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All the ideas for 'Mathematical Methods in Philosophy', 'Magna Carta' and 'On Sense and Reference'

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43 ideas

3. Truth / A. Truth Problems / 5. Truth Bearers
Frege was strongly in favour of taking truth to attach to propositions [Frege, by Dummett]
     Full Idea: Frege was strongly in favour of taking truth to attach to propositions, which he called 'thoughts' and regarded as being expressed by sentences.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Truth and the Past 1
     A reaction: Sometimes it is necessary to know the time, the place, and the speaker before one can evaluate the truth of a proposition. Not just indexical words, but the indexical aspect of, say, "the team played badly".
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
     Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1)
     A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark.
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
     Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise.
5. Theory of Logic / F. Referring in Logic / 1. Naming / a. Names
We can treat designation by a few words as a proper name [Frege]
     Full Idea: The designation of a single object can also consist of several words or other signs. For brevity, let every such designation be called a proper name.
     From: Gottlob Frege (On Sense and Reference [1892]), quoted by Bernard Linsky - Quantification and Descriptions 1
     A reaction: Frege regards names and descriptions as in the same class. Russell, and then Kripke, had things to say about that.
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
Proper name in modal contexts refer obliquely, to their usual sense [Frege, by Gibbard]
     Full Idea: According to Frege, a proper name in a modal context refers obliquely; its reference there is its usual sense.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Allan Gibbard - Contingent Identity V
     A reaction: [he cites the fourth page of Frege's 'Sense and Reference'] One can foresee problems with the word 'usual' here. Frege might be offering something better than Kripke does here.
A Fregean proper name has a sense determining an object, instead of a concept [Frege, by Sainsbury]
     Full Idea: We could think of a referring expression in Fregean terms as what he calls a proper name (Eigenname): its Sinn (sense) is supposed to determine an object as opposed to a concept as its Bedeutung (referent).
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Mark Sainsbury - The Essence of Reference 18.1
     A reaction: The problem would be that the same expression could precisely indicate an object on one occasion, nearly do so on another, and totally fail on a third.
People may have different senses for 'Aristotle', like 'pupil of Plato' or 'teacher of Alexander' [Frege]
     Full Idea: In the case of an actual proper name such as 'Aristotle' opinions as to the sense may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great.
     From: Gottlob Frege (On Sense and Reference [1892], note), quoted by Bernard Linsky - Quantification and Descriptions 1
     A reaction: This note is 'notorious', and was a central target for Kripke's critique. Frege says people's senses may vary on this, and thinks the sense of 'Aristotle' can be accurately expressed.
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
The meaning of a proper name is the designated object [Frege]
     Full Idea: The meaning of a proper name is the object itself which we designate by using it.
     From: Gottlob Frege (On Sense and Reference [1892], p.30)
     A reaction: I can't actually make sense of this. How can a physical object be identical with a meaning? What sort of thing is a 'meaning'? Meanings are just 'in the head', I suspect.
5. Theory of Logic / F. Referring in Logic / 1. Naming / d. Singular terms
Frege ascribes reference to incomplete expressions, as well as to singular terms [Frege, by Hale]
     Full Idea: Frege ascribes reference not only to singular terms, but equally to expressions of other kinds (the various kinds of incomplete expressions).
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Bob Hale - Abstract Objects Ch.3 Intro
     A reaction: The incomplete expressions presumably make reference to concepts. Frege may not seem, therefore, to have a notion of reference as what plugs language into reality - except that he is presumably a platonist about concepts.
5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names
If sentences have a 'sense', empty name sentences can be understood that way [Frege, by Sawyer]
     Full Idea: Frege's theory of 'sense' showed how sentences with empty names can have meaning and be understood. One just has to grasp the sense of the sentence (the thought expressed), and this is available even in the absence of a referent for the name.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Sarah Sawyer - Empty Names 2
     A reaction: My immediate reaction is that this provides a promising solution to the empty names problem, which certainly never bothered me before I started reading philosophy. Sawyer says co-reference and truth problems remain.
It is a weakness of natural languages to contain non-denoting names [Frege]
     Full Idea: Languages have the fault of containing expressions which fail to designate an object.
     From: Gottlob Frege (On Sense and Reference [1892], p.40)
     A reaction: Wrong, Frege! This is a strength of natural languages! Names are tools. It isn't a failure of your hammer if you can't find any nails.
