So Pythagoras didn't examine any real triangles to formulate his theorem.
You think the dude didn't know what a triangle was? Either way, it's not like the theory was going to work on a real triangle. No perfect triangles exist in "reality," but only in concept.
Incidently there are a variety of caveats to the Pythagorean Theorem which are discounted in the instruction of "plane" geometry. The biggest one is that the triangle exist in a Euclidean plane with a Pythagorean metric.(This nomenclature may be obsolete. It has been 40 years since my last math class).
None of this matters.
So the Pythagorean Theorem is not "absolutely" true. It is only true for special cases.
Given certain assumptions, it is indeed absolutely true.
But you've lost the point... Geometry is (roughly) a study of real world objects, and yet it is deductive in methodology. Is geometry invalid as well?
-- Edited by ImSoAnarchist on Sunday 6th of March 2011 12:15:29 PM
So Pythagoras didn't examine any real triangles to formulate his theorem?
Incidently there are a variety of caveats to the Pythagorean Theorem which are discounted in the instruction of "plane" geometry. The biggest one is that the triangle exist in a Euclidean plane with a Pythagorean metric.(This nomenclature may be obsolete. It has been 40 years since my last math class).
So the Pythagorean Theorem is not "absolutely" true. It is only true for special cases.
"Man is not a rational animal, man is a rationalizing animal".
-- Edited by BigG on Monday 13th of December 2010 07:19:24 PM
-- Edited by BigG on Monday 13th of December 2010 07:20:49 PM
-- Edited by BigG on Monday 13th of December 2010 07:21:49 PM
-- Edited by BigG on Monday 13th of December 2010 07:24:12 PM
And, as I've said before, facts require interpretation to be meaningful. To even come to the conclusion that facts are a way by which to gain economic knowledge would require deductive theory.
Deductions are suppositions which can only be "proven" by their ability to predict actual real world events.
This is just wrong. Is Pythagorean's theorem just a "supposition" that needs to be tested (i.e. go around doing calculations on triangles) to be proven true, or is it absolutely true?
Individual human actors are unpredictable.
What's unpredictable about a human's necessity to chose to do that which he assumes will provide him the most satisfaction? Are there times in which humans do not chose to do what they most want (to the best of their knowledge)?
Deductions are suppositions which can only be "proven" by their ability to predict actual real world events.
Individual human actors are unpredictible. Mankind in its masses is predictible.
Curiously enough a version of this is true in the physical sciences. There is no way to predict when a particular atom of radioactive material will decay. But we can determine and predict the decay rate of a few grams with excellent accuracy.
The key is how large the sample has to be for predictibility. A mole of thorium has many more individual atoms than there are individual human beings.
When does the unpredictible collection of individuals merge into the predictible group?
-- Edited by BigG on Monday 13th of December 2010 10:32:02 AM
-- Edited by BigG on Monday 13th of December 2010 10:32:44 AM
In "real" science, the theory is changed to fit the data, not vice versa.
You mean in the physical sciences, where it has proven to be very successful. The point of deduction as a means of gaining economic understanding is not to be overstated. While empirical justification is excluded as a point from which to create economic theory, it does not follow that empirical facts and historical events have no place in economics. However, their place is in economic history . Economics history can certainly elucidate theory, but it cannot prove a theory.
This is because there are no constants or ceteris paribus conditions in economics, and thus controlled experiments as they exist in the physical sciences cannot in economics, where human actors are present.
Economic history itself tells us nothing, requiring interpretation (i.e. deductive theory; praxeology).
What happens when theory and logic do not agree with observed data?
This is kind of like asking "what if I find a triangle with four sides?" The point is, if something is deduced, it is absolutely true. The facts cannot disagree with the data. However, as explained earlier, there are no constants in an economy, and certain facts are not subject to measurement.
Geometry is a deductive science. Are not the conclusions come to by way of logic in geometry absolutely true?