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All the ideas for 'Mathematical Methods in Philosophy', 'Mental Content' and 'Analyticity Reconsidered'

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34 ideas

2. Reason / D. Definition / 4. Real Definition
A sentence may simultaneously define a term, and also assert a fact [Boghossian]
     Full Idea: It doesn't follow from the fact that a given sentence is being used to implicitly define one of its ingredient terms, that it is not a factual statement. 'This stick is a meter long at t' may define an ingredient terms and express something factual.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: This looks like a rather good point, but it is tied in with a difficulty about definition, which is deciding which sentences are using a term, and which ones are defining it. If I say 'this stick in Paris is a meter long', I'm not defining it.
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 / I. Semantics of Logic / 2. Formal Truth
Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian]
     Full Idea: Conventualism is a factualist view: it presupposes that sentences of logic have truth values. It differs from a realist view in its conception of the source of those truth values, not on their existence. I call the denial of truths Non-Factualism.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: It barely seems to count as truth is we say 'p is true because we say so'. It is a truth about an agreement, not a truth about logic. Driving on the left isn't a truth about which side of the road is best.
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.
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.
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian]
     Full Idea: Isn't it overwhelmingly obvious that 'Either snow is white or it isn't' was true before anyone stipulated a meaning for it, and that it would have been true even if no one had thought about it, or chosen it to be expressed by one of our sentences?
     From: Paul Boghossian (Analyticity Reconsidered [1996], §I)
     A reaction: Boghossian would have to believe in propositions (unexpressed truths) to hold this - which he does. I take the notion of truth to only have relevance when there are minds around. Otherwise the so-called 'truths' are just the facts.
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian]
     Full Idea: The central impetus behind the analytic explanation of the a priori is a desire to explain the possibility of a priori knowledge without having to postulate a special evidence-gathering faculty of intuition.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §I)
     A reaction: I don't see at all why one has to postulate a 'faculty' in order to talk about intuition. I take an intuition to be an apprehension of a probable truth, combined with an inability to articulate how the conclusion was arrived at.
That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian]
     Full Idea: The analytic theory of the apriority of logic arose indirectly, as a by-product of the attempt to explain in what a grasp of the meaning of the logical constants consists.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: Preumably he is referring to Wittgenstein's anguish over the meaning of the word 'not' in his World War I notebooks. He first defined the constants by truth tables, then asserted that they were purely conventional - so logic is conventional.
We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian]
     Full Idea: If there is no sentence I must hold true if it is to mean what it does, then there is no basis on which to argue that I am entitled to hold it true without evidence.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: He is exploring Quine's view. Truth by convention depends on agreeing which part of the usage of a term constitutes its defining sentence(s), and that may be rather tricky. Boghossian says this slides into the 'dreaded indeterminacy of meaning'.
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian]
     Full Idea: It is consistent with a belief's being a priori in the strong sense that we should have pragmatic reasons for dropping it from our best overall theory.
     From: Paul Boghossian (Analyticity Reconsidered [1996], n 6)
     A reaction: Does 'dropping it' from the theory mean just ignoring it, or actually denying it? C.I. Lewis is the ancestor of this view. Could it be our 'best' theory, while conflicting with beliefs that were strongly a priori? Pragmatism can embrace falsehoods.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian]
     Full Idea: If we learn geometrical truths by intuition, how could this faculty have misled us for so long?
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: This refers to the development of non-Euclidean geometries, though the main misleading concerns parallels, which involves infinity. Boghossian cites 'distance' as a concept the Euclideans had misunderstood. Why shouldn't intuitions be wrong?
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Some explanations offer to explain a mystery by a greater mystery [Schulte]
     Full Idea: An 'obscurum per obscurius' explanation is explaining something mysterious by something even more mysterious,
     From: Peter Schulte (Mental Content [2023], 6)
     A reaction: Schulte's example is trying to explain mental content in terms of phenomenal experience. That is, roughly, explaining content by qualia, when the latter is the 'hard problem'.
18. Thought / C. Content / 1. Content
Phenomenal and representational character may have links, or even be united [Schulte]
     Full Idea: Some theorists maintain that all states with representational content or intentionality must have phenomenal character …and we can also ask whether all states with phenomenal character also have representional content.
     From: Peter Schulte (Mental Content [2023], 2.4)
     A reaction: He mentions that beliefs could involve inner speech. And pains and moods may be phenomenal but lack content. He also asks which determines which.
Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte]
     Full Idea: A 'naturalistic' explanation of content excludes primitive mental or normative notions, but allows causation, counterfactual dependence, probabilistic dependence or structural similarity.
     From: Peter Schulte (Mental Content [2023], 4)
     A reaction: Apart from causation, what is permissible to naturalists (like me) all sounds rather superficial (and thus not very explanatory). I'm sure we can do better than this. How about using non-primitive mental notions?
Maybe we can explain mental content in terms of phenomenal properties [Schulte]
     Full Idea: The phenomenal intentionality approach says that the content properties of mental states can be explained in terms of the phenomenal properties of mental states.
     From: Peter Schulte (Mental Content [2023], 6)
     A reaction: [Searle and Loar are cited] Tends to be 'non-naturalistic'. We might decide that content derives from the phenomenal, but still without saying anything interesting about content. Mathematical content? Universally generalised content?
Naturalist accounts of representation must match the views of cognitive science [Schulte]
     Full Idea: Recent naturalisation of content now also has to offer a matching account of representational explanations in cognitive science.
     From: Peter Schulte (Mental Content [2023], 08.1)
     A reaction: [He cites Cummins, Neander and Shea] This is in addition to the 'status' and 'content' questions of Idea 23796. This seems to be an interesting shift to philosophers working backwards from the theories of empirical science. Few are qualified for this job!
