What is the Objectivist answer to this?
asked
KineticPhilosophy Greg Perkins ♦♦ |

Expanding a little on what others have already said, there's a way to frame this with respect to a broader epistemological point that might be of interest: Mathematics is Consider Platonists (Extreme Realists), who hold that concepts/universals/essences exist as real entities in another realm: their answer would be that these things are obviously discovered, not invented -- the opposite would be incoherent to them. And consider Nominalists in contrast, who hold that concepts/universals/essences are basically chosen by us: their answer would be that these things are inventions, not discovered -- the opposite would be incoherent to them. In contrast to both, there is Objectivism, which explains that concepts/universals/essences are That's all pretty abstract, so maybe I should risk an example... Consider color concepts: Our culture has dozens if not hundreds of color terms in broad use, yet there have also been cultures which have used just two color terms, one for all the colors we might recognize as darker, and one for all the colors we would recognize as lighter. Does this mean one is right and the other is wrong? (Yep, the Realist would say, at most one of them could have discovered The One True Set Of Color Concepts "out there".) Or is it just that color is subjective? (Yep, the Nominalist would say, this is just another illustration of how universals aren't "out there" and so they must be "in here" and simply invented.) An Objectivist will explain that both cultures are indeed attending objectively to the facts out there: the metaphysically-given range of the electromagnetic spectrum that humans perceive, and the properties of things which cause them to reflect those frequencies -- and that these facts are discovered, not invented. But at the same time, it is not written on reality how many "buckets" Thou Shalt Use to For a much better understanding, I suggest reading Rand's short monograph on concept formation,
answered
Greg Perkins ♦♦ |

2+2=4 What is the method we arrived at this? Did we discover or invent it? Objectivism, per se, does not address this issue directly. So one might ask: what are the methods that might lead to it indirectly? Pat Corvini might offer some fodder for thought on this matter. (One might start with "Two, Three, Fours and All of That") Number is objective. The number line consists of an open ended set of concepts that, depending on the direction, persist as one more than, or one less than, the direction traveled, i.e., in accordance with a quantified application of Aristotle's view of the more or less. The concepts of "two", "three", "four", are 'invented' to designate the specific quantities referred to. Metaphysically, "two" differs from "three" in the same respect as "three" differs from "four". The relationship of any two numbers being one unit apart was the discovery while the concepts were invented to concretize this relationship in conceptual form. In this sense, the relationships are discovered, while the specific concepts are "invented" or assigned to differentiate the discoveries one from another. "Two", "three" and "four" take their place in the number line as "||", "|||" & "||||" differing - ultimately getting their identity from their relationship to the group with one of its members taken as a unit.
answered
dream_weaver ♦ |

The Objectivist answer is "yes" -- i.e., math is
answered
Ideas for Life ♦ |

Good question. An invention does not exist prior to its being invented. A discovery does exist prior to its discovery. So the two are mutually exclusive.

If by "math" you mean the body of facts which fall under the category of math, then it is discovered.

If by "math" you mean the techniques that humans have developed to solve certain types of problems (mathematical ones), then it is invented.

If by "math" you mean the study of patterns, then it's neither invented nor discovered, it's practiced.

This is not "the Objectivist answer" to this, though.