25 ideas
7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
Full Idea: There is, in addition to the external world of physical objects and the internal world of ideas, a third realm of non-spatio-temporal objective objects, among which are thoughts. | |
From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Joan Weiner - Frege Ch.7 | |
A reaction: This seems to be Platonism, and, in particular, to give a Platonic existent status to propositions. Personally I believe in propositions, but as glimpses of how our brains actually work, not as mystical objects. |
19466 | The word 'true' seems to be unique and indefinable [Frege] |
Full Idea: It seems likely that the content of the word 'true' is sui generis and indefinable | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60)) | |
A reaction: This is the view I associate with Davidson, though fans of Axiomatic Truth give up defining it, and just describe how it behaves. Defining it is very elusive, but I don't accept that nothing can be said about the contents of the concept of truth. |
19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
Full Idea: If truth can be explicitly defined, it can be eliminated. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
A reaction: That we could just say p corresponds to the facts, or p coheres with our accepted beliefs, or p is the aim of our enquiries, and never mention the word 'true'. Definition is a strategy for reduction or elimination. |
19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
Full Idea: It is essential that the reality shall be distinct from the idea. But then there can be no complete correspondence, no complete truth. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327 (60)) | |
A reaction: He thinks that logic can give a perfect account of truth, or at least the extension of truth, where ordinary language will always fail. I wonder what he would have thought of Tarski's theory? |
19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
Full Idea: If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3) | |
A reaction: I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction. |
19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
Full Idea: Semantic approaches to truth usually necessitate the use of a metalanguage that is more powerful than the object-language for which it provides a semantics. It is usually taken to include set theory. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1) | |
A reaction: This is a motivation for developing an axiomatic account of truth, that moves it into the object language. |
19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
Full Idea: Although the theory is materially adequate, Tarski thought that the T-sentences are deductively too weak. …Also it seems that the T-sentences are not conservative, because they prove in PA that 0=0 and ¬0=0 are different, so at least two objects exist. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.2) | |
A reaction: They are weak because they can't prove completeness. This idea give two reasons for looking for a better theory of truth. |
19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
Full Idea: If a natural theory of truth is added to Peano Arithmetic, it is not necessary to add explicity global reflection principles to assert soundness, as the truth theory proves them. Truth theories thus prove soundess, and allows its expression. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.2) | |
A reaction: This seems like a big attraction of axiomatic theories of truth for students of metamathematics. |
19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
Full Idea: If truth does not have any explanatory force, as some deflationists claim, the axioms of truth should not allow us to prove any new theorems that do not involve the truth predicate. That is, a deflationary axiomatisation of truth should be 'conservative'. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.3) | |
A reaction: So does truth have 'explanatory force'? These guys are interested in explaining theorems of arithmetic, but I'm more interested in real life. People do daft things because they have daft beliefs. Logic should be neutral, but truth has values? |
19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
Full Idea: It is a virtue of the Friedman-Sheard axiomatisation that it is thoroughly classical in its logic. Its drawback is that it is ω-inconsistent. That is, it proves &exists;x¬φ(x), but proves also φ(0), φ(1), φ(2), … | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.3) | |
A reaction: It seems the theory is complete (and presumably sound), yet not fully consistent. FS also proves the finite levels of Tarski's hierarchy, but not the transfinite levels. |
19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
Full Idea: KF is formulated in classical logic, but describes a non-classical notion of truth. It allow truth-value gluts, making some sentences (such as the Liar) both true and not-true. Some authors add an axiom ruling out such gluts. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 4.4) | |
A reaction: [summary, which I hope is correct! Stanford is not wholly clear] |
19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
Full Idea: The sentence 'I smell the scent of violets' has just the same content as 'It is true that I smell the scent of violets'. So it seems that nothing is added to the thought by my ascribing to it the property of truth. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.328 (61)) | |
A reaction: This idea predates Ramsey's similar proposal, for which, oddly, Ramsey always seems to get the credit. To a logician they may have identical content, but pragmatically they are likely to differ in context. 'True' certainly doesn't add to the thought. |
19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
Full Idea: Thoughts are neither things in the external world nor ideas. A third realm must be recognised. Anything in this realm has it in common with ideas that it cannot be perceived by the senses, and does not need an owner to belong with his consciousness. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.337(69)) | |
A reaction: This important idea is the creed for modern platonists. We don't have to accept Forms, or any particular content, but there is a mode of existence which is distinct from both mental and physical, and is the residence of 'abstracta'. I deny it! |
19471 | A fact is a thought that is true [Frege] |
