Posted on 06/17/2009 8:19:30 AM PDT by GodGunsGuts
Thanks for pinging me to who_would_fardels_bear excellent post.
I guess that those who deny that science is based on any philosophy don’t see that that is a philosophy in and of itself.
2. You are correct in that theories can be stated in sentences or even represented by diagrams and do not necessarily need to be stated as mathematical formulas. However, in order to make measurements and verify theories it is often convenient to ultimately formulate the theory as a mathematical formula. This is not yet possible in fields such as biology, but the hope of all empricists is that this will one day be true.
3. From the Stanford Encyclopedia of Philosophy (http://plato.stanford.edu/entries/set-theory/):
Set Theory is the mathematical science of the infinite. It studies properties of sets, abstract objects that pervade the whole of modern mathematics. The language of set theory, in its simplicity, is sufficiently universal to formalize all mathematical concepts and thus set theory, along with Predicate Calculus, constitutes the true Foundations of Mathematics.
So my logic ladder from 1 to 3 remains unbroken.
4. There is no such thing as a set with no cardinality. Even the null set has a cardinality of zero. A set's cardinality is one of its main properties. If you meant to say a set with cardinality of zero, then this is a very important set in both logic and mathematical set theory. Being able to say that there is nothing of a certain type (logically) or that there are no functions that have specific properties (mathematically) is a very important thing to be able to state and prove.
5. Again, math was developed from logic, and not the other way around. There were several points in time where mathematics started going off the rails and mathematicians had to go back to logic and basic set theory in order to get things back on track. See anything on Russell, Godel, Dedekind, Cantor, Peano, etc.
And as far as Codd goes, most people think that "relational" databases are called relational because they allow someone to relate something like EMPLOYEE to something like DEPARTMENT. Codd used the term "relational" to refer to what happens within a single table, i.e. everything in a table is related by being in the same relation, or set. All of database theory is firmly planted on set theory. And since databases do not necessarily need to contain mathematical data, what I and Codd are talking about is "set theory" and not the limited version of set theory that you consider merely "a branch of mathematics."
6. I stand on my statement that without philosophy there is no science. In order for us to come up with theories about things there has to be something to theorize about. We call that "ontology". If there is something to know something about, how do we go about trying to learn what we can, and what are the limits of what we can know? We call this "epistemology". We don't have the time or ability to make all of the investigations ourselves so how can be construct a society or subculture to ensure that others are conducting their investigations in a proper manner? We call this "axiology" or "ethics".
Most of us are capable of driving automobiles without understanding how combustion engines work. Most scientists are capable of conducting good experiments without being fully aware of ontology, epistemology, and axiology. However, there would be no cars for us to drive if noone knew about combustion engines (or electric motors, etc.), and noone would be conducting proper scientific experiments if the proper philosophical groundwork had not been laid by Pythagoras, Archimedes, Aristotle, Descartes, Locke, Hume, Russell, etc.
As far as your generous offer goes I already have "An Introduction to Database Systems" by Date (wherein he describes the implications of 3VL) and Codd's "The Relational Model for Database Management Version 2".
Throwing in 3VL is an interesting attempt to make me look like an idiot. It turns out that in fact I am an idiot; but then we all are when we divide the sum total of all we know by all that can be known.
There are all kinds of logics now: fuzzy logic, paraconsistent logic, connexive logic, hybrid logic, modal logic, many-valued logic (of which 3VL is just one form), etc. These are all the product of much fruitful, and often useful philosophical investigations.
Some of these results are actually turned into useful products and used to help us better understand the universe. Fuzzy logic is a major success in this regard.
Databases somehow seem to work even with Null values despite Date's criticisms. Codd was not very happy about the way certain real-world databases were implemented, but Ellison has made out like a bandit with his thoroughly useful, although not mathematically rigourous, Oracle product.
Absolutely lovely display of logic..
Didn’t Hitler also believe that the earth rotated around the sun? Anyone else sharing that view must be evil.
