whynot wrote:I have a philosophical question, although it's more in tune with the semantics of mathematics than science, it is directly derived from the latter so hopefully the mods will tolerate its asking in this forum. I am given to understand that the impetus of scientific investigation has evolved an entire discipline of mathematical modeling and follows a paradigm specifically attenuated to quantitative values such that the math involved has developed many rather clever terms, formulea, systems, logics and such etc....so my question involves the issue of quality or qualitative approaches as in when making comparisons or reaching for the next generation of an existing result or product. Do the same mathematical terms, rules and logic apply to qualitative issues as apply to quantitative values? Or does this necessitate additional mechanisms in the translation?
neuro wrote:whynot wrote:I have a philosophical question, although it's more in tune with the semantics of mathematics than science, it is directly derived from the latter so hopefully the mods will tolerate its asking in this forum. I am given to understand that the impetus of scientific investigation has evolved an entire discipline of mathematical modeling and follows a paradigm specifically attenuated to quantitative values such that the math involved has developed many rather clever terms, formulea, systems, logics and such etc....so my question involves the issue of quality or qualitative approaches as in when making comparisons or reaching for the next generation of an existing result or product. Do the same mathematical terms, rules and logic apply to qualitative issues as apply to quantitative values? Or does this necessitate additional mechanisms in the translation?
I am not quite sure what you are talking about, but if you are asking whether mathematical modeling is important and useful for qualitative depiction of observable processes, then yes, it certainly is.
Actually, mathematical modeling is particularly important in reproducing qualitative aspects, such as time courses, responses and reactions, tendential values, stability, etc. If it succeeds in doing this, then it significantly contributes to UNDERSTANDING the process under study.
As for quantitative aspects, once a qualitatively correct model has been built, the question simply becomes that of finding the right set of parameters. Which does not add much, in my opinion, unless such set cannot be found, in which case one would suspect that the model is invalid.
owleye wrote:If there's something interesting that can be said about 'quality' that differentiates it from being quantitative, say for example, one's quality of life, or one's experience of a color, where putting a number on some facet of it might be seen unreasonable -- where even trying to situate it in a model using the terms: harmony and balance is making use of a vocabulary that doesn't apply -- then I suppose the Pythagoreans march toward quantifying quality will come to a halt. Even Kant, insofar as he adopted this category as a primitive, made use of quantity in speaking about it (say when he spoke of intensity). The legacy of Plato is written in science's need to quantify.
Let me be among those who have an aversion to quantifying all things, especially those surrounding 'value'. Economics and accounting, established around the idea of making life a series of quantitative transactions, seems to me to treat it rather shallowly. Yes, I would generally adhere to a contract form of moral conduct, but when it becomes quantified, something seems to get drained out of it. If I make a promise, with my vow to make good on it, with a gesture, such as a shake of the hand, that represents my commitment, I am morally obligated to honor it and will do my very best to earn the trust involved in it. Yes, there will be consequences of my default that register in not living up to that commitment. Yes, these consequences can affect my reputation as well as my character. However, though such a contract can lead to all these things, justice is not strictly a thing that comes down to a quantity. Living up to one's commitment is something we try to accomplish and we shouldn't take such things lightly when we enter into them. However, in making judgments about the future and our abilities to live up to such commitments we are constrained, to say the least, and risks must be considered on all sides. When it comes to dispensing justice, it's not a simple set of calculations that will resolve it all, should things go awry. Mediation is best served when we are not strangers, when we represent ourselves in good faith, when we accept responsibility for our actions, when we seek restitution on the basis of our own faults as well as the faults of others.
I see I'm getting to sound like a preacher, now, so I'll leave off. I do have a theory of justice, of sorts, some of which I've expounded above, but I get passionate about it from time to time and it leaks out, perhaps when I get carried away. My apologies.
Forest_Dump wrote:I too am not really sure what the question is about but some clarity might come about from recognising that there are different kinds of data or observations that reflect different kinds of possible meaning and are subject to different kinds of mathematical functions and manipulations. I will try to keep this simple and order the kinds of data from qualitative to quantitative.
Nominal categories are the most simple discrete (qualitative) categories. A classical example might be ping-pong balls that either have a black stripe ("x") or don't ("y"). There is no in between and there is no necessary order to the categories. This kind of data is subject to the most simple of mathematical manipulation such as simple counts or comparative percentages (i.e. percentage of "x" vs. "y").
Ordinal categories have a natural order but the size of the categories and/or the "spacing" between the categories is not necessarily even or equal. A common example is the hardness scale of minerals where, for example, the difference in hardness between diamonds (hardness of 10) and rubies (hardness of 9) is much, much greater than the difference between talc (hardness of 1) and gypsum (hardness of 2). You can do a bit more fancy math with ordinal data than you can with nominal data but not much.
Interval data has more precisely and equally defined distances between categories but doesn't have a necessary fixed starting point. "Time" can be an example here IF YOU DON"T SPECIFY a precise start point or time "0" because seconds, minutes, years, etc., have equal length to each other and would numerically come in an order of, for example, oldest to youngest BUT this example only works if there is not precisely defined start point. The math that you can apply to interval data is generally more precise and powerful than above but there are also limits.
Ratio data, the most quantitative, are like interval data but there is a natural "start point". Examples could include mass or length where there is a natural start point or "zero". Ratio data allows the most sophisticated mathematical manipulation, quantification, etc.
There are a couple of problems and implications about thinking about data in these ways. For example, above I mentioned that perhaps ping-pong balls might come in two categories of striped or not. It wouldn't make any sense, therefore, to talk about some being more "striped" than others unless you start to use a different kind of measure such as measuring the intensity of colour of the the stripe (potentially ordinal or interval data) or width of the stripe (now ratio data).
Mathophiles tend to like to work with ratio data as much as possible in the belief (usually true) that more precise measurements and more powerful math will reveal greater insights. On the other hand, it has been argued that anthropologists and archaeologists work more with people who used discrete, perhaps normative categories so that, for example, big pots were used for burials and small pots were used for cooking. Here the categories can be measured with variances recorded, statistical manipulations made, etc., but when you get down to it, the pots were either for burial or cooking and never both so that all the stats in the world really are only done to put things into (and perhaps describe) one category or the other and there is no necessary order: pots of type x are on site type A while pots of type y are on site type B but there is no necessary reason to define site type A as being either a food cooking site and not the burial site.
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