empiricism vs deduction

[treis]

@George Kaplin

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”

You’re right, they both can’t be true. The question is, given disparate accounts which trumps which? If the NASA engineers check, double check, and triple check their logic and conclude that the craft is on the asteroid, I can disprove that by plunking the craft down on the table.

Of course given perfect logic and perfect axioms you will find the truth. But given perfect observations you will also find the truth. If you use logic to come to one conclusion, and I observe a differing conclusion who wins?

[Gorsnak]

@Liberal

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?

Yes, more or less. The theory itself is just a series of propositions, but our grounds for believing it are ultimately observation and induction. There may be plenty of deductive steps along the way, but an argument with 99 deductive steps and 1 inductive step is an inductive argument, not a deductive argument.

[I_Love_Me_Vol.I]

@treis

Of course given perfect logic and perfect axioms you will find the truth. But given perfect observations you will also find the truth. If you use logic to come to one conclusion, and I observe a differing conclusion who wins?

Neither perfect logic nor perfect observation has yet been grasped by humans. We only have the best possible logic and observational tools that can be known at this time.

So “perfect logic” (meaning using logic as we currently understand it to be) can be wrong; and so can “perfect observation”. Both because of the great unknown “x”.

Also-- Logic itself is an observation, IMO.

[magellan01]

@treis

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.

No, no, no. You’re assuming that the application of reason is always pure, correct, complete, and non-assumptive. (Yes, some of that is redundant.)

If you try to hit a castle with a cannonball and it misses, do you think logic is at fault, or aim. If it misses it wide, either the cannon is not true, your alignment is off, or you didn’t account for a strong wind or the rotation of the earth. If you fix all these things abd use the appropriate charge and angle, and make adjustments as needed, the cannonball will hit the house. The logic being applied in the successful event is identical to that initially employed. The execution was just sloppy.

[bitwise]

I think people are arguing different things here. No one is saying that logically deduced theorems can be proven false by experiment. What they are saying is that experiments validate the applicability of those theorems to the physical world. I regard the application of logic to the physical world to lie outside the scope of logic. Logic only tells you something about symbols (Read my post above).

[magellan01]

@bitwise

I regard the application of logic to the physical world to lie outside the scope of logic.

Of course. Once you take logic outside of itself what is at issue is the application of it. “It” and it’s application are two distinct things. The logic can be flawless, yet the application wanting. And often is.

@bitwise

Logic only tells you something about symbols (Read my post above).

I view logic, symbolic or not, to be a way to categorize and understand the physical world. It is not about symbols, it uses symbols to examine relationships among things in the physical world more cleanly.

[bitwise]

@magellan01

I view logic, symbolic or not, to be a way to categorize and understand the physical world. It is not about symbols, it uses symbols to examine relationships among things in the physical world more cleanly.

When you’ve arrived at at a formula, and you decide what that formula says about they physical world, do you that consider that logic itself or the application of logic?

Do you think it is necessary to understand what the symbols represent to deduce correct theorems?

[magellan01]

@bitwise

When you’ve arrived at at a formula, and you decide what that formula says about they physical world, do you that consider that logic itself or the application of logic?

The formula itself represents logic itself. Your interpretation of it or what you decide to do with it is its application.

Do you think it is necessary to understand what the symbols represent to deduce correct theorems?

I’m a little unclear as to the question, but I’d say yes. Just as you have to understand the symbols that make up any language.

[magellan01]

Oops. It should have looked like this:

@bitwise

When you’ve arrived at at a formula, and you decide what that formula says about they physical world, do you that consider that logic itself or the application of logic?

The formula itself represents logic itself. Your interpretation of it or what you decide to do with it is its application.

@bitwise

Do you think it is necessary to understand what the symbols represent to deduce correct theorems?

I’m a little unclear as to the question, but I’d say yes. Just as you have to understand the symbols that make up any language.