Also, thanks for bringing Natural Law into this discussion. I've never heard Natural Law and science discussed in the same context except in reference to ethical considerations related to technology.
Then maybe you'd enjoy Robert Rosen's book, Life Itself. He finds that Natural Law provides the foundation that we require to relate formal systems and natural systems — which is the heart of science. That is, Natural Law is integral to the development of his theory, not some external criterion that can be invoked against it (e.g., ethical considerations). His method is relentlessly mathematical. And I do believe that he would have appreciated the comments you made to Freedumb2003, and (based on my reading so far) likely would have agreed with them.
Anyhoot, I thought your insights were excellent who-would-fardels-bear! FWIW. Thank you so very much!
ok thanks
As I remember, Hitler believed in Madame Curie's research into nuclear reactions. These reactions have the same theories that are used to develope the radioactive dating of fossils and rocks declaring the earth billions of years old. I guess we have to put Madame Curie on the list of the evil people of the world.
Whoa. You have really jumped the shark!
Didn’t Hitler ‘uncritically accept’ the flight theories developed by the Wright brothers? I guess that puts them on you list of the evil people of the world.
"Not yet possible" but definitely being worked on. Developing a theoretical biology on a firm mathematical basis (as is the case with physics) evidently was the purpose of Robert Rosen's life work. He was a student of Nicolas Rashevsky — another mathematical physicist profoundly intrigued by biological problems. Rashevsky has mostly been ignored by the scientific establishment. Maybe Rosen will get a better break. To me, his ideas look like potential "game-changers." (So that could be an uphill battle....)
It may seem I'm hyping Rosen and his book, Life Itself. The truth is I am — because I'm finding it so deeply insightful and "radical" (in the sense of "go to the root") that I'm just dying to find someone to discuss it with! LOL! I know Alamo-Girl will be reading it soon; I must remember to be patient.... :^)
Oh no, on the contrary. Seems to be quite sticky and eminently quotable, lol. Check out the other active crevo threads for yourself.
Didn’t Hitler also embrach the theories of Hermann Oberth! Anyone embracing rocketry and space travel must be considered evil!
Hitler was the founder of the Autobahnen which impressed Eisenhower who built our interstate highway system. Now, if anyone drives on our interstates, are they evil? Is Eisenhower on your list of evil people?
Hitler considered himself an artist and was deeply influenced by Disney cartoons. Is Disney on your list of evil people?
That is the belief by those who claim to have more certain knowledge because their observations are of solid physical stuff ... rather than informed by faith or religious experience. I think that this belief is basically hokum.
I recently finished a course in ethics which focused on moral epistemology. I presented a paper in opposition to Gilbert Harman's essay on moral observation. His claim is that moral observation is not the same as physical observation. In his mind moral observations only amount to people stating their opinions about something, e.g. I don't like it when kids burn cats alive. (Sorry but that was the example he used.) Moral observations he claimed say nothing about what is in fact right or wrong to do.
My argument went something like this:
1. For intelligent humans there is no such thing as pure perception. When we see/hear/smell something we immediately combine the raw sensual input with all of the concepts that we have archived into our consciousness.
2. Scientific theories are concepts.
3. Comparing our conceptualized perceptions with our conceptualized theories to see if in fact our theory matches our perceptions is a conceptual activity.
4. This is true whether we are making "physical" observations or "moral" observations.
5. Either theorizing in general is a hopeless pursuit, or moral observations informed by concepts such as faith, spirituality, etc. are no better and no worse than physical observations informed by concepts such as measurement, the nature of matter/energy, etc.
Currently we all "see through a glass darkly". We all need to exhibit a huge amount of humility when proposing theories about the way things are in this vast, complicated, and wonderful universe that we live in.
Scientists who claim that they are more in touch with reality, are only admitting that they have a very narrow view of reality.
As G. K. Chesterton said: The cosmos is about the smallest hole that a man can hide his head in.
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