No, they do not rely on math. They rely on the theory of gravity, which happens to be expressible in mathematical form. Math alone will tell you absolutely nothing about what trajetory to use to get something to enter a Martian orbit. And our theory of gravity? It was developed by means of “a long series of experiemental firings and observations.” Well, not so much firings as observations. But the point remains, orbital mechanics isn’t a deductive enterprise. It was the painstaking observations made by people like Copernicus and Brahe and Kepler that were eventually put together by Newton into a theory which accurately predicted planetary motion - almost. According to Newtonian physics, Mercury was orbiting wrong. That didn’t make the observations of Mercury wrong. That made the physical theory wrong. The problem of Mercury, as I’m sure you know, is one of those discrepencies that Einstein’s Theory of Relativity cleared up.
The fact that physics depends greatly on math to be expressed and thought about doesn’t mean that it’s not the case that in the end, we know it’s (mostly) right based on observation, and not deduction.
And if we ever develop economics to the point where it can reasonably accurately predict human economic activity, it won’t be because we’ve more accurately deduced the logical consequences of the Austrian axioms. It will be because we’ve refined those axioms to be more accurate based on observation of human activity. (No doubt using a great deal of logic, both deductive and inductive, along the way to discover the implications of our observations.)
Oh, and Euclidean geometry is not limited to two dimensions. That three-dimensional space is not accurately describable in Euclidean terms is a perfectly good example. You yourself brought up Euclid here as if his axioms should prove something: “Without Euclid’s postulates, what would your straightedge prove?” And yet, based on the existence of gravitational lenses, we know that at least one of Euclid’s axioms does not hold in the real world. And if this is so, how on earth does they prove anything with regard to my straightedge and the Hering Illusion?
What exactly is “a priory theory”? I need to know what that is before I can weigh in on the first part of the quote.
I can, however, understand that logic trumps observation. I think the confusion some people are having is that they are thinking that means observation does not trump one’s assumptions. Of course it does, or it can. When our observations conflict with our assumptions, we 1) change our assumptions so that when we apply logic to them, they explain our observations or 2) find out what was wrong with our observations. But we never abandon logic.
A priori is Latin for “from the former”, and implies knowledge that is before experience; in other words, propositional knowledge. Things like math and logic. And I think your explanation is very good about the possible misunderstanding. As I said in the other thread, if the axioms fail, so does the logical argument. Observation is good for testing axioms.
Gorsnak, just to be sure I understand you correctly — setting aside Newton’s and Einstein’s equations — are you saying that because observations are inductive in nature that the theory of gravity, having been put together by observation, is inductive?
I actually do know what it means in latin, but didn’t quite know what an a priori theory was. After your explanation, I’m not sure what the phrase “a priori theory trumps and corrects experience” means. Is that what you meant when you referenced optical illusions? Is that an example of a priori theory correcting experience? Seems like it more an example of logic overruling observation.
Silly me, I didn’t even realize that “reason” and “empiricism” were competitors. It seems to me that reason gets us from assumptions to conclusions that are true if the assumptions are true. Empiricism, or observation, gives evidence that our assumptions were or were not in accord with the behavior of the physical world.
Can someone give an example of “A priori theory trumping and correcting experience”? I’m having trouble understanding what this means. Is it operationally different from logic overruling observation?
Yes, measurement is a complex chain (maybe, chain is not the correct word here) of observation and deduction, especially with the sophisticated instrumentation we have today. I don’t think this means that role of observation is secondary, however.
“Logic” can be used in two senses: informal logic and formal logic. I tend to use the term to mean formal logic, primarily because I don’t really understand how informal logic is distinguished from reason or rationality in general.
In my view, formal logic is about symbol pushing, and how it applies to the physical world is beyond its scope. For instance, consider proprositional logic. Assuming A => B evaluates to T and A evaluates to T, we conclude that B evaluates to T. I regard T and F has an uninterpreted symbols; how we relate them to our everyday notions of truth and falsity lies beyond the scope of propositional logic.
I don’t think we understand the relationship between “semantics” in the strict formal-logic sense and “meaning” in the everyday sense. Perhaps, if ever develop strong AI, it will help clarify this relationship; perhaps, how we assign meaning is really a large, complicated formal system. However, we are nowhere near such understanding, so I don’t see how one can say that logic trumps observation. To disregard data that contradicts your deductions simply because you’ve proven them seems foolhardy.
Yes, I regard them as complementary. I put “vs” in the thread title, because Liberal seemed to imply some kind of conflict with deduction dominating in a previous thread.
I guess I don’t understand this. If NASA misses an asteroid by 30 miles, they don’t say “Well, the math was right so us observing the miss must be wrong.” Experience, i.e. seeing that you missed the asteroid, trumps any and all logical arguments showing that you should have hit the asteroid.
Bad example. They go back and recheck their math, or recheck the spacecraft for problems, but they don’t say that math, itself, is wrong. 2+2 sill equals 4.
No, its a fine example. If the math is right but I observe the craft flying past the asteroid, which of those corrects the other? Does the correct logic trump the obersvation, or does the observation show the logic to be wrong.
These are mutually exclusive propositions. If the maths is correct, the spacecraft could not possibly miss the asteroid.
The only reasons why a spacecraft could miss the asteroid are (a) incorrect maths, or (b) a failure to take something or other into account when doing the maths.
This would be the point. Which trumps which? My axiomically derived proof that the craft will hit the asteroid, or my observation that the craft did not hit the asteroid?
If ALL factors were accounted for and the calculations were correct, barring an unexpected event taking place during flight, the craft will hit the asteroid. If it misses, either a calculation was wrong or a contributing factor, e.g., gravity from a another massive asteroid) was not taken into consideration.
In scientific terms, I believe “observation” means anything that can be sensed, noticed or detected using any available tools (two examples: eyes, mass spectrometers).
It seems to me that much of the hangup here is that some people are using the word “observation” in this way, but others (such as the folks positing that optical illusions such as the’ pencil in a glass of water’ can not be accurately understood by observation) are using “observation” to mean “physically seeing with one’s eyes” and nothing more.
Usually when scientists say, “we see here that…” or, “we are now able to observe that…” they are NOT just talking about the image formed in one’s brain by the eyes sensing light refecting off an object.
Exactly, logic falters in the face of observation. If I observed that the craft missed the asteroid, it is the logic that is wrong not my observation. The logic is what must conform to what is observed, not the observations to the logic.
I might be missing your point, but it seems to me that the situation you present cannot possibly occur in reality. If the maths is correct and everything has been taken into account, the only way you would see the craft miss the asteroid would be if you were hallucinating, in which case the axioms would trump your “observation”
The underlined part is the fly in the ointment of logic. Everything can’t possibly be taken into account. The observation over long experience is that there is no possible way of knowing in advance what precise impulse the rocket motor will give to the spacecraft. That’s why, as a result of many observations, some rocket fuel is saved for mid course trajectory corrections and for final targeting when you get really close to the asteroid.
