What is truth?
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From: Igor on 16 Apr 2010 13:28 On Apr 16, 7:18 am, troll <trolid...(a)go.com> wrote: > Gradually, I have started getting the idea that goodness > has no real meaning at all. Entropy and information > has a clear definition in physics and mathematics, but > goodness is just a nice sounding word and no one > can ever agree on what it actually means. > > Recently, however, I have started to wonder whether > truth has any real meaning. Is there a mathematical > or physical definition of truth, and if so what is it? > > I get the idea that I am missing something simple, > but I am not sure what it is. What is the definition > of truth in physics and mathematics? At least a > very simple web search ends up getting choked > with meaningless drivel from philosophers. Concepts of truth in mathematics and physics differ. In math, basically anything that is internally consistent can be said to be true. But in physics, as in all sciences, the notion of truth is much more elusive, being tied to the concept of empirical falsification.
From: troll on 16 Apr 2010 15:09 On Apr 16, 10:28 am, Igor <thoov...(a)excite.com> wrote: > On Apr 16, 7:18 am, troll <trolid...(a)go.com> wrote: > > > Gradually, I have started getting the idea that goodness > > has no real meaning at all. Entropy and information > > has a clear definition in physics and mathematics, but > > goodness is just a nice sounding word and no one > > can ever agree on what it actually means. > > > Recently, however, I have started to wonder whether > > truth has any real meaning. Is there a mathematical > > or physical definition of truth, and if so what is it? > > > I get the idea that I am missing something simple, > > but I am not sure what it is. What is the definition > > of truth in physics and mathematics? At least a > > very simple web search ends up getting choked > > with meaningless drivel from philosophers. > > Concepts of truth in mathematics and physics differ. In math, > basically anything that is internally consistent can be said to be > true. So in mathematics, as long as both sides of an equation reduces to equivalent terms, this is said to be true? What is meant by the words internally consistent? > But in physics, as in all sciences, the notion of truth is much > more elusive, being tied to the concept of empirical falsification. And empiricism is the basis of truth in physics.
From: jbriggs444 on 16 Apr 2010 15:35 On Apr 16, 10:50 am, "Peter Olcott" <NoS...(a)OCR4Screen.com> wrote: > "troll" <trolid...(a)go.com> wrote in message > > news:f30197f1-cd4e-417b-b696-60f427a9c3a4(a)q23g2000yqd.googlegroups.com... > > > > > Gradually, I have started getting the idea that goodness > > has no real meaning at all. Entropy and information > > has a clear definition in physics and mathematics, but > > goodness is just a nice sounding word and no one > > can ever agree on what it actually means. > > Good is merely one side of the continuum of better and > worse. That is ALL there is to it. [Not really disagreeing with you here, except with the assertion that that's _ALL_ there is to it] It's not a one dimensional continuum. What's "good" for you may not be "good" for me. What's good for the both of us may not be good for the society in which we are both members. What's "good" in one circumstance may not be "good" in another circumstance. What I think is good for me may not match what you think is good for me and may not match what's really good for me. Short term good, long term good, good done by the policy versus good done by the act which conforms to the policy. There are oh so many ways to spin things. Still, just because one can quibble that it's really complicated doesn't mean that it can't also be quite simple. Hugging your mom is a good thing. Eating too many french fries is a bad thing. Don't get so hung up searching for the ultimate meaning of "good" or "true" that you can't tell when "the traffic light is green" becomes true. You might never get home from work. Don't think that just because the dividing lines can't be precisely defined and clearly drawn that all categories are meaningless. The real world is shades of gray. But it's also sometimes black and white. Or red and green.
From: ben6993 on 16 Apr 2010 15:35 On Apr 16, 8:09 pm, troll <trolid...(a)go.com> wrote: > So in mathematics, as long as both sides of an equation reduces to > equivalent terms, this is said to be true? What is meant by the words > internally consistent? In statistics, if an outcome is a composite of a number of parts, and if each part perfectly points to the same outcome, then every part would correlate perfectly with every other part. The internal consistency is the average correlation between parts and in this case would be +1. But life is not perfect and the correlations would in practice be less than +1. The higher the average correlation, the greater would be the internal consistency. Even with perfect internal consistency, the total outcome is not necessarily pointing at what it is aimed at (i.e. 'the truth'?). When a set of outcomes clusters around what they are aimed at then the average correlation of the outcomes would give the validity. An example is a set of arrows thrown at the bull of a dart board. If the three arrows all hit treble twenty then that is high internal consistency. But a second set of three arrows all hitting the bull has high internal consistency and high validity since they are hitting the correct or true target.
From: Daryl McCullough on 16 Apr 2010 16:34
ben6993 says... >I don't really understand why focussing only on falsification is so >productive for science as true/false should be opposite poles of a >single dimension, with symmetric usefulness. Let's go through some example sentences of different complexity to see where "falsifiability" comes in: 1. The simplest sentences are "decidable" sentences (that's what they would be called in mathematical logic; I think Karl Popper called them "observational" sentences). These are sentences whose truth value is checkable. An example is: "It is raining". You can step outside and see if it's true or not. 2. "Verifiable" sentences. A verifiable sentence is one that, if true, can eventually be shown to be true. For example: "It will eventually rain". There are two possibilities: either it's true, and eventually you find out that it is true, or it's false. In the latter case, you might never know for sure whether it is false. 3. "Falsifiable" sentences. These are sentences that make a universal statement of the form: "It always rains". If such a sentence is false, then you can eventually come to know that it is false (if it ever stops raining, you'll know). If it is true, then you may never come to know for sure that it is true (because you never know whether the rain will keep up). Karl Popper suggested that "natural laws" are in the form of falsifiable sentences. They all take the form: "Such and such will always happen" or "Such and such will never happen". It only takes one observation to prove them false, but no finite number of observations can prove them true. So it's not that there is a big distinction between falsifiability and verifiability, it's that (according to Popper) falsifiable sentences are the right kind of sentences to be natural laws. -- Daryl McCullough Ithaca, NY |