisation as 'If A can be either a premise or a conclusion, you can bypass it'. The first version is just transitivity (which by-passes the middle step). |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| Full Idea: Only the cut rule can have a conclusion that is less complex than its premises. Hence when cut is not used, a derivation is quite literally constructive, building up from components. Any theorem obtained by cut can be obtained without it. | |
| From: Ian Hacking (What is Logic? [1979], §08) |
| 4632 | 'Natural' systems of deduction are based on normal rational practice, rather than on axioms [Baggini /Fosl] |
| Full Idea: A 'natural' system of deduction does not posit any axioms, but looks instead for its formulae to the practices of ordinary rationality. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.09) | |
| A reaction: Presumably there is some middle ground, where we attempt to infer the axioms of normal practice, and then build a strict system on them. We must be allowed to criticise 'normal' rationality, I hope. |
| 4631 | In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use [Baggini /Fosl] |
| Full Idea: In ideal circumstances, an axiom should be such that no rational agent could possibly object to its use. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.09) | |
| A reaction: Yes, but the trouble is that all our notions of 'rational' (giving reasons, being consistent) break down when we look at unsupported axioms. In what sense is something rational if it is self-evident? |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication. | |
| From: Ian Hacking (What is Logic? [1979], §15) | |
| A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation? |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours. |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds. | |
| From: Ian Hacking (What is Logic? [1979], §13) |
| 4638 | The principle of bivalence distorts reality, as when claiming that a person is or is not 'thin' [Baggini /Fosl] |
| Full Idea: Forcing everything into the straightjacket of bivalence seriously distorts the world. The problem is most acute in the case of vague concepts, such as thinness. It is not straightforwardly true or false that a person is thin. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.03) | |
| A reaction: Can't argue with that. Can we divide all our concepts into either bivalent or vague? Presumably both propositions and concepts could be bivalent. |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties. | |
| From: Ian Hacking (What is Logic? [1979], §09) | |
| A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth. |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier. | |
| From: Ian Hacking (What is Logic? [1979], §11) | |
| A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea... |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic. | |
| From: Ian Hacking (What is Logic? [1979], §13) | |
| A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 4640 | If identity is based on 'true of X' instead of 'property of X' we get the Masked Man fallacy ('I know X but not Y') [Baggini /Fosl, by PG] |
| Full Idea: The Masked Man fallacy is when Leibniz's Law is taken as 'X and Y are identical if what is true of X is true of Y' (rather than being about properties). Then 'I know X' but 'I don't know Y' (e.g. my friend wearing a mask) would make X and Y non-identical. | |
| From: report of J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.17) by PG - Db (ideas) | |
| A reaction: As the book goes on to explain, Descartes is guilty of this when arguing that I necessarily know my mind but not my body, so they are different. Seems to me that Kripke falls into the same trap. |
| 4647 | 'I have the same car as you' is fine; 'I have the same fiancée as you' is not so good [Baggini /Fosl] |
| Full Idea: If you found that I had the same car as you, I don't suppose you would care, but if you found I had the same fiancée as you, you might not be so happy. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §4.17) | |
| A reaction: A very nice illustration of the ambiguity of "same", and hence of identity. 'I had the same thought as you'. 'I have the same DNA as you'. |
| 4639 | Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects [Baggini /Fosl] |
| Full Idea: Leibniz's Law ('if identical, must have same properties') defines identity according to the properties possessed by the object itself, but the Identity of Indiscernibles defines identity in terms of how things are conceived or grasped by the mind. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.16) | |
| A reaction: This is the heart of the problem of identity. We realists must fight for Leibniz's Law, and escort the Identity of Indiscernibles to the door. |
| 4646 | Is 'events have causes' analytic a priori, synthetic a posteriori, or synthetic a priori? [Baggini /Fosl] |
| Full Idea: Of the proposition that "all experienced events have causes", Descartes says this is analytic a priori, Hume says it is synthetic a posteriori, and Kant says it is synthetic a priori. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §4.01) | |
| A reaction: I am not sympathetic to Hume on this (though most people think he is right). I prefer the Kantian view, but he makes a very large claim. Something has to be intuitive. |
| 7447 | Probability was fully explained between 1654 and 1812 [Hacking] |
| Full Idea: There is hardly any history of probability to record before Pascal (1654), and the whole subject is very well understood after Laplace (1812). | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.1) | |
| A reaction: An interesting little pointer on the question of whether the human race is close to exhausting all the available intellectual problems. What then? |
| 7448 | Probability is statistical (behaviour of chance devices) or epistemological (belief based on evidence) [Hacking] |
| Full Idea: Probability has two aspects: the degree of belief warranted by evidence, and the tendency displayed by some chance device to produce stable relative frequencies. These are the epistemological and statistical aspects of the subject. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.1) | |
| A reaction: The most basic distinction in the subject. Later (p.124) he suggests that the statistical form (known as 'aleatory' probability) is de re, and the other is de dicto. |
| 7449 | Epistemological probability based either on logical implications or coherent judgments [Hacking] |
| Full Idea: Epistemological probability is torn between Keynes etc saying it depends on the strength of logical implication, and Ramsey etc saying it is personal judgement which is subject to strong rules of internal coherence. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.2) | |
