20 ideas
| 7493 | Let us reason together, saith the Lord [Isaiah] |
| Full Idea: Come now, and let us reason together, saith the Lord. | |
| From: Isaiah (23: Book of Isaiah [c.680 BCE], 01.18) | |
| A reaction: A verse which not only offers Biblical support for philosophy, but would also seem to be a challenge to Christian fideists. |
| 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. |
| 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] |
| 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. |
| 23514 | The cerbellum has a huge number of neurons, but little involvement in consciousness [Seth] |
| Full Idea: The cerebellum [at the back] has about four times as many neurons as the rest of the brain put together, but seems barely involved in consciousness. | |
| From: Anil Seth (Being You [2021], I.2) | |
| A reaction: I wonder if it also has four times as many connections? |
| 23513 | Single neurons can carry out complex functions [Seth] |
| Full Idea: It is increasingly apparent that even single neurons are capable of carrying out highly complex functions all by themselves. | |
| From: Anil Seth (Being You [2021], I.1 n) | |
| A reaction: Bang goes the simple connectionist account of consciousness. |
| 23516 | Maybe a system is conscious if the whole generates more information than its parts [Seth] |
| Full Idea: The main claim of Tononi's 'integrated information theory' is that a system is conscious to the extent that its whole generates more information than its parts. | |
| From: Anil Seth (Being You [2021], I.3) | |
| A reaction: Seth seems to present this as an 'interesting' proposal. I find it unlikely that consciousness could be explain in terms of information, or that a machine constructed on this principle would thus become conscious. (Databases pass this test). |
| 23519 | The self is embodied, perspectival, volitional, narrative and social [Seth, by PG] |
| Full Idea: The elements of a self are 1) embodied - related directly to the body, 2) perspectival - having a viewpoint, 3) volitional - being an agent, 4) narrative - aware of past and future, and 5) social - as others perceive me. | |
| From: report of Anil Seth (Being You [2021], III.8) by PG - Db (ideas) | |
| A reaction: [summarised] Seth says there are distinctive emotions associated with each of these aspects of the self. This list is very helpful, as a discouragement for anyone who wants to pick one of these as the sole true nature of the self. |
| 23518 | Modern AI is mostly machine-based pattern recognition [Seth] |
| Full Idea: Much of today's AI is best described as sophisticated machine-based pattern recognition. | |
| From: Anil Seth (Being You [2021], IV.13) | |
| A reaction: Personally I wouldn't want to underestimate the extent to which human intelligence is also pattern recognition (across time as well as in space). |
| 23517 | Volition is felt as doing what you want, with possible alternatives, and a source from within [Seth] |
| Full Idea: The experience of volition is defined by 1) the feeling that I am doing what I want to do, 2) that I could have done otherwise, and 3) that voluntary actions seem to come from within. | |
| From: Anil Seth (Being You [2021], III.11) | |
| A reaction: Note that these can all be cited without reference to their feeling 'free'. |
| 23515 | Human exceptionalism plagues biology, and most other human thinking [Seth] |
| Full Idea: Human exceptionalism has repeatedly plagued biology, and has darkened the history of human thought everywhere. | |
| From: Anil Seth (Being You [2021], I.2) | |
| A reaction: I increasingly agree with this, as much in philosophy as in biology. We really need to get used to our place in evolution. |
| 7608 | The world is established, and cannot be moved [Isaiah] |
| Full Idea: The world is also established, that it cannot be moved. | |
| From: Isaiah (23: Book of Isaiah [c.680 BCE], 93.1) | |
| A reaction: This verse caused big trouble for Galileo. The only reason I can think of for Isaiah to write this is that occasionally people were prone to panic, and worry that the Earth might suddenly and abruptly be moved. |
| 7343 | Beside me there is no God [Isaiah] |
| Full Idea: I am the first, and I am the last; and beside me there is no God. | |
| From: Isaiah (23: Book of Isaiah [c.680 BCE], 44.06) | |
| A reaction: This seems to be the first clear statement (c. 680 BCE) of monotheism, certainly preceding any Greek views on the subject (cf. Idea 2629,Idea 7347). It is not just an arrogant assertion by the jews, but a humble sacrifice, donating their god to humanity. |