26 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. |
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? |
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. |
12204 | The logic of metaphysical necessity is S5 [Rumfitt] |
Full Idea: It is a widely accepted thesis that the logic of metaphysical necessity is S5. | |
From: Ian Rumfitt (Logical Necessity [2010], §5) | |
A reaction: Rumfitt goes on to defend this standard view (against Dummett's defence of S4). The point, I take it, is that one can only assert that something is 'true in all possible worlds' only when the worlds are all accessible to one another. |
12195 | Soundness in argument varies with context, and may be achieved very informally indeed [Rumfitt] |
Full Idea: Our ordinary standards for deeming arguments to be sound vary greatly from context to context. Even the package tourist's syllogism ('It's Tuesday, so this is Belgium') may meet the operative standards for soundness. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
A reaction: No doubt one could spell out the preconceptions of package tourist reasoning, and arrive at the logical form of the implication which is being offered. |
12199 | There is a modal element in consequence, in assessing reasoning from suppositions [Rumfitt] |
Full Idea: There is a modal element in consequence, in its applicability to assessing reasoning from suppositions. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) |
12201 | We reject deductions by bad consequence, so logical consequence can't be deduction [Rumfitt] |
Full Idea: A rule is to be rejected if it enables us to deduce from some premisses a purported conclusion that does not follow from them in the broad sense. The idea that deductions answer to consequence is incomprehensible if consequence consists in deducibility. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) |
12194 | Contradictions include 'This is red and not coloured', as well as the formal 'B and not-B' [Rumfitt] |
Full Idea: Overt contradictions include formal contradictions of form 'B and not B', but I also take them to include 'This is red all over and green all over' and 'This is red and not coloured'. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) |
12198 | Geometrical axioms in logic are nowadays replaced by inference rules (which imply the logical truths) [Rumfitt] |
Full Idea: The geometrical style of formalization of logic is now little more than a quaint anachronism, largely because it fails to show logical truths for what they are: simply by-products of rules of inference that are applicable to suppositions. | |
From: Ian Rumfitt (Logical Necessity [2010], §1) | |
A reaction: This is the rejection of Russell-style axiom systems in favour of Gentzen-style natural deduction systems (starting from rules). Rumfitt quotes Dummett in support. |
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. |
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. |
14532 | A distinctive type of necessity is found in logical consequence [Rumfitt, by Hale/Hoffmann,A] |
Full Idea: Rumfitt argues that there is a distinctive notion of necessity implicated in the notion of logical consequence. | |
From: report of Ian Rumfitt (Logical Necessity [2010]) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 2 |
12200 | A logically necessary statement need not be a priori, as it could be unknowable [Rumfitt] |
Full Idea: There is no reason to suppose that any statement that is logically necessary (in the present sense) is knowable a priori. ..If a statement is logically necessary, its negation will yield a contradiction, but that does not imply that someone could know it. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) | |
A reaction: This remark is aimed at Dorothy Edgington, who holds the opposite view. Rumfitt largely defends McFetridge's view (q.v.). |
12193 | Logical necessity is when 'necessarily A' implies 'not-A is contradictory' [Rumfitt] |
Full Idea: By the notion of 'logical necessity' I mean that there is a sense of 'necessary' for which 'It is necessary that A' implies and is implied by 'It is logically contradictory that not A'. ...From this, logical necessity is implicated in logical consequence. | |
From: Ian Rumfitt (Logical Necessity [2010], Intro) | |
A reaction: Rumfitt expresses a commitment to classical logic at this point. We will need to be quite sure what we mean by 'contradiction', which will need a clear notion of 'truth'.... |
12202 | Narrow non-modal logical necessity may be metaphysical, but real logical necessity is not [Rumfitt] |
Full Idea: While Fine suggests defining a narrow notion of logical necessity in terms of metaphysical necessity by 'restriction' (to logical truths that can be defined in non-modal terms), this seems unpromising for broad logical necessity, which is modal. | |
From: Ian Rumfitt (Logical Necessity [2010], §2) | |
A reaction: [compressed] He cites Kit Fine 2002. Rumfitt glosses the non-modal definitions as purely formal. The metaphysics lurks somewhere in the proof. |
12203 | If a world is a fully determinate way things could have been, can anyone consider such a thing? [Rumfitt] |
Full Idea: A world is usually taken to be a fully determinate way that things could have been; but then one might seriously wonder whether anyone is capable of 'considering' such a thing at all. | |
From: Ian Rumfitt (Logical Necessity [2010], §4) | |
A reaction: This has always worried me. If I say 'maybe my coat is in the car', I would hate to think that I had to be contemplating some entire possible world (including all the implications of my coat not being on the hat stand). |
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'? |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |