Timeline for Why are true and false the only truth values used in mathematics?
Current License: CC BY-SA 3.0
26 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2 at 5:04 | answer | added | user62871 | timeline score: 0 | |
| Sep 24, 2020 at 3:25 | vote | accept | tox123 | ||
| Apr 17, 2018 at 8:16 | comment | added | Overmind | They are not. Division by zero is an example of value '2' = Undetermined. | |
| Apr 16, 2018 at 6:49 | history | tweeted | twitter.com/StackPhilosophy/status/985772104254619648 | ||
| Apr 10, 2018 at 3:55 | answer | added | Dan Christensen | timeline score: 0 | |
| S Apr 9, 2018 at 18:46 | history | suggested | Discrete lizard | CC BY-SA 3.0 |
attempt to clarify
|
| Apr 9, 2018 at 11:57 | review | Suggested edits | |||
| S Apr 9, 2018 at 18:46 | |||||
| Apr 9, 2018 at 11:54 | comment | added | Discrete lizard | @TimBII Ah, I see what you mean. Well, then lets see if editing helps. | |
| Apr 9, 2018 at 11:32 | comment | added | Tim B II | @Discretelizard I actually don't disagree with you about it being preferable in many cases to have bivalent logic; what I was saying above is that the title refers to there only being true and false, and then the body of the question not only shows that not to be the case, but then wants to know why the former is the case again, while asking if the latter can be a good idea. The question is actually a good one, but is written (IMHO) in a confusing manner. Your answer to it reflects a good understanding of the intent, but that doesn't mean the question's wording can't be improved. | |
| Apr 9, 2018 at 11:23 | comment | added | Discrete lizard | @TimBII How does this question answer the question why two-valued logic is used? I mean, there are valid reasons to prefer non two-valued logics for certain cases, fuzzy logic has had practical uses, for instance. | |
| Apr 9, 2018 at 11:21 | comment | added | Tim B II | @Discretelizard if that's the case, then he's answered his own question by mentioning related many valued logics. Not all logic IS bivalent (although admittedly most is) and why bring in imaginary numbers at all? Seems like a lot of chaff in the way of what could be a clear question. | |
| Apr 9, 2018 at 11:16 | comment | added | Discrete lizard | @TimBII I think the question is clear, the question asks why mathematics has chosen for a two-valued logic system and whether 'other-valued' logic systems could be useful. | |
| Apr 9, 2018 at 10:59 | answer | added | user9166 | timeline score: 1 | |
| Apr 9, 2018 at 10:46 | comment | added | user20253 | There is also meaningless and undecidable, giving four possible values. | |
| Apr 9, 2018 at 10:23 | comment | added | The_Sympathizer | I'd suppose the more "philosopher's" type answer (since you're asking it on the Philosophy Stack Exchange) is that if "truth" is taken as the interval [0, 1] and "zero truth" means "total falsehood" and "1 truth" means "total truth" to have a truth value "less than 0" (i.e "-1 truth") would mean it would have to somehow be "even falser than absolutely/completely false" - so what would that mean? It's a bit like asking "what's north of the North Pole"? or "what does it mean to move more slowly than sitting absolutely still?" | |
| Apr 9, 2018 at 10:19 | comment | added | MichaelK | The question is kind of like asking "Why are there only 10 digits?". Well, in the decimal system there is 10, because that is what defines it as a decimal system!. But in others, there are more or less digits. So short answer: the question is faulty, there is not at all only "true" and "false"; how many values there are depends entirely depends on what system you use. If you are not happy with using systems that are true/false binary, then use one that is not binary. | |
| Apr 9, 2018 at 10:08 | answer | added | Discrete lizard | timeline score: 4 | |
| Apr 9, 2018 at 6:52 | answer | added | Jo Wehler | timeline score: 1 | |
| Apr 9, 2018 at 6:44 | comment | added | Mauro ALLEGRANZA | 0 and 1 in logic are not numbers but Boolean values. | |
| Apr 9, 2018 at 6:43 | comment | added | Mauro ALLEGRANZA | The ides that there are TRUE statement is very deeply grounded in our language, and also bivalence, i.e. the fact that what is not TRUE is FALSE. But, at the same time, the Vagueness phenomenon is widely present in our language an daily life, and this does not fit well with bivalence. | |
| Apr 9, 2018 at 5:53 | comment | added | Mauro ALLEGRANZA | Maybe not; see Three-valued logic and Many-Valued Logic. | |
| Apr 9, 2018 at 4:27 | review | Close votes | |||
| Apr 10, 2018 at 4:58 | |||||
| Apr 9, 2018 at 4:16 | answer | added | Alexander | timeline score: 3 | |
| Apr 9, 2018 at 3:50 | comment | added | Tim B II | Welcome to Philosophy SE. This question is not completely clear in what you're asking and could benefit from some clarification. The simple answer is that true and false have specific meanings in certain contexts which would not admit other concepts; remember that mathematics and philosophy both add value to human thought primarily through what they disallow, not what they allow. Order is in effect the containment of thought to specific concepts deemed to be valid as a model within the universe that also seems to constrain events to a given valid set we interpret as order. | |
| Apr 9, 2018 at 3:10 | review | First posts | |||
| Apr 9, 2018 at 3:51 | |||||
| Apr 9, 2018 at 3:02 | history | asked | tox123 | CC BY-SA 3.0 |