| A reaction: See Idea 7449 for epistemological probability. My immediate intuition is that the Ramsey approach sounds much more plausible. In real life there are too many fine-grained particulars involved for straight implication to settle a probability. |
| 4645 | 'A priori' does not concern how you learn a proposition, but how you show whether it is true or false [Baggini /Fosl] |
| Full Idea: What makes something a priori is not the means by which it came to be known, but the means by which it can be shown to be true or false. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §4.01) | |
| A reaction: Helpful. Kripke in particular has labelled the notion as an epistemological one, but that does imply a method of acquiring it. Clearly I can learn an a priori truth by reading it the newspaper. |
| 7450 | In the medieval view, only deduction counted as true evidence [Hacking] |
| Full Idea: In the medieval view, evidence short of deduction was not really evidence at all. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.3) | |
| A reaction: Hacking says the modern concept of evidence comes with probability in the 17th century. That might make it one of the most important ideas ever thought of, allowing us to abandon certainties and live our lives in a more questioning way. |
| 7451 | Formerly evidence came from people; the new idea was that things provided evidence [Hacking] |
| Full Idea: In the medieval view, people provided the evidence of testimony and of authority. What was lacking was the seventeenth century idea of the evidence provided by things. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.4) | |
| A reaction: A most intriguing distinction, which seems to imply a huge shift in world-view. The culmination of this is Peirce's pragmatism, in Idea 6948, of which I strongly approve. |
| 4582 | Basic beliefs are self-evident, or sensual, or intuitive, or revealed, or guaranteed [Baggini /Fosl] |
| Full Idea: Sentence are held to be basic because they are self-evident or 'cataleptic' (Stoics), or rooted in sense data (positivists), or grasped by intuition (Platonists), or revealed by God, or grasped by faculties certified by God (Descartes). | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.01) | |
| A reaction: These are a bit blurred. Isn't intuition self-evident? Isn't divine guarantee a type of revelation? How about reason, experience or authority? |
| 7452 | An experiment is a test, or an adventure, or a diagnosis, or a dissection [Hacking, by PG] |
| Full Idea: An experiment is a test (if T, then E implies R, so try E, and if R follows, T seems right), an adventure (no theory, but try things), a diagnosis (reading the signs), or a dissection (taking apart). | |
| From: report of Ian Hacking (The Emergence of Probability [1975], Ch.4) by PG - Db (ideas) | |
| A reaction: A nice analysis. The Greeks did diagnosis, then the alchemists tried adventures, then Vesalius began dissections, then the followers of Bacon concentrated on the test, setting up controlled conditions. 'If you don't believe it, try it yourself'. |
| 4644 | A proposition such as 'some swans are purple' cannot be falsified, only verified [Baggini /Fosl] |
| Full Idea: The problem with falsification is that it fails to work with logically particular claims such as 'some swans are purple'. Examining a million swans and finding no purple ones does not falsify the claim, as there might still be a purple swan out there. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.29) | |
| A reaction: Isn't it beautiful how unease about a theory (Popper's) slowly crystallises into an incredibly simple and devastating point? Maybe 'some swans are purple' isn't science unless there is a good reason to propose it? |
| 4584 | The problem of induction is how to justify our belief in the uniformity of nature [Baggini /Fosl] |
| Full Idea: At its simplest, the problem of induction can be boiled down to the problem of justifying our belief in the uniformity of nature. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.03) | |
| A reaction: An easy solution to the problem of induction: we treat the uniformity of nature as axiomatic, and then induction is all reasoning which is based on that axiom. The axiom is a working hypothesis, which may begin to appear false. Anomalies are hard. |
| 4583 | How can an argument be good induction, but poor deduction? [Baggini /Fosl] |
| Full Idea: The problem of induction is the problem of how an argument can be good reasoning as induction but poor reasoning as deduction. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.03) | |
| A reaction: Nicely put, and a good defence of Hume against the charge that he has just muddled induction and deduction. All reasoning, we insist, should be consistent, or it isn't reasoning. |
| 7459 | Follow maths for necessary truths, and jurisprudence for contingent truths [Hacking] |
| Full Idea: Mathematics is the model for reasoning about necessary truths, but jurisprudence must be our model when we deliberate about contingencies. | |
| From: Ian Hacking (The Emergence of Probability [1975], Ch.10) | |
| A reaction: Interesting. Certainly huge thinking, especially since the Romans, has gone into the law, and creating rules of evidence. Maybe all philosophers should study law and mathematics? |
| 4634 | Abduction aims at simplicity, testability, coherence and comprehensiveness [Baggini /Fosl] |
| Full Idea: There are some 'principles of selection' in abduction: 1) prefer simple explanations, 2) prefer coherent explanations (consistent with what is already held true), 3) prefer theories that make testable predictions, and 4) be comprehensive in scope. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §2.01) | |
| A reaction: Note that these are desirable, but not necessary (pace Ockham and Ayer). I cannot think of anything to add to the list, so I will adopt it. Abduction is the key to rationality. |
| 4637 | To see if an explanation is the best, it is necessary to investigate the alternative explanations [Baggini /Fosl] |
| Full Idea: The only way to be sure we have the best explanation is to investigate the alternatives and see if they are any better. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.01) | |
| A reaction: Unavoidable! Since I love 'best explanation', I now seem to be committed to investigation every mad theory that comes up, just in case it is better. I hope I am allowed to reject after a very quick sniff. |
| 4629 | Consistency is the cornerstone of rationality [Baggini /Fosl] |
| Full Idea: Consistency is the cornerstone of rationality. | |
| From: J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §1.06) | |
| A reaction: This is right, and is a cornerstone of Kant's approach to ethics. Rational beings must follow principles - in order to be consistent in their behaviour. 'Consistent' now requires a definition…. |