In a logically perfect language every well-formed proper name designates an object [Frege]
     Full Idea: A logically perfect language should satisfy the conditions that every expression grammatically well constructed as a proper name out of signs already introduced shall in fact designate an object.
     From: Gottlob Frege (On Sense and Reference [1892], p.41)
     A reaction: This seems to cramp your powers of reasoning, if you must know the object to use the name ('Jack the Ripper'), and reasoning halts once you deny the object's existence ('Pegasus'), or you don't know if names co-refer ('Hesperus/Phosphorus').
5. Theory of Logic / I. Semantics of Logic / 6. Intensionalism
Frege is intensionalist about reference, as it is determined by sense; identity of objects comes first [Frege, by Jacquette]
     Full Idea: Intensionalism of reference is owing to Frege (in his otherwise extensionalist philosophy of language). Sense determines reference, so intension determines extension. An object must first satisfy identity requirements, and is thus in a set.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Dale Jacquette - Intro to 'Philosophy of Logic' §4
     A reaction: The notion that identity of objects comes first sounds right - you can't just take objects as basic - they have to be individuated in order to be discussed.
Frege moved from extensional to intensional semantics when he added the idea of 'sense' [Frege, by Sawyer]
     Full Idea: Frege moved from an extensional semantic theory (that countenances only linguistic expressions and their referents) to an intensional theory that invokes in addition a notion of sense.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Sarah Sawyer - Empty Names 2
     A reaction: This was because of Frege's famous 'puzzles', such as the morning/evening star. Quine loudly proclaimed himself an 'extensionalist', implying that he had extensional solutions for Frege's Puzzles.
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
     Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea.
7. Existence / A. Nature of Existence / 1. Nature of Existence
If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
     Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2)
     A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting.
8. Modes of Existence / D. Universals / 1. Universals
We can't get a semantics from nouns and predicates referring to the same thing [Frege, by Dummett]
     Full Idea: Frege is denying that on a traditional basis we can construct a workable semantics for a language; we can't regard terms like 'wisdom' as standing for the very same thing as the predicate 'x is wise' stands for.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14
     A reaction: This follows from Idea 10532, indicating how to deal with the problem of universals. So predicates refer to concepts, and singular terms to objects. But I see no authoritative way of deciding which is which, given that paraphrases are possible.
9. Objects / F. Identity among Objects / 1. Concept of Identity
Frege was asking how identities could be informative [Frege, by Perry]
     Full Idea: A problem which Frege called to our attention is: how can identities be informative?
     From: report of Gottlob Frege (On Sense and Reference [1892]) by John Perry - Knowledge, Possibility and Consciousness §5.2
     A reaction: E.g. (in Russell's example) how is "Scott is the author of 'Waverley'" more informative than "Scott is Scott"? A simple answer might just be that informative identities also tell you of a thing's properties. "The red ball is the heavy ball".
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
     Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory.
The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
     Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
     Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
     A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular).
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
     Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3)
     A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds.
Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
     Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial.
     From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5)
     A reaction: They accept lots of successes in modelling necessity and time.
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
'The concept "horse"' denotes a concept, yet seems also to denote an object [Frege, by McGee]
     Full Idea: The phrase 'the concept "horse"' can be the subject of a sentence, and ought to denote an object. But it clearly denotes the concept "horse". Yet Fregean concepts are said to be 'incomplete' objects, which led to confusion.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Vann McGee - Logical Consequence 4
     A reaction: This is the notorious 'concept "horse"' problem, which was bad news for Frege's idea of a concept.
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Frege failed to show when two sets of truth-conditions are equivalent [Frege, by Potter]
     Full Idea: Frege's account suffered from a lack of precision about when two sets of truth-conditions should count as equivalent. (Wittgenstein aimed to rectify this defect).
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 50 Intro
The meaning (reference) of a sentence is its truth value - the circumstance of it being true or false [Frege]
     Full Idea: We are driven into accepting the truth-value of a sentence as constituting what it means (refers to). By the truth-value I understand the circumstance that it is true or false.
     From: Gottlob Frege (On Sense and Reference [1892], p.34)
     A reaction: Sounds bizarre, but Black's translation doesn't help. The notion of what the whole sentence refers to (rather than its sense) is a very theoretical notion. 'All true sentences refer to the truth' sounds harmless enough.
