So the first step into objectivity that can be made explicit (creating strings and languages formally from symbols) is founded upon a step that cannot or has not been made explicit (understanding what a symbol is or how they work). To be clear, I think this inexplicit step is objective. — mrcoffee
The point I would make is that mathematics is not necessarily objective, because it's purely inferential or logical - if this then that. — Wayfarer
I suppose what I especially mean by 'objective' here is 'not a matter of opinion.' — mrcoffee
The beauty of a symbolic approach to math is its metaphysical neutrality — mrcoffee
If I use a pencil or a typewriter to make the mark 'a' several times, then these individual marks are not strictly identical. Moreover they are in different places. But we can recognize the marks as representing or intending the same symbol. A rose is a rose is a rose, and an 'a' is an 'a' is an 'a.' If I can't recognize that two different but similar marks intend the same abstract, distinct but otherwise undetermined entity, then I cannot understand Sipser's Theory of Computation, for instance. — mrcoffee
This fundamental first step, to overlook the fact that two distinct instances of "a" are not identical in an absolute way and are therefore not actually "the same", for the sake of calling them "the same", is the basic incoherency of logic — Metaphysician Undercover
A similar incoherency is found in the first step of mathematics, relating to the nature of "unity". The numeral "1" signifies a basic unity. The numeral "2" signifies two distinct unities, but also one unity as "two", at the same time. In performing mathematical operations we must overlook the fundament fact that "2" signifies two distinct unities, (just like we must overlook the fact that two distinct instances of "a" are not the same), and treat it as if it represents one unity. — Metaphysician Undercover
These incoherencies are fundamental to the logical process. Nevertheless we must overlook them, ignore them, to proceed into the logical realm. However, they are significant, and these flaws indicate that mathematics and logic are less than ideal. — Metaphysician Undercover
Yes - but then you’re in engineering, not philosophy as such. — Wayfarer
You’re still concerned with instrumental utility. — Wayfarer
I’m not trying to hijack the meaning of the word ‘objectivity’, but to draw attention to that as a criterion. — Wayfarer
I don't think you actually said anything though. It's as if you pointed at something and then mention that you pointed at something. And now that's a footnote? I'm not trying to be rude, and I'm happy to drop it. — mrcoffee
Mathematics is not objective. They are meaningless symbols upon which humans apply meaning. — Rich
Whatever is outputted by a computer (a tool created by humans) must still be interpreted by humans with different opinions. Hence the phrase garbage in garbage out.
Objectivity cannot exist in a subjective human experience. — Rich
the criterion of objectivity is not necessarily applicable to mathematics (or logic for that matter), as the ‘objects’ of mathematics are only ‘objects’ in a metaphorical sense. — Wayfarer
https://en.wikipedia.org/wiki/Objectivity_(philosophy)Objectivity is a central philosophical concept, related to reality and truth, which has been variously defined by sources. Generally, objectivity means the state or quality of being true even outside a subject's individual biases, interpretations, feelings, and imaginings. — Wiki
The meaninglessness of the symbols is one of the reasons that it is objective. — mrcoffee
For instance, if I have only a king left on the board, then there is no way that I can checkmate my opponent. — mrcoffee
1+1 =2 — mrcoffee
, however, we specify a particular convention — mrcoffee
Objective about what if they are meaningless. What is objective about this: _-++&__? — Rich
Rules are meaningless without a human interpreting them and applying then. — Rich
Absolutely meaningless until a human applies some subjective interpretation. Often there is all kinds of differences opinion about what math means because of some ambiguity and it ends up in court. I know this from working on insurance policies. — Rich
These are objective truths in any reasonable sense of the word. — mrcoffee
Sure, and the sun rises in the morning. Who has or would say otherwise? Are you sure you aren't tilting your lance at windmills here? — mrcoffee
You may desire objectivity, but where humans are involved, there never is. What you have possibly it's some concensus within a consenting group - maybe. — Rich
objectivity doesn't exist, then the word is meaningless. — mrcoffee
Moreover, if objectivity does not exist, then you are just spouting opinion above. — mrcoffee
doesn't shatter the gold statue of Objectivity — mrcoffee
This is what I had in mind, and this seems to be the standard definition. — mrcoffee
I suppose what I can't see is what philosophical work you see the notion of Objectivity doing. What do we get from calling mathematics Objective that we don't already have and that is available to someone that says mathematics is just a family of language games, with each language game being based on a set of rules agreed by a certain set of people, and that these language games sometimes seem useful in deciding what to do next? — andrewk
It exists as a concept as opposed to subjective. Whether a human can be objective, I have yet to find the case. — Rich
Exactly. I am saying the concept cannot be applied to anything perceived by humans. Others have their own subjective opinions about objectivity. — Rich
Yes, people have their faith and their God and their idols. It just seems that it is part of the human character. — Rich
If you are saying that humans are biased, then of course. Objectivity is something we pursue. — mrcoffee
We don't have to see an impossibly perfect instantiation of the concept to apply the concept. — mrcoffee
I doubt that anyone honestly believes that some disciplines aren't more objective than others. — mrcoffee
Some people do, others don't, most couldn't care less. — Rich
My preference is recognizing it as just another human creation and then dealing with it for v what it is. U have no need to gain higher ground by claiming objectivity. — Rich
I think they only hope that the operation succeeds. Even if there is a right way to transplant a heart, doing it that way does not guarantee success, which is all the patient cares about. Further, I bet the humans of 500 years' time would say that the way the world's most esteemed heart surgeons currently transplant hearts is the wrong way compared to what they do.They sure hope that there is a right way to transplant a heart, for instance. — mrcoffee
I think they only hope that the operation succeeds. Even if there is a right way to transplant a heart, doing it that way does not guarantee success, which is all the patient cares about. — andrewk
Instead we can just say that as humans we have evolved to instinctively trust what has worked in the past, so we trust surgeons, techniques and theories about how hearts function, that have worked in the past. — andrewk
see what you mean, but I also think logic is impossible without this first step. In other words, the logic you think is violated by the many-to-one map from marks to symbols is itself founded on this map, at least to the degree that it can be formalized. — mrcoffee
When numbers are constructed in set theory, they are sometimes sets that contain all preceding numbers, where 0 is the empty set. Or 0, {0}, {{0}}, ... where the 'depth' of the empty set represents the number. In these representations, the nested 'unification' is apparent. — mrcoffee
I think math and logic are pretty ideal. For them not be to ideal, in my view, would mean that we could imagine something better. If we could imagine something better, then that would already be within math and logic, since anything better would conform to mathematical and logical requirements. — mrcoffee
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