Hume's principle - Factbites

Hume's principle - Factbites
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Topic: Hume's principle

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	Frege's Logic, Theorem, and Foundations for Arithmetic
		The claim that Hume's Principle is an analytic principle of logic is subject to the same problem just posed for Basic Law V. The equinumerosity of F and G does not, as a matter of meaning, imply (identity claims that entail) the existence of numbers.
		This consistent principle, known in the literature as "Hume's Principle", asserts that for any concepts F and G, the number of F-things is equal to the number G-things if and only if there is a one-to-one correspondence between the F-things and the G-things.
		So by setting aside the derivation of Hume's Principle from the inconsistent Basic Law V and focusing on Frege's proofs of the basic propositions of arithmetic, his theoretical accomplishment emerges much more clearly, for his work shows us how to prove the Dedekind/Peano axioms for number theory from Hume's Principle in second-order logic.
	plato.stanford.edu /entries/frege-logic (15095 words)

	Causal reasoning is embedded in our thinking process
		Because his idea of a justification is a deductive one, he confirms that a justification of the uniformity principle is impossible.
		David Hume claims that we must be able to justify the uniformity of nature--that the future will resemble the past--if we are to justify causal inferences; and claims that this is impossible.
		In evaluating Hume's requirement of the uniformity of nature for the justification of causal reasoning, I refer to a lectures on Hume given by Alison Simmons in Emerson Hall, Harvard University, in December 1998 and Chapter Three from Hume by Barry Stroud (Routledge: New York, 1977).
	www.uweb.ucsb.edu /~thong/122_long2_final.html (2686 words)

	Scepticism - Lecture 9b
		One readily identifiable element within those grounds is Hume’s claim that it is not possible to give a demonstrative or intuitive proof of the uniformity principle.
		Thus his elimination of the possibility of a demonstrative argument in favour of the uniformity principle allows him to conclude that any cogent argument offered on behalf of the supposition that the course of nature is not subject to arbitrary changes must appeal at some point to the evidence provided by past experience.
		The role originally allocated to the uniformity principle was precisely that of providing a foundation for our inferences from premisses about phenomena that have been observed to conclusions about phenomena that have not yet been observed.
	www.webspawner.com /users/alanbailey/scept9b.html (1086 words)

	In a nutshell, Hume’s comes up with three basic questions:
		Thus, the principle of uniformity of nature mentioned by Hume as an intermediate premise is no longer needed.
		Since our attempts to justify the uniformity principle have failed, we have to conclude that there is no legitimate method which would let us infer a general rule about regularities and predict such regularities in the future based on the limited scope of observations of regularities in the past and the present.
		Thus, to infer uniformity of nature from the previous observations and legitimately expand it to the future times we have to presuppose this principle in the premises.
	www.bcc.ctc.edu /ArtsHum/Materials/phil/Payne/spring03/160HumeproblemSp03.htm (3467 words)

	The Principle of Sufficient Reason - Cambridge University Press
		Discussing various forms of the PSR and selected historical episodes, from Parmenides, Leibnez, and Hume, Pruss defends the claim that every true contingent proposition must have an explanation against major objections, including Hume’s imaginability argument and Peter van Inwagen’s argument that the PSR entails modal fatalism.
		The Principle of Sufficient Reason (PSR) says that all contingent facts must have explanation.
		In this volume, the first on the topic in the English language in nearly half a century, Alexander Pruss examines the substantive philosophical issues raised by the Principle Reason.
	www.cambridge.org /catalogue/catalogue.asp?ISBN=052185959X (276 words)

	David Hume
		Usually called the "Copy Principle," Hume's distinctive brand of empiricism is often identified with his commitment to it.
		Hume managed to extricate himself from this situation, and accepted the invitation of his cousin, Lieutenant-General James St. Clair, to be his Secretary ("I wore the uniform of an officer.") on a military expedition against the French in Quebec.
		Hume sometimes describes benevolence as a manifestation of our "natural" or "social sympathy." In both texts, Hume's central point is that we experience this "feeling for humanity" in ourselves and observe it in others, so "the selfish hypothesis" is "contrary both to common feeling and to our most unprejudiced notions" (EPM, 298).
	plato.stanford.edu /entries/hume (8104 words)

	Cosmological Argument
		As Hume argued, there is no reason for thinking that the Causal Principle is true a priori, for we can conceive of effects without conceiving of their being caused (Enquiry Concerning Human Understanding, IV).
		Leibniz uses the principle to argue that the sufficient reason for the “series of things comprehended in the universe of creatures” (§36) must exist outside this series of contingencies and is found in a necessary being that we call God.
		Kant held that the cosmological argument, in concluding to the existence of a necessary being, argues for the existence of a being whose nonexistence is absolutely inconceivable.
	plato.stanford.edu /entries/cosmological-argument (8104 words)

	The New York Review of Books: The Right to Be Rich or Poor
		According to utilitarian theory, espoused by David Hume, Jeremy Bentham, and later utilitarians, principles of justice are rules that work for the greater good of all.
		This is because in any society governed according to any principle other than the maximin principle there would always be a group of people at least as badly off as the worst-off in a maximin-ruled society.
		Under the maximin rule, after all, the better-off may have to make substantial sacrifices to help the worst-off, perhaps much greater sacrifices than they would have to make to satisfy the principle of utility.
	www.nybooks.com /articles/9252 (8104 words)

	Confirmation Theory
		Hume does not need to assume that there is a 'principle of induction' in the sense of a single thing that is either (a) common to every induction or (b) presupposed in an induction in addition to the explicit premises.
		Suppose that h and h' are two empirically equivalent theories and e is the evidence presented for one of them.
		Empirically equivalent theories not equally confirmed: If e confirms h and h' is empirically equivalent to h, there is no suggestion on my theory that h' has to be equally confirmed, or even confirmed at all; for if h explains e, it doesn't follow that h' also explains e, even though h' might predict e.
	www.user-friendly.net /articles/confirmation.htm (11519 words)

	Monkeys, Typewriters, and Birthdays: A Dilemma
		However, if the principle is false, then the objection considered by David Hume fails to go through and (barring other difficulties) the version of the design argument given here seems successful.
		Now, we could call this principle "the principle of plenitude" or perhaps "the Diodorian principle" after the Greek philosopher Diodorus who apparently held a variant of this principle.
		However, notice that this entails the denial of the principle of plenitude.
	startthinking.homestead.com /files/Monkss.htm (11519 words)

	Cardinal Basil Hume talks to Interchurch Families
		The Cardinal stressed almost exclusively the first basic principle which governs sacramental sharing: the eucharist is the sign of unity in faith, worship and community life, and source of the unity of the Christian community so that eucharistic communion is inseparably linked to full ecclesial communion and its visible expression.
		The Cardinal particularly drew our attention to the question of eucharistic belief, and to the Catholic understanding that eucharistic faith implies faith in the church which celebrates the eucharist - and the Roman Catholic Church is the "Petrine Church" as he expressed it.
		The main focus of the Cardinal's interest was one of the conditions which must be met by an individual who seeks admission to communion in the Roman Catholic Church, once such need is recognised as genuine.
	www.aifw.org /journal/97su02.shtm (1853 words)

	Encyclopedia: Hume's principle
		Hume's principle is a standard for comparing any two sets of objects as to size.
		The principle become the foundation of modern Logicism is one of the schools of thought in the Philosophy of mathematics.
		The principle was taken up independently by Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845 – January 6, 1918) was a mathematician who was born in Russia and lived in Germany for most of his life.
	www.nationmaster.com /encyclopedia/Hume%27s-principle (1492 words)

	Oxford Scholarship Online: Philosophical Interpretations
		The interpretations are governed by a semantic principle of charity, namely, that there is a very strong presumption in favor of holding that philosophers meant to say precisely what they did say, and that what they did say means precisely what it seems to mean.
		Hume and Berkeley on the Proofs of Infinite Divisibility
		3 Hume and Berkeley on the Proofs of Infinite Divisibility
	www.oxfordscholarship.com /oso/public/content/philosophy/019507162X/toc.html (1492 words)

	Linguistics 001 -- Syntax
		The logical positivists made Hume's "principle of verification" an article of faith:
		This is the principle of compositionality: language is intricately structured, and linguistic messages are interpreted, layer by layer, in a way that depends on their structure.
		Among the corollaries of this perspective is the principle of operationalism, which requires that any concept involved in "experimental reasoning concerning matters of fact and existence" must be defined in terms of clearly defined operations, to be performed in any given situation in order to decide whether an instance of that concept has been observed.
	www.ling.upenn.edu /courses/Fall_2001/ling001/syntax.html (1492 words)

