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# Philosophy, science and mathematics

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I am often puzzled when it comes to the difference between philosophy and many aspects of science. In philosophy, one begins with a premise (eq. meaning of life is...). One then uses logic to connect data to make a correlation that can support the premise. If one uses the pure logic of mathematics, instead of logic and regular language, to do the same thing, why is it called science, instead of philosophy.

The question becomes is the language of math and math logic something different than logic via spoken language. I recognise that math is a far more universal language, common to all humans, but it is still a language contrained by a premise and logic. As such, can mathematical logic be used to support a premise, and still remain philosophy (even if it is called science)?

To me the difference between philosophy and science (in the rigorous sense) is that science is the universal consensus of opinion. For example, the moon goes around the earth. This premise can be supported with language, data, logic and mathematics-logic to reach a consensus to almost all humans. How the moon ended up around the earth begins to create a divergence of philosphical opinions, whether one uses math or language logic to support their premise. The philosophy of science will call the divergence philosophy that uses math and tech support, "science". But doesn't this subtle distinction stem from the philosophy of science. In other words, it is philosophy saying that this approach is not philosophy even though it does not form a consensus.

I am knit picking because the practical reality is, once something is philosophically bumped up, by the philosophy of science, and called science, it carries more subjective weight in culture. It can still be philosophy, but the science philosophy bump-up can make it look like it carries more weight that it actually does. Religon sort of does the same thing, in that its philosophy, such as Creationism, is given a bump-up due to the prestige of God. The net result is a cat fight between two philosophical bump-ups. They both see the affect in the other but can't see it in themselves.

For example, If I came up with the philosophical premise that gravity was due to the repulsion of matter by space, this premise would conceptually create the same results as we observe. If I then use the existing equations of gravity and do a type of inverse to get the math that I need, is this philosophy now bumped up to science due to math logic? Say it led to a practical correlation that could be used to place a satelite into orbit and I also uses some high tech equipment to test the theory. What would the philosophy of science say? This is science. I would say no because it is a philosophical divergence, even though it is supported with math and hi-tech. But technically, according to the philosphophy of science, it should be called science, or would it?

Does the philosophical bump-up to science have other hidden factors to allow only certain philosophy to get the subjective bump-up? One possible mechanism is politics. This is what decides what gets the tools and the support to make one philosophy more scientific looking. For example, global warming and greehouse gases; if that philosophy gets political support, it can get more resources, compared to other reasonable philosophies. This might create a huge "science" bump-up, creating the social illusion that it is now consenus science, when it never was more than philosophy.

I believe that science, and not the philosophy of science, needs to make a distinction between convergence and divergence science philosophy and limit the term "science" only to convergence. We then call all the philosophical aspects of science, "science philosophy". I am not saying we should not support "science philosophy". Only it needs to stay in the minor leagues unti it creates consensus, then we call it science.

Consider the difference in the social affect by calling Greehouse Gases the only source of global warming, either science or philosophy. If you call it science, people are ready to jump on the divergence bandwagon, with no idea where they are going. Just go for the ride until it ends. You call it science philosophy, which is closer to reality, and most people will wait for the next train. They will still argue science philosophy but at least they are aware of its philosophical limitation.

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I am often puzzled when it comes to the difference between philosophy and many aspects of science.
I find it useful, in discussing any variation of the famous philosophical question “what is philosophy?” to consider the entomology of the word: “philo”=love + “sophia”=wisdom. This leads to the following definition, given as the first in the 1913 Webster dictionary:
Literally, the love of, inducing the search after, wisdom; in actual usage, the knowledge of phenomena as explained by, and resolved into, causes and reasons, powers and laws.
So, importantly, and contrary to its common usage, philosophy, this activity of a philosopher, is not a field of study (a ____–ology), not the practice of a discipline (the activity of a ____-ist), but an act of loving (a ____-philia). An alternate form of “philosophy” could be “sophiaphilia”, but not “sophology”, “the study of wisdom”.

“Science” has an equally peculiar entomology, sharing the same root as “conscious”, meaning literally “to know”. 1913 Webster’s first definition is

Knowledge; knowledge of principles and causes; ascertained truth of facts.
A scientist, then, is literally “one who knows things”.

