25 ideas
| 13338 | '"It is snowing" is true if and only if it is snowing' is a partial definition of the concept of truth [Tarski] |
| Full Idea: Statements of the form '"it is snowing" is true if and only if it is snowing' and '"the world war will begin in 1963" is true if and only if the world war will being in 1963' can be regarded as partial definitions of the concept of truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.404) | |
| A reaction: The key word here is 'partial'. Truth is defined, presumably, when every such translation from the object language has been articulated, which is presumably impossible, given the infinity of concatenated phrases possible in a sentence. |
| 13337 | A language: primitive terms, then definition rules, then sentences, then axioms, and finally inference rules [Tarski] |
| Full Idea: For a language, we must enumerate the primitive terms, and the rules of definition for new terms. Then we must distinguish the sentences, and separate out the axioms from amng them, and finally add rules of inference. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: [compressed] This lays down the standard modern procedure for defining a logical language. Once all of this is in place, we then add a semantics and we are in business. Natural deduction tries to do without the axioms. |
| 13335 | Semantics is the concepts of connections of language to reality, such as denotation, definition and truth [Tarski] |
| Full Idea: Semantics is the totality of considerations concerning concepts which express connections between expressions of a language and objects and states of affairs referred to by these expressions. Examples are denotation, satisfaction, definition and truth. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.401) | |
| A reaction: Interestingly, he notes that it 'is not commonly recognised' that truth is part of semantics. Nowadays truth seems to be the central concept in most semantics. |
| 13336 | A language containing its own semantics is inconsistent - but we can use a second language [Tarski] |
| Full Idea: People have not been aware that the language about which we speak need by no means coincide with the language in which we speak. ..But the language which contains its own semantics must inevitably be inconsistent. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.402) | |
| A reaction: It seems that Tarski was driven to propose the metalanguage approach mainly by the Liar Paradox. |
| 13339 | A sentence is satisfied when we can assert the sentence when the variables are assigned [Tarski] |
| Full Idea: Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405) | |
| A reaction: Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration. |
| 13340 | Satisfaction is the easiest semantical concept to define, and the others will reduce to it [Tarski] |
| Full Idea: It has been found useful in defining semantical concepts to deal first with the concept of satisfaction; both because the definition of this concept presents relatively few difficulties, and because the other semantical concepts are easily reduced to it. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.406) | |
| A reaction: See Idea 13339 for his explanation of satisfaction. We just say that a open sentence is 'acceptable' or 'assertible' (or even 'true') when particular values are assigned to the variables. Then sentence is then 'satisfied'. |
| 13341 | Using the definition of truth, we can prove theories consistent within sound logics [Tarski] |
| Full Idea: Using the definition of truth we are in a position to carry out the proof of consistency for deductive theories in which only (materially) true sentences are (formally) provable. | |
| From: Alfred Tarski (The Establishment of Scientific Semantics [1936], p.407) | |
| A reaction: This is evidently what Tarski saw as the most important first fruit of his new semantic theory of truth. |
| 9240 | Love creates a necessity concerning what to care about [Frankfurt] |
| Full Idea: The necessity with which love binds the will puts an end to indecisiveness concerning what to care about. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.13) | |
| A reaction: I put this here as a reminder that there may be more to necessity than the dry concept of metaphysicians and logicians. 'Why did you rescue that man first?' 'Because I love him'. Kit Fine recognises many sorts of necessity. |
| 9228 | Ranking order of desires reveals nothing, because none of them may be considered important [Frankfurt] |
| Full Idea: Ranking desires in order of preference is no help, because a person who wants one thing more than another may not regard the former as any more important to him than the latter. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.5) | |
| A reaction: A salutary warning. Someone may pursue something with incredible intensity, but only to stave off a boring and empty existence. The only way I can think of to assess what really matters to people is - to ask them! |
| 9238 | Morality isn't based on reason; moral indignation is quite unlike disapproval of irrationality [Frankfurt] |
| Full Idea: The ultimate warrant for moral principles cannot be found in reason. The sort of opprobrium that attaches to moral transgressions is quite unlike the sort of opprobrium that attaches to the requirements of reason. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.5 n6) | |
| A reaction: More like a piece of evidence than a proper argument. We may not feel indignant if someone fails a maths exam, but we might if they mess up the arithmetic of our bank account, even though they meant well. |
| 9234 | If you don't care about at least one thing, you can't find reasons to care about anything [Frankfurt] |
| Full Idea: It is not possible for a person who does not already care at least about something to discover reasons for caring about anything. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.11) | |
| A reaction: This is the key idea of this lovely book. Without a glimmer of love somewhere, it is not possible to bootstrap a meaningful life. The glimmer of caring about one thing is transferable. See the Ancient Mariner and the watersnake. |
| 9232 | It is by caring about things that we infuse the world with importance [Frankfurt] |
| Full Idea: It is by caring about things that we infuse the world with importance. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.10) | |
| A reaction: This book is a lovely attempt at getting to the heart of where values come from. 'Football isn't a matter of life and death; it's more important than that' - Bill Shankly (manager of Liverpool). Frankfurt is right. |