[bitwise]

@magellan01

Oops. It should have looked like this:

The formula itself represents logic itself. Your interpretation of it or what you decide to do with it is its application.

Agreed.

@magellan01

@bitwise

Do you think it is necessary to understand what the symbols represent to deduce correct theorems?

I’m a little unclear as to the question, but I’d say yes. Just as you have to understand the symbols that make up any language.

What I had in mind was things like automated theorem provers. Do you think computers understand the meaning of the symbols they manipulate? Do you think they understand the meaning you assign to the symbols? Do they assign their own meaning? Is the meaning of the symbols actually determined by their relationship to each other?

(Note I do not believe it is impossible for computers to assign meaning to symbols, but I don’t think our technology has arrived at that point yet. Also, I don’t think we really understand what it means to “assign meaning”, so any conversation about it is bound to be vague.)

[magellan01]

@bitwise

What I had in mind was things like automated theorem provers. Do you think computers understand the meaning of the symbols they manipulate? Do you think they understand the meaning you assign to the symbols? Do they assign their own meaning? Is the meaning of the symbols actually determined by their relationship to each other?

I don’t know much about computers or automated theroem provers, but my guess is that the only understanding they can have is with the relationships between the symbols. Naturally, it starts with what meanings or values you assign, but I wouldn’t really consider that aspect of it “understanding”. More like a flavor of programming. (Not to be confused with what we usually mean by computer coding.)

I’ll stop now before I start talking out of my ass. In fact, I might be too late.

[bitwise]

@magellan01

I don’t know much about computers or automated theroem provers, but my guess is that the only understanding they can have is with the relationships between the symbols. Naturally, it starts with what meanings or values you assign, but I wouldn’t really consider that aspect of it “understanding”. More like a flavor of programming. (Not to be confused with what we usually mean by computer coding.)

I’ll stop now before I start talking out of my ass. In fact, I might be too late.

My point was that computers can take your axioms and rules of inference and deduce theorems without understanding how you interpret the symbols.

The semantics of logic which is the study of the meaning of formal languages, but I’m not sure we understand how to relate that to the physical world. One can talk about Peano axioms, models, and incompleteness and remain within the scope of logic, but I think once we start talking about counting chickens we leave that scope. That’s what I meant when I said logic is about symbols.

[magellan01]

@bitwise

My point was that computers can take your axioms and rules of inference and deduce theorems without understanding how you interpret the symbols.

The semantics of logic which is the study of the meaning of formal languages, but I’m not sure we understand how to relate that to the physical world. One can talk about Peano axioms, models, and incompleteness and remain within the scope of logic, but I think once we start talking about counting chickens we leave that scope. That’s what I meant when I said logic is about symbols.

I think I see what you mean. But if I had to choose to say that logic is about one thing, I’d pick “relationships”. Relationships among things, which we have assign symbols to.

[Triskadecamus]

So, I observe that the space probe does not land on the asteroid. I suppose I observe this with instruments. (Obviously I cannot see the probe out there, even if I somehow see the asteroid.) Now, I have undoubtedly been observing the asteroid since before I launched the probe. I have logically determined a location and a logically chosen time at which the asteroid should have be. (If my logic is valid.) I also have a probe built and tested to act according to my logic, and operated so as to take it to the exact same place and time using the same logic and understanding of forces that provided me with those coordinates for the asteroid.

Now, I find my instruments do not report to me the expected stimuli which my logic predicted would indicate the intersection of those objects.

If logic must prevail over observation, then my logic must include at least one axiom that is hereby proven false. (Since my logic provides me with both the event, and the ability to observe it, any different outcome is a failure from a logical perspective, including an “optical illusion” that the probe missed.) A new set of axioms must be developed that have characteristics which allow logic to predict the observed facts. The new logic must then be exercised to predict a new probe and target, and a new intersection.