I think an appreciation of the fundamental peculiarity in the entomology of these terms is critical to understanding the fine, and commonly confused, distinction between philosophical and scientific activity. No matter how much the terms have mutated from the meaning implied by their entomology, philosophy contains an essential element of emotional love, while science contains an essential implication of the existence of and knowability of objective facts.

In a sense, philosophy is bigger than science, because science is necessarily a particular kind of philosophical conclusion: objective materialism, or an alternate term, realism. A distinguishing characteristic of this philosophical position is that it holds that “reality” and “facts” exist independently of our knowledge of them – in other words, that the universe functions according to the laws of science whether any scientist knows any of these laws. Many other philosophies draw contradicting conclusions, holding that facts don’t exist until they are “known”, and that objective reality has not existence independent of an observer.

In philosophy, one begins with a premise (eq. meaning of life is...). One then uses logic to connect data to make a correlation that can support the premise.
In light of the preceding definition, this is an overly restrictive description of what one does “in philosophy”. Although unusual in current, recognized philosophical communities, an approach in which one contemplates a thought (eg: the meaning of life) until one experiences a state of ecstatic emotion agitation, then concludes whatever comes to mind, is an equally valid philosophical approach. Philosophy requires only that the philosopher love wisdom – it does not prescribe how he loves it.

In ordinary, modern usage, philosophy and science have come to mean very different things than implied by their entomology. Definitions abound. One of my favorite is the wry “a [philosopher|scientist] is one who reads and publishes papers in [philosophy|science] journals”.

In summary, I stop short of the conclusion that “philosophy” is a term used in so many different ways that it’s unhelpful in discussion, and conclude that one should be very careful when using it, remaining cognizant at all times that “philosopher” is a much more vaguely defined term than “machinist”, “physicist”, or “mathematician”.

If one uses the pure logic of mathematics, instead of logic and regular language, to do the same thing, why is it called science, instead of philosophy[?].
I don’t believe the claims implied by this question is true.

Much philosophy – both in the “what is published in philosophy journals”, and the “done out of a love of wisdom” senses – relies heavily on mathematic language to persuade and instill a sense of wonder (“wonder” and “love” are commonly equated in philosophy). Much science relies on arguments using natural language to persuade and reach determinations of fact. Therefore, the use of mathematics does not define writing as science, nor its absence define it as philosophy.

I don’t consider logic to be outside of the domain of mathematics. Rather, mathematical logic (sometimes termed Boolian, formal, symbolic, etc.) is logic that can be done using relatively small collections of explicitly defined rules for manipulating data - marks on slates or paper, or their electronic equivalent – while philosophical logic is permitted to make conclusions for which no such rules and data exists – to rely on self-evident fact, common sense, etc. In practice, mathematical logic is more difficult to use, practically impossible to apply to vaguely defined propositions (eg: the meaning of life is …), but much easier to check for errors.

The question becomes …
Hydrogen bond introduces many more ideas in his post, which I think are most effectively left to be discussed in separate posts, so I’ll apply Brooks law and end this post having considered the origin of and distinctions between the terms “philosophy”, “science”, “mathematical language”, “natural language”, and “logic”.
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the meaning of life is...

a=2a

--it's that simple.

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“philo”=love + “sophia”=wisdom.
Much depends on what we mean by love and by wisdom. This common translation is somewhat misleading to those who don't follow etymology in detail.

The ancient Greek word φιλíα is translated with a very broad range of acceptions, according to how it's used in specific cases. The range includes love but I think "care" is more relevant. Aristotle's use of it is discussed here and what I found in a Greek dictionary was broader. The word φιλος has a less wide range but can be thought of as "friend", there are also these remarks and this page about the prefix phil- in English words. Wisdom is a bit more than just knowledge, although the English words wisdom and wise have their etymus in one of the German verbs meaning "to know" and wisdom is one of the many acceptations of the Greek word σοφία too. Curiously, in the Greek version of 1 Kings, chapter 10 neither of the words σοφία or σοφος appear where king Solomon's wisdom is mentioned, although σοφίαν does in some of the other verses mentioning it.