| 9233 | Our criteria for evaluating how to live offer an answer to the problem [Frankfurt] |
| Full Idea: Identifying the criteria to be employed in evaluating various ways of living is also tantamount to providing an answer to the question of how to live. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.10) | |
| A reaction: Presumably critical reflection is still possible about those criteria, even though he implies that they just arise out of you (in a rather Nietzschean way). The fear is that critical reflection on basic criteria kills in infant in its cradle. |
| 9229 | What is worthwhile for its own sake alone may be worth very little [Frankfurt] |
| Full Idea: What is worth having or worth doing for its own sake alone may nonetheless be worth very little. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.5) | |
| A reaction: That is one of my cherished notions sunk without trace! Aristotle's idea that ends are what matter, not means, always struck me as crucial. But Frankfurt is right. Collecting trivia is done for its own sake. Great tasks are performed as a means. |
| 9235 | Rather than loving things because we value them, I think we value things because we love them [Frankfurt] |
| Full Idea: It is often understood that we begin loving things because we are struck by their value. ..However, what I have in mind is rather that what we love necessarily acquires value for us because we love it. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.3) | |
| A reaction: The uneasy thought here is that this makes value much less rational. If you love because you value, you could probably give reasons for the value. If love comes first it must be instinctive. He says he loved his children before they were born. |
| 9237 | The paradigm case of pure love is not romantic, but that between parents and infants [Frankfurt] |
| Full Idea: Relationships that are primarily romantic or sexual do not provide very authentic or illuminating paradigms of love. ...The love of parents for their small children comes closest to offering recognizably pure instances of love. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.4) | |
| A reaction: Excellent. Though perhaps a relationships which began romantically might settle into something like the more 'pure' love that he has in mind. Such a relationship must, I trust, be possible between adults. |
| 9239 | I value my children for their sake, but I also value my love for them for its own sake [Frankfurt] |
| Full Idea: Beside the fact that my children are important to me for their own sakes, there is the additional fact that loving my children is important to me for its own sake. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.7) | |
| A reaction: This is at the heart of Frankfurt's thesis, that love is the bedrock of our values in life, and we therefore all need to love in order to generate any values in our life, quite apart from what our love is directed at. Nice thought. |
| 9236 | Love can be cool, and it may not involve liking its object [Frankfurt] |
| Full Idea: It is not among the defining features of love that it must be hot rather than cool, ..and nor is it essential that a person like what he loves. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.4) | |
| A reaction: An interesting pair of observations. The greatness of love would probably be measured by length, or by sacrifice. Extreme heat makes us a little suspicious. It would be hard to love something that was actually disliked. |
| 9227 | We might not choose a very moral life, if the character or constitution was deficient [Frankfurt] |
| Full Idea: People who are scrupulously moral may nonetheless be destined by deficiencies of character or of constitution to lead lives that no reasonable person would freely choose. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.2) | |
| A reaction: This fairly firmly refutes any Greek dream that all there is to happiness is leading a virtuous life. Frankfurt is with Aristotle more than with the Stoics. It would be tempting to sacrifice virtue to get a sunny character and good health. |
| 9230 | People want to fulfill their desires, but also for their desires to be sustained [Frankfurt] |
| Full Idea: Besides wanting to fulfil his desire, the person who cares about what he desires wants something else as well: he wants the desire to be sustained. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.6) | |
| A reaction: Plato, in 'Gorgias', makes this fact sound like a nightmare, resembling drug addiction, but in Frankfurt's formulation it looks like a good thing. If you want to make your family happy because you love them, you would dread finding your love had died. |
| 9241 | Loving oneself is not a failing, but is essential to a successful life [Frankfurt] |
| Full Idea: Far from demonstrating a flaw in character or being a sign of weakness, coming to love oneself is the deepest and most essential - and by no means the most readily attainable - achievement of a serious and successful life. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.14) | |
| A reaction: Obviously it will be necessary to dilineate the healthy form of self-love, which Frankfurt attempts to do. Ruthless vanity and self-seeking certainly look like the worst possible weaknesses of character. With that proviso, he is right. |
| 9300 | Boredom is serious, not just uncomfortable; it threatens our psychic survival [Frankfurt] |
| Full Idea: Boredom is a serious matter. It is not a condition that we seek to avoid just because we do not find it enjoyable. ..It threatens the very continuation of conscious mental life. ..Avoiding bored is a primitive urge for psychic survival. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 2.8) | |
| A reaction: Presumably nihilism will flood into the emptiness created by boredom. Frankfurt will see it as a lack of love for anything in your life, and hence an absence of value. Frankfurt is very good. |
| 9231 | Freedom needs autonomy (rather than causal independence) - embracing our own desires and choices [Frankfurt] |
| Full Idea: What counts as far as freedom goes is not causal independence, but autonomy. It is a matter of whether we are active rather than passive in our motives and choices, whether those are what we really want, and not alien to us. | |
| From: Harry G. Frankfurt (The Reasons of Love [2005], 1.8) | |
| A reaction: This is why setting your own targets is excellent, but having targets set for you by authorities is pernicious. These kind of principles need to be clear before any plausible theory of liberalism can be developed. |
| 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. |