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
Holism says all language use is also a change in the rules of language [Frege, by Dummett]
     Full Idea: Frege thought of a language as a game played with fixed rules, there being all the difference in the world between a move in the game and an alteration of the rules; but, if holism is correct, every move in the game changes the rules.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege's Distinction of Sense and Reference p.248
     A reaction: Rules do shift over time, so there must be some mechanism for that - the rules can't sit in sacrosanct isolation. People play games with the language itself, as well as using it to play other games.
19. Language / B. Reference / 1. Reference theories
The reference of a word should be understood as part of the reference of the sentence [Frege]
     Full Idea: I have transferred the relation between the parts and the whole of the sentence to its reference, by calling the reference of the word part of the reference of the sentence, if the word itself is part of the sentence.
     From: Gottlob Frege (On Sense and Reference [1892], p.35)
     A reaction: Since Frege says the reference of a true sentence is simply to truth, words have reference insofar as they make contributions to attempts at stating truths.
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
Frege's Puzzle: from different semantics we infer different reference for two names with the same reference [Frege, by Fine,K]
     Full Idea: Frege's Puzzle: If two sentences convey different information, they have different semantic roles, so the names 'Cicero' and 'Tully' are semantically different, in which case they are referentially different - but they are not referentially different.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Kit Fine - Semantic Relationism 2.A
     A reaction: [this is my summary of Fine's summary] Given the paradox, the question is which of these premisses should be challenged. Fregeans reject their being referentially different. Referentialists reject the different semantic roles.
Frege's 'sense' is ambiguous, between the meaning of a designator, and how it fixes reference [Kripke on Frege]
     Full Idea: Frege should be criticised for using the term 'sense' in two senses. He takes the sense of a designator to be its meaning; and he also takes it to be the way its reference is determined. …They correspond to two ordinary uses of 'definition'.
     From: comment on Gottlob Frege (On Sense and Reference [1892]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1
     A reaction: Stalnaker quotes this, but seems unconvinced that Frege is guilty. If the 'meaning' largely consists of a way of determining a reference, Frege would be in the clear.
Every descriptive name has a sense, but may not have a reference [Frege]
     Full Idea: It may perhaps be granted that every grammatically well-formed expression representing a proper name always has a sense. But this is not to say that to this sense there also corresponds a reference.
     From: Gottlob Frege (On Sense and Reference [1892]), quoted by Bernard Linsky - Quantification and Descriptions 3.1
     A reaction: Presumably this concerns fictional names such as 'Pegasus'. It seems to be good simple evidence for the distinction between sense and reference.
Frege started as anti-realist, but the sense/reference distinction led him to realism [Frege, by Benardete,JA]
     Full Idea: In the Grundlagen of 1884 Frege was an anti-realist, but in Grundgesetze of 1893 he is a realist, who has profited by his interim discovery of the sense/reference distinction.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by José A. Benardete - Logic and Ontology
     A reaction: This is the germ of the new realist philosophy which seems to be growing out of Kripke and co's causal theory of reference. The very notion of reference is realist (hence Russell's realism).
The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense [Frege]
     Full Idea: The meaning (reference) of 'evening star' is the same as that of 'morning star', but not the sense.
     From: Gottlob Frege (On Sense and Reference [1892], p.27)
     A reaction: Max Black translates 'bedeutung' as 'meaning', but nowadays everyone calls it 'reference'. This is Frege's crucial distinction, which greatly clarified analytical philosophy. Nevertheless, is it a sharp distinction? E.g. referring to a fictional name?
In maths, there are phrases with a clear sense, but no actual reference [Frege]
     Full Idea: The expression 'the least rapidly convergent series' has a sense but demonstrably there is no reference, since a less rapidly convergent series (for any given series) can always be found.
     From: Gottlob Frege (On Sense and Reference [1892], p.28)
     A reaction: A nice example. 'The second Kennedy assassin' has a clear meaning, but does it have a reference? The meaning 'points at' a possible reference. We yet discover an identity.
We are driven from sense to reference by our desire for truth [Frege]
     Full Idea: The striving for truth drives us always to advance from the sense to the thing meant (the reference).
     From: Gottlob Frege (On Sense and Reference [1892], p.33)
     A reaction: As in, we want to know the reference of 'the person who shot Kennedy'. I always perk up if truth is mentioned in a discussion of language, because it reminds us of the point of the whole thing. In 'Is he the best man?' I have the reference, not the truth.