Full Idea: A fact is a thought that is true. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.342(74)) | |
A reaction: It strikes me as pretty obvious that facts are not thoughts, because they concern the contents of thoughts. You can't discuss facts without the notion of what a thought is 'about'. If I think about my garden, the relevant fact is aspects of my garden. |
19121 | We can reduce properties to true formulas [Halbach/Leigh] |
Full Idea: One might say that 'x is a poor philosopher' is true of Tom instead of saying that Tom has the property of being a poor philosopher. We quantify over formulas instead of over definable properties, and thus reduce properties to truth. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
A reaction: [compressed] This stuff is difficult (because the axioms are complex and hard to compare), but I am excited (yes!) about this idea. Their point is that you need a truth predicate within the object language for this, which disquotational truth forbids. |
19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
Full Idea: The reduction of second-order theories (of properties or sets) to axiomatic theories of truth is a form of reductive nominalism, replacing existence assumptions (e.g. comprehension axioms) by innocuous assumptions about the truth predicate. | |
From: Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 1.1) | |
A reaction: I'm currently thinking that axiomatic theories of truth are the most exciting development in contemporary philosophy. See Halbach and Horsten. |
9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
Full Idea: Earlier, Frege divided objects into subjective, actual objective, and non-actual objective; in the 'Grundgesetze' he emphasised logical objects; but in 'The Thought' the non-actual objects become exclusively thoughts and their constituent senses. | |
From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
A reaction: Sounds to me like Frege was finally waking up and taking a dose of common sense. The Equator is the standard example of a non-actual objective object. |
19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
Full Idea: We distinguish the grasp of a thought, which is 'thinking', from the acknowledgement of the truth of a thought, which is the act of 'judgement', from the manifestation of this judgement, which is an 'assertion'. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.329 (62)) |
8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
Full Idea: For Frege, thoughts belong to a special realm of reality, which he called the 'realm of sense' and distinguished from the 'realm of reference'. | |
From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Thought and Reality 1 | |
A reaction: A thought is, for Frege, a proposition. There is a halfway Platonism possible here, where the 'realm' for such things exists, but within that realm the objects might be conventional, or some such. Real possible worlds containing fictions! |
9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
Full Idea: On Frege's view, what distinguishes thoughts from everything else is that they may meaningfully be called 'true' and 'false'. | |
From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Michael Dummett - Frege philosophy of mathematics Ch.2 | |
A reaction: A lot of thinking is imagistic, and while the image may or may not truly picture the world, we tend to think that the truth or otherwise of daydreaming is simply irrelevant. Does Frege take all thought to be propositional? |
16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
Full Idea: When Dr Lauben thinks he has been wounded, ..only Dr Lauben can grasp thoughts determined in this way. But he cannot communicate a thought which only he can grasp. To say 'I have been wounded' he must use 'I' in a sense graspable by others. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918]), quoted by François Recanati - Mental Files 16.1 | |
A reaction: [compressed] This seems to be the first, and very influential, attempt to explain the unusual and revealing semantics of indexicals. It seems to be the ultimate source of 2-D semantics, by introducing two modes of meaning for one term. |
19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
Full Idea: I call a 'thought' something for which the question of truth can arise at all. ...So I can say: thoughts are senses of sentences, without wishing to assert that the sense of every sentence is a thought. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.327-8 (61)) | |
A reaction: This builds on his distinction between sense and reference. The reference of every truth sentence is just 'the true', and the sense is the proposition. The concept of a proposition seems indispensable to logic, I would say. |
19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
Full Idea: Only a sentence with the time-specification filled out, a sentence complete in every respect, expresses a thought. | |
From: Gottlob Frege (The Thought: a Logical Enquiry [1918], p.343(76)) | |
A reaction: I take the 'every respect' to include the avoidance of ambiguity, and some sort of perspicacious reference for the terms. I wish philosophers would focus on the thoughts in their subject, and not nit-pick about the sentences. Does he mean 'utterances'? |
21995 | Must production determine superstructure, or could it be the other way round? [Singer on Marx] |
Full Idea: Once the 'interaction' between the superstructure and the productive forces is admitted, is it still possible to maintain that production determines the superstructure, rather than the other way round? | |
From: comment on Karl Marx (Capital Vol. 1 [1867]) by Peter Singer - Marx 7 | |
A reaction: It is much harder to defend historical determinism if Singer is right about this. Modern capitalism won't admit of the sort of simple distinctions that mark was looking for. |
20577 | Even decently paid workers still have their produce bought with money stolen from them [Marx] |
Full Idea: Even if the workers are paid a fair wage, the whole thing still remains the age-old activity of the conqueror, who buys commodities from the conquered with the money has has stolen from them, | |
From: Karl Marx (Capital Vol. 1 [1867], p.728), quoted by Johanna Oksala - Political Philosophy: all that matters Ch.8 | |
A reaction: [Penguin edition cited] The word 'stolen' is obviously dubious here. 'Exploitation' is a much more accurate word. One might talk of 'blackmail' or 'extortion' rather than theft. |