IMHO an appropriate translation of philosophy is "care of knowledge" whereas the original meaning of science is "knowledge" (from the Latin rather than the Greek). The current meaning of science is more or less what used to be called natural philosophy but, if you look up the texts of past times, such as the Andrew Motte translation of Newton's "Philosophiæ Naturalis Principia Mathematica" you find that the terms philosophy and philosophers appear very frequently, while the term science is used in the Latin sense and indicates the result of philosophy i. e. knowledge.

Logic, of course, is what mathematics is fully based upon.

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• 3 months later...
To me the difference between philosophy and science (in the rigorous sense) is that science is the universal consensus of opinion. For example, the moon goes around the earth. This premise can be supported with language, data, logic and mathematics-logic to reach a consensus to almost all humans. How the moon ended up around the earth begins to create a divergence of philosophical opinions, whether one uses math or language logic to support their premise. The philosophy of science will call the divergence philosophy that uses math and tech support, "science". But doesn't this subtle distinction stem from the philosophy of science. In other words, it is philosophy saying that this approach is not philosophy even though it does not form a consensus.

Hopefully this thread is just dormant and not quite dead yet. But just some quick thoughts. Science should never be equated with philosophy or logic. Certainly science could be considered (perhaps should be considered) and branch of philosophy—a branch of epistemology to be specific. But it's only a branch, and a very limited one at that. Science is limited to the realm of processes that are predictable due to the fact that they repeat. Thus if God didn't create a world of repeating processes, science would have no value at all. It could make no predictions for the future, nor formulate any theories about the past. And if this God intervenes from time to time, science could neither verify nor falsify His direct interventions (i.e. miracles). In order to formulate its theories, science must assume, a priori, that nature has run its course in the past, and will run its course in the future. But unfortunately, that presupposition is the subject of much debate among philosophers and theologians. And unfortunately, science can't help us in that debate. Logic tells us that we can't draw a conclusion based on a starting assumption (circular reasoning). A much broader epistemology is therefore required. Hope that helps.

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To all,

I think Philosophy at its best should be considered a 'general form of science' and at its worst an 'artform'.

Science has become more specialised in the last one hundred years splitting off into chemistry, physics and biology.... Inside these specialisations there are yet more specialisations, where philosophy has become less useful as the problems being encountered are counter-intuitive and difficult.

I think this is the impasse between science and philosophy now in that philosophy wishes to remain 'general' darting this way and that and achieving little progress in knowledge.

While science is increasingly focusing its efforts in tighter and tighter circles achieving more and more knowledge at a pace where technology and medicine is progressing so fast that individuals and governments struggle to keep up with the pace of change.

I don't think scientists hate philosophers but I do think they feel philosophy is less useful to them than it would have been in 1795 for instance.

Cheers

;)

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I think Philosophy at its best should be considered a 'general form of science' and at its worst an 'artform'.

Wow! While scientists are generally brilliant when thinking within the confines of their field, unfortunately the opposite seems to be the rule once they get outside of it. They generally make the mistake of believing that everything is a matter of science—in this case, even philosophy. It's like saying fruit is a category of apples. Science was born of philosophy, not the other way around. In fact there are many philosophical assumptions that must be affirmed a priori before any science can be conducted.

Science has become more specialized in the last one hundred years splitting off into chemistry, physics and biology.... Inside these specialisations there are yet more specialisations, where philosophy has become less useful as the problems being encountered are counter-intuitive and difficult.

An example would be helpful in understanding this very vague statement. A definition of philosophy would be helpful as well.

I think this is the impasse between science and philosophy now in that philosophy wishes to remain 'general' darting this way and that and achieving little progress in knowledge.

An impasse between science and philosophy? Do you see an impasse between fruit and apples?

While science is increasingly focusing its efforts in tighter and tighter circles achieving more and more knowledge at a pace where technology and medicine is progressing so fast that individuals and governments struggle to keep up with the pace of change.

Like, huh?

I don't think scientists hate philosophers but I do think they feel philosophy is less useful to them than it would have been in 1795 for instance.