	Belief
		Hume’s claim that we could conceive of the Uniformity Principle’s being false is independent of the discussion of the circularity of the probabilistic argument for the Uniformity Principle.
		Roughly, since the Uniformity Principle is about how things must be, it isn’t clear to me why we must be certain that it is true, as opposed to simply believing it, in order to use reason to draw causal inferences.
		As long as we can conceive of the Uniformity Principle’s being false, reason could not use it: the conclusions of reason cannot be conceived to be false but that would not be so if reason used the Uniformity Principle.
	humanities.uchicago.edu /faculty/mgreen/HumeW05/Notes/Belief.shtml (2276 words)

	David Hume
		While Hume's empiricism is usually identified with the Copy Principle, it is actually his use of its reverse in his account of definition that is really the most distinctive element of his empiricism.
		Hume locates "three principles of connexion" or association: resemblance, contiguity, and cause and effect.
		Even in applied mathematics, where we use abstract reasoning and geometrical methods to apply principles we regard as laws to particular cases in order to derive further principles as consequences of these laws, the discovery of the original law itself was due to experience and observation, not to a priori reasoning.
	plato.stanford.edu /entries/hume (8104 words)

	Science and Rationality
		Hume’s problem of induction was to find a rational argument to the conclusion that reason, or that portion of it embodied in inductive reasoning, (probably) works.
		Rationality comes closer to being scientific when the desire is to aim at objective truth, but there are many other aims than just this one, that reasons can be associated with, including many areas not open to testability, but still open to criticism.
		Rationality, customarily defined as giving reasons for actions or for holding beliefs, is truly the sophist servant of desire.
	home.comcast.net /~reillyjones/popper.html (8104 words)

	cars - Talk:Measurement in quantum mechanics
		One of the solutions to this paradox, or contradiction, is based on the actualism philosophy of Immanuel Kant, George Berkeley, David Hume, Henri Poincaré and Niels Bohr.
		According to locality principle, however, it should take at least a second for particle B to notice that particle A's wave function has changed.
		According to it, the collapsing of the wave function is not a physical process or interaction, but rather a logical process which is an outcome of the observer's mind that interprets the events according to his apriori conventions.
	www.carluvers.com /cars/Talk:Measurement_in_quantum_mechanics (8104 words)

	Hume
		So let’s see how we might justify the P.U.N. Before giving my version of Hume=s argument, distinguish two accounts of probability: logical (Principle of Indifference) and relative frequency.
		Now the Principle of the Uniformity of Nature is not an obvious truth.
		But there seems no a priori reason why the Principle of Indifference should hold in the world.
	uwadmnweb.uwyo.edu /Philosophy/humePartTwo.htm (1070 words)

	Janus Head 4.1 / Gavin Miller
		As the insufficiency of this principle is discovered, however, so there develops, as in the work of Hume, a sceptical philosophy detached from the consequently downgraded interests of everyday life.
		The philosopher â“ guided, as she must seemingly be, by the principle of non-contradiction â“ is forced to limit her ego to a realm of phenomenologically-attenuated imaginary symbolisations.
		This is the philosopher, and the most certain principle of all is that regarding which it is impossible to be mistaken.
	www.janushead.org /4-1/miller.cfm (6088 words)

	Principle of Sufficient Reason
		Note that (2) is consistent when x=y; but by a sufficient cause, Hobbes, Locke and Hume would insist that it has to be something that is not the thing that it caused, that it must be distinct from and precede the caused event; so:
		Since human actions are themselves events, PSR would entail that every action has a sufficient reason, and PS, that every action has a sufficient cause.
		Condition (2) detaches the intelligibility of our actions from their having been caused—if an action is intelligible in the light of character and practical reason, then the issue of whether it is causally determined need not concern us.
	socrates.berkeley.edu /~loyhc/ph109/Principle_of_Sufficient_Reason.html (1212 words)

	Discussion of Principle of Sufficient Reason
		His rejection of Wolff is also a rebuttal of Hume's scepticism with regard to the principle of cause.
		The reason that this principle is so signficant is, to put it very simply, that we believe that anything that is has a reason why it is, and that with either sufficient reflection and/or investigation (depending upon whether you are an empiricist or rationalist or some mixture) we can always, in principle, grasp that reason.
		And because of this, he rejects the Wollfians reduction of the principle of sufficient reason to the principle of contradiction.
	hume.ucdavis.edu /mattey/kant/PSR.HTM (1131 words)

	Lectures on Immanuel Kant
		How can the understanding supply principles which serve to produce the unified whole we call "nature?" As Hume observed, such principles cannot be derived from perception, since we can observe only conjunction, not connection.
		For they imply that any alleged principle of sufficient reason is based on experience, in which objects of one kind are found to be associated with objects of another.
		The principle of substance is that every change is the change of the properties of a substance (which rules out the coming-to-be or passing away of any substance).
	www-philosophy.ucdavis.edu /mattey/phi023/kantLEC.HTM (7001 words)