On the whole, referential content is seen as broad, and sense content as narrow [Schulte]
     Full Idea: We can say that non-Fregean content [reference] is (virtually) always contrued as broad, while Fregean content [sense] is usually contrued as narrow.
     From: Peter Schulte (Mental Content [2023], 3.2)
     A reaction: I can't make sense of mental content actually being outside the mind, so I see all content as narrow - but that doesn't mean that externals are irrelevant to it. If I think that is an oak, and it's an elm, the content is oak.
Naturalists must explain both representation, and what is represented [Schulte]
     Full Idea: Naturalistic accounts of content ask 1) what makes a state qualify as a representational state?, and 2) what makes a representational state have one specific content rather than another?
     From: Peter Schulte (Mental Content [2023], 4)
     A reaction: [As often in this collection, the author uses algebraic letters, but I prefer plain English] I would say that the first question looks more amenable to an answer than the second. Do we know the neuronal difference between seeing red and blue?
18. Thought / C. Content / 9. Conceptual Role Semantics
Conceptual role semantics says content is determined by cognitive role [Schulte]
     Full Idea: Conceptual role semantics says the content of a representation is determined by the cognitive role it plays with a system.
     From: Peter Schulte (Mental Content [2023], 4.5)
     A reaction: Obvious problem: if 'swordfish' is the password, its role is quite different from its content. I've never thought that the role of something tells you anything about what it is. Hearts pump blood, but how do they fulfil that role?
18. Thought / C. Content / 10. Causal Semantics
Cause won't explain content, because one cause can produce several contents [Schulte]
     Full Idea: A simple causal theory of content has the 'content indeterminacy' problem - that the presence of a cow causes 'a cow is present', but also 'an animal is present' and 'a biological organism is present'.
     From: Peter Schulte (Mental Content [2023], 4.1)
     A reaction: That only rules out the 'simple' version. We just need to add that the cause (cow experience) is shaped by current knowledge and interests. Someone buying cows and someone terrified of them thereby produce different concepts.
18. Thought / C. Content / 11. Teleological Semantics
Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte]
     Full Idea: The core idea of teleosemantics is that we need to explain how content can be accurate or inaccurate, true or false, realised or unrealised …which must appeal to the distinction between proper functioning and malfunctioning.
     From: Peter Schulte (Mental Content [2023], 4.4)
     A reaction: My immediate reaction to this is that you don't learn about content by assessing its success. Surely (as with eyesight) you first need to understand what it does, and only then judge its success. …Though success and failure are implicit in function.
Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte]
     Full Idea: Teleosemantic theories usually give a causal account of mental functions …where some trait has a particular function if it was selected for that function by a process of natural selection.
     From: Peter Schulte (Mental Content [2023], 4.4)
     A reaction: This is an idea I like - that something has a specific function if without that function it wouldn't have come into existence (eyes, for example). But presumably the function of a mind is to collect content - which does nothing to explain content!
18. Thought / C. Content / 12. Informational Semantics
Information theories say content is information, such as smoke making fire probable [Schulte]
     Full Idea: Information theories of content [usually assume that] a column of smoke over there carries the information that fire is over there because it raises the probability of fire being over there.
     From: Peter Schulte (Mental Content [2023], 4.2)
     A reaction: Theorists usually add further conditions to this basic one. Fred Dretske is the source of this approach. Not promising, in my opinion. Surely the content is just smoke, and fire is one of dozens of possible inferences from it?
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian]
     Full Idea: Conceptual Role Semantics must explain what properties an inference or sentence involving a logical constant must have, if that inference or sentence is to be constitutive of its meaning.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: This is my perennial request that if something is to be defined by its function (or role), we must try to explain what properties it has that make its function possible, and those properties will be the more basic explanation.
'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian]
     Full Idea: 'Conceptual role semantics' says the logical constants mean what they do by virtue of figuring in certain inferences and/or sentences involving them and not others, ..so some inferences and sentences are constitutive of an expression's meaning.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §III)
     A reaction: If the meaning of the terms derives from the sentences in which they figure, that seems to be meaning-as-use. The view that it depends on the inferences seems very different, and is a more interesting but more risky claim.
19. Language / A. Nature of Meaning / 8. Synonymy
Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian]
     Full Idea: Could there be a fact of the matter about what each expression means, but no fact of the matter about whether they mean the same?
     From: Paul Boghossian (Analyticity Reconsidered [1996], §II)
     A reaction: He is discussing Quine's attack on synonymy, and his scepticism about meaning. Boghossian and I believe in propositions, so we have no trouble with two statements having the same meaning. Denial of propositions breeds trouble.
19. Language / E. Analyticity / 2. Analytic Truths
There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins]
     Full Idea: Boghossian distinguishes metaphysical analyticity (truth purely in virtue of meaning, debunked by Quine, he says) from epistemic analyticity (knowability purely in virtue of understanding - a notion in good standing).
     From: report of Paul Boghossian (Analyticity Reconsidered [1996]) by Carrie Jenkins - Grounding Concepts 2.4
     A reaction: [compressed] This fits with Jenkins's claim that we have a priori knowledge just through understanding and relating our concepts. She, however, rejects that idea that a priori is analytic.
19. Language / E. Analyticity / 3. Analytic and Synthetic
Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian]
     Full Idea: The epistemological notion of analyticity: a statement is 'true by virtue of meaning' provided that grasp of its meaning alone suffices for justified belief in its truth; the metaphysical reading is that it owes its truth to its meaning, not to facts.
     From: Paul Boghossian (Analyticity Reconsidered [1996], §I)
     A reaction: Kripke thinks it is neither, but is a purely semantic notion. How could grasp of meaning alone be a good justification if it wasn't meaning which was the sole cause of the statement's truth? I'm not convinced by his distinction.