25 ideas
| 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. |
| 7621 | Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein] |
| Full Idea: Einstein's interpretation of special relativity was operationalist in spirit (in marked contrast to the interpretation he gave to general relativity). | |
| From: comment on Albert Einstein (works [1915]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: The late twentieth century was polluted with daft relativism, and I hold Einstein partly responsible, suspecting that he was a bad philosopher. The later development of Einstein's view noted here is interesting. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 22955 | Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield] |
| Full Idea: It is difficult to overplay Einstein's commitment to the concept of causality as the bedrock of physics. | |
| From: report of Albert Einstein (works [1915]) by P Coveney / R Highfield - The Arrow of Time 3 'problem' | |
| A reaction: I normally avoid arguments from authority, but this carries a bit of weight (e.g. when Russell tries to oppose it). What happens to Einstein's theories if you remove causation from them? |
| 20638 | General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close] |
| Full Idea: Einstein came to general relativity from the principles that the laws of nature are the same in all frames of reference. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Cosmological' | |
| A reaction: I wish physicists would tell us a bit more about the ontological status of the 'laws of nature'. Presumably they are not supernatural, so there is an aspect of nature which is constant in all frames of reference. Explanation please. |
| 20636 | Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close] |
| Full Idea: Einstein's general relativity included Newton's theory as a special case: Newton's theory corresponds to the speed of light being infinite relative to the speed of the interacting bodies. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Gravity' | |
| A reaction: So Newton's theory was NOT wrong, but he made the false assumption that the speed of light was infinite. |
| 21230 | The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo] |
| Full Idea: Einstein's first theory is 'special' because it only deals with observers who move in a straight line at constant speeds with respect to one another. | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: Most theories of this period seem to have focused on the simplest cases, for obvious reasons. |
| 21231 | Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo] |
| Full Idea: Einstein assumed that when each observer measures the speed of light in a vacuum, they find the same value, regardless of their speed; and that measurements will lead to agreement on the laws of physics. | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: So are the laws of physics constant for all observers, irrespective of their speed? |
| 20634 | General Relativity says there is no absolute force or acceleration [Einstein, by Close] |
| Full Idea: Einstein's General Theory arose from the idea that there is no absolute measure of force and acceleration. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Gravity' | |
| A reaction: If absolutely everything is only true relative to something else you wonder what the point of measuring anything is. How big can a 'frame of reference' or 'inertial frame' be. Is the multiverse a frame of reference? |
| 20648 | Mass is a measure of energy content [Einstein] |
| Full Idea: The mass of a body is the measure of its energy content. | |
| From: Albert Einstein (works [1915]), quoted by Peter Watson - Convergence 04 'Intro' | |
| A reaction: If I knew what energy was, this would be very illuminating. This idea is e=mc^2 in words. We now have the Higgs field to consider when trying to understand mass. |
| 21232 | Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo] |
| Full Idea: Einstein noted that the measurements of space and time are not independent but inextricably linked, leading to the idea of unified space-time (introduced by his former teacher Minkowski). | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: Notice the instrumentalist assumptions behind this. |
| 7626 | I do not believe in a personal God [Einstein] |
| Full Idea: I do not believe in a personal God and I have never denied this but have expressed it clearly. | |
| From: Albert Einstein (works [1915]), quoted by Richard Dawkins - The God Delusion Ch.1.15 | |
| A reaction: This is an important corrective to those who claim Einstein as religious, on the basis of remarks about God not playing dice etc. See the whole of Dawkins's chapter on Einstein for full discussion. |