This ironically is true. Scientists have been so deified in our society, people are looking to them to answer questions that are outside the realm of science—questions of ontology, of origins, even the supernatural. The problem is, scientists must, of course, be methodological naturalists and therefore cannot be objective when in comes to anything out side the realm of naturalism (at least while conducting science). Scientists, would be much more helpful if they understood their limitations.

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Unfortunately, as natural philosophy evolved into what is now called science, there has come to be an increasing antagonism between opposing camps. Let's try to avoid being too heated here. :cheer:

Most people are scarce in patience for the abstract, this has always been so, and tend to consider most philosophical questions as hogwash of no practical value. Science has becom very popular by having led to great improvments in technology, and the average Joe in the street thinks of these when hearing the word "science" and may even care little about cosmology or fundamental particle physics. "Can't see how these things could be useful, like for makin' a better TV or something..."

Unfortunately, today many scientists focus on the tangible and show distaste for reflections of, say, epistemology. Many a practicle lab physicist will say "But, I can measure this!" without reasoning all that much further down than how the measuring instrument works. People need to feel they are walking on solid ground, at least under their boots if the ground isn't directly touched by the skin of their feet.

There are, nevertheless, many scientists that see the more general underlying philosophy, and care about it, just as there are philosophers how are able to, and do, get into the science without considering it beneath their dignity. These, both, are the people that don't call each other names or try to come out superior. :hihi:

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The sentence "scientists, would be much more helpful if they understood their limitations" (post 7) is interesting. I dont know how scientists would be more helpful but I get the general drift that some scientists habitually overlook the limitations of the scientific method.

Science assumes the general reliability of inductive reasoning, so what could be more natural than for scientists to inductively reason that all phenomena are amenable to scientific understanding. To put it another way, overlooking (or refusing to acknowledge) limitations of science is an inbuilt consequence of science.

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• 2 weeks later...

Philosophy is the study of all human knowledge. Everything else we know and do is a subset of philosophy, and things we learn through philosophy (that are correct) can be applied to every other discipline.

A person has a built in statistics gathering engine, although it is less precise than doing it manually. Though it is definitely capable of determing when something is almost always true, or almost always false. And one of those things we determine using this is that A=A is almost always true and therefore deductive reasoning exists. And mathematics arises from using deductive reasoning once we have visually defined numbers, which is often forgotten since we decide it useful to memorize the deducted truths of mathematics rather than to rereason them over and over.

Science is a specialized approach to investigation that arose from philosophy.

It has differences which impede it's usefulness in certain situations. For example it is very useful in investigating classical physics. But external observers have to be able to see the results of every action, nothing can change because you observe it, you must be able to control factors etc.

Science also implies that there can be knowledge that does not belong to any one person but rather is a consensus of many people's beliefs. If I see that a dog in a box has brown hair, and you look when there is less light and see dark hair, then we each believe what we have seen because we saw it ourselves. However we will tell each other what we have seen, and neither will believe the other because first person experience is more valuable than what someone else tells you who could be lying, be biased, or misinterpreted what they have seen. If you can't believe what you see yourself than you certainly cannot believe what others tell you.

Perhaps a scientist or philosopher either one could then test 30 times in dark and light and tell you that perhaps you saw different because of the light, and this allows you to reason based on your own experience rather than just taking someone else's word for it. You can also perform additional tests to see if what he said is true. How many tests you do might depend on how much you trust the other person.

But if a scientist tells you something you have no experience of, it is still worth less than something you do have experience of. So in other words, the pecking order is:

Some guy saying something you don't understand (foreign philosophy) > Some guy saying something you don't understand but who claims to be an objective reasoner (Foreign science or good philosophy) > Some guy who convinces you of what he is saying (Philosopher or Science Philosopher who shows you how to reason their findings based on your personal experience or replicate their experiments)

Only the last is really capable of stirring people to action, and for good reason. Imagine science saying that you should take this new pill to lose weight and the next year saying that doing so will cause you great suffering. The person started out knowing that they weren't there and therefore couldn't gauge the quality of reasoning or biases involved in the proposition, and it was proven that these factors produced an erroneous claim by science. The better a person is at reasoning themselves, the less likely they are to accpet claims by science because they know mistakes that can be made in reasoning.

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