	A Restricted Principle of Sufficient Reason and the Cosmological Argument
		“The Hume-Edwards Principle and the Cosmological Argument,” International Journal for the Philosophy of Religion 43 (1998), 149-65.
		A Restricted Principle of Sufficient Reason and the Cosmological Argument
		One of the main points of introducing the RPSR instead of the PSR was to placate opponents of the PSR who thought that this sort of thing can happen, so this possibility cannot be rejected without the RPSR's defender falling back on the PSR.
	www.georgetown.edu /faculty/ap85/papers/RPSR.html (1838 words)

	Glenn Shafer - c.v.
		"Huygens, Bernoulli, and Hume: The Art of Causal Conjecture." Harrisburg Chapter of the American Statistical Association.
		"Implications of Cournot's Principle for Machine Learning and Finance." Department of Computer Science, Royal Holloway College, June 29, 2004.
		The significance of Jacob Bernoulli's Ars Conjectandi for the philosophy of probability today.
	www.glennshafer.com /cv.html (3895 words)

	Friedrich A. Hayek
		The influence of the Kant-Friesian tradition on Hayek is evident in his use of two precepts: Hume's principle that the propositions of ethics cannot be proven, and Popper's principle that scientific knowledge proceeds by falsification, not by verification.
		Nevertheless, Hayek's Kantian understanding of Hume and his use of Popper's Friesian logic do provide us with epochal principles of political economy that are ultimately conformable to Kant-Friesian principles.
		Hayek thus shared with Hume a profound conviction that we should be "sensible of our ignorance." Hayek also shared with Hume the conviction that the "foundation of the inference" to propositions of ethics or politics was not necessarily available to us.
	www.friesian.com /hayek.htm (760 words)

	Friedrich A. Hayek
		The influence of the Kant-Friesian tradition on Hayek is evident in his use of two precepts: Hume's principle that the propositions of ethics cannot be proven, and Popper's principle that scientific knowledge proceeds by falsification, not by verification.
		Nevertheless, Hayek's Kantian understanding of Hume and his use of Popper's Friesian logic do provide us with epochal principles of political economy that are ultimately conformable to Kant-Friesian principles.
		Hayek thus shared with Hume a profound conviction that we should be "sensible of our ignorance." Hayek also shared with Hume the conviction that the "foundation of the inference" to propositions of ethics or politics was not necessarily available to us.
	www.friesian.com /hayek.htm (760 words)

	Friedrich A. Hayek
		The influence of the Kant-Friesian tradition on Hayek is evident in his use of two precepts: Hume's principle that the propositions of ethics cannot be proven, and Popper's principle that scientific knowledge proceeds by falsification, not by verification.
		Nevertheless, Hayek's Kantian understanding of Hume and his use of Popper's Friesian logic do provide us with epochal principles of political economy that are ultimately conformable to Kant-Friesian principles.
		Hayek thus shared with Hume a profound conviction that we should be "sensible of our ignorance." Hayek also shared with Hume the conviction that the "foundation of the inference" to propositions of ethics or politics was not necessarily available to us.
	www.friesian.com /hayek.htm (760 words)

	EJAP 5:3: Dieterle, "Julius Ceasar and the Number 2"
		In Chapter 4 of (1983), Crispin Wright derives Peano's postulates in second-order logic with Hume's principle as an added axiom.
		Hume's principle is, of course, Frege's contextual definition of number.
		[2] In Frege's Conception of Numbers as Objects, Crispin Wright argues that Frege's context principle-- "Never to ask for the bedeutung of a word in isolation, but only in the context of a sentence"-- should be interpreted as a principle concerning reference (as opposed to sense).
	ejap.louisiana.edu /EJAP/1997.spring/dieterle976.html (6292 words)

	Frege's Logic, Theorem, and Foundations for Arithmetic
		Frege's derivation of Hume's Principle was invalidated by the fact that it appeals to the inconsistent Basic Law V. Nevertheless, it is instructive to consider why Frege thought the derivation was valid.
		In the Grundgesetze, Frege used Basic Law V to derive Hume's Principle, but the derivations of the fundamental propositions of arithmetic from Hume's Principle do not essentially require Basic Law V.
		Since it is only in the context of a proposition that words have any meaning, our problem becomes this: To define the sense of a proposition in which a number word occurs.
	plato.stanford.edu /entries/frege-logic (15095 words)

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In the News (Mon 4 Jun 12)