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Expressions always give ways of thinking of referents, rather than the referents themselves [Frege, by Soames]
     Full Idea: For Frege, expressions always contribute ways of thinking of their referents, rather than the referents themselves, to the thoughts expressed by sentences.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Scott Soames - Philosophy of Language 1.16
     A reaction: I have some sympathy for Frege. It always strikes me as daft to think that if I say 'my dustbin is empty', the dustbin becomes 'part' of my sentence. Sentences don't contain large plastic objects.
19. Language / C. Assigning Meanings / 5. Fregean Semantics
'Sense' gives meaning to non-referring names, and to two expressions for one referent [Frege, by Margolis/Laurence]
     Full Idea: Frege notes that an expression without a referent ('Pegasus') needn't lack a meaning, since it still has a sense, and the same referent (Eric Blair) can be associated with different expressions (George Orwell) because they convey different senses.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by E Margolis/S Laurence - Concepts 1.3
     A reaction: A nice neat summary of the value of Frege's introduction of the sense/reference distinction, which seems to me to be virtually undeniable (a rare event in modern philosophy).
Frege was the first to construct a plausible theory of meaning [Frege, by Dummett]
     Full Idea: Frege was the first to construct a plausible theory of meaning, that is, a theory of how a human language functions.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Thought and Reality 1
     A reaction: Presumably Frege had an advantage because he was the first to distinguish sense from reference, and hence to identify the subject-matter of the theory. Essentially Frege's theory is that of truth-conditions.
Earlier Frege focuses on content itself; later he became interested in understanding content [Frege, by Dummett]
     Full Idea: Earlier Frege was interested solely in the content of our statements, not in our grasp of that content. His notion of 'sense' from 1891 onwards, has to do with understanding; the sense of an expression is something we grasp.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Frege philosophy of mathematics Ch.2
     A reaction: The important point must be that the later theory depends on the earlier, so we can hardly give theories of understanding, if we don't have a view about what it is that is understood.
Frege divided the meaning of a sentence into sense, force and tone [Frege, by Dummett]
     Full Idea: Frege distinguished three components of the meaning of a sentence: sense, force and tone; he used no single term for 'linguistic meaning' in general. ...The sense is only what bears on the truth or falsity of what the sentence expresses.
     From: report of Gottlob Frege (On Sense and Reference [1892]) by Michael Dummett - Thought and Reality 3
     A reaction: Modern theories of meaning seem to assume that there is one item called 'meaning' which needs to be explained, but presumably this is 'strict and literal meaning', leaving the rest to pragmatics.
Frege uses 'sense' to mean both a designator's meaning, and the way its reference is determined [Kripke on Frege]
     Full Idea: Frege should be criticised for using the term 'sense' in two senses. For he takes the sense of a designator to be its meaning; and he also takes it to be the way its reference is determined.
     From: comment on Gottlob Frege (On Sense and Reference [1892]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1
     A reaction: This criticism doesn't surprise me, as heroic pioneers like Frege seem to have been extremely unclear about what they were claiming. Kripke has helped, but we still need some great mind to step in and sort out the mess.
Frege explained meaning as sense, semantic value, reference, force and tone [Frege, by Miller,A]
     Full Idea: Frege analysed the intuitive notion of meaning in terms of the notions of sense, semantic value, reference, force and tone.
     From: report of Gottlob Frege (On Sense and Reference [1892], Pref) by Alexander Miller - Philosophy of Language Pref
     A reaction: This suggests that there are two approaches to the explanation of meaning: either a simple identity with some other mental fact, or an analysis (as here) into a range of components. I remain open-minded on that.
25. Social Practice / D. Justice / 2. The Law / b. Rule of law
Magna Carta forbids prison without trial, and insists on neutral and correct process [-, by Charvet]
     Full Idea: The Magna Carta forbids the King to imprison indefinitely without trial, and also binds the King to follow due process in his courts and not allow the justice provided to be for sale.
     From: report of - (Magna Carta [1215]) by John Charvet - Liberalism: the basics 02
     A reaction: Very exasperating for a medieval monarch. In current times British law is exceedingly slow (so long imprisonment before trial), and the necessary effective advocates cost vastly too much for all but a tiny minority. So it's going badly.