If observation must prevail over logic, then I must have failed to observe the original conditions or the resulting conditions accurately. From a scientific point of view, both possibilities should be examined. Turns out that the asteroid is a torus, and the probe just happened to pass through the hole. Or, I neglected to compute the effect of solar wind on the extended communications antenna, and the direction of my thrusts was off by a tiny percentage. Logic remains valid, but the conditions under which it applies are more stringent than my original axioms.

Neither logic, nor empiricism is “better” than the other. Observations of existing phenomena cannot, by themselves provide predictions of unobserved phenomena. Logic alone cannot create information about observed phenomena, or possible phenomena, other than to predict relationships between different sets of assumptions. Using both and using them as tests to each other can allow the creation and evaluation of new phenomena.

Perhaps my logic in this example included an unstated assumption that the extended antenna had no effect on the trajectory. That assumption was false. My logic is invalid.

But my observations were based on assumptions, so they are also invalid. My observations predicted a solid shape for the asteroid, not a torus. My observations were invalid. The absence of the stimuli expected did not mean that I missed the asteroid, but rather that the probe passed exactly through the center. A perfect solution, but not the expected phenomenon.

Tris

[John_Mace]

@treis

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.

What you are missing is that there are many things that could be wrong, including the calculations. But all of those things that could be wrong are assumptions that we put into the equations. No one doubts the equations. What we might doubt is the force generated from the thrusters or the direction from the steering mechanism or some other operational problem. Like I said earlier, if the spacecraft doesn’t reach it’s target. no one says: Hey, maybe 2+2 doesn’t equal 4 afterall.

[David_Simmons]

I’m still not seeing the conflict between logic and observation. Logic is a game played with symbols. As long as the assumptions underlying the logic don’t conflict with each other the game is valid and its output is certain. That is, all outputs are contained in the original assumptions. Whether or not those outputs have any correspondence to what happens in the physical world depends upon whether or not the assumptions were related to the physical world. I believe that forming assumptions that correspond to the physical world is a matter of observation.

For example, you can get as fancy as you want with the assumptions underlying arithmetic, but basically it all comes down to counting things.

[David_Simmons]

I think a good example of the non-combative relationship between logic and observation is land surveying. Surveyors use the logic of plane geometry. Suppose we start two teams of surveyers. One team starts in Chicago and goes west surveying a line of square plots. Another team does the same thing going east from Sioux Falls, SD. They meet near Mason City, IA and lo and behold, their surveys are in violent disagreement. Both have done their work accurately and their logic is impeccable but their surveys don’t agree at the junction point.

Their problem is that they are using the wrong logic. The surface of the earth is not a plane. Surveyors insist on using plane geometry because to use spherical geometry for most of their work would be silly. In order to get around the obvious flaw in using plane geometry on the surface of the earth they break the surface into plane facets and survey those. Sort of like the mirrored facets on those light reflecting balls hanging in dance clubs. Plane geometry works just fine over the limited area of each facet. At the junctions of facets there is a discontinuity but that doesn’t matter for this purpose. Just about 25 miles east of Sioux City, IA there is a little spot on the map called Correctionville. Its main street runs along the division line between two surveys, i.e. two facets. The streets run along property lines and those north of main street are offset from those south of mainstreet because of the accumulated errors. Those errors arise from using the wrong logic in surveying the surface of the earth.

Observation tells us that we must use the logic of spherical geometry if we want surveying accuracy over large distances. Either that or we must use the logic of plane geometry for a series of short distances laid end to end and accept the resulting errors.

However, if we get even fussier observations tells us that the logic of spherical geometry doesn’t quite work either. More careful observation discloses that the logic of the geometry of an oblate spheroid is needed.

But, Goddammit, even closer observation shows us that that logic isn’t exact either and we must create an arbitrary surface calledthe Geoid in order to best describe the surface of the earth.

So, we use logic to work out survey problems on the surface. Observation tells us which logic to use for the purpose at hand.

There ain’t no damned conflict between them.

[BrainGlutton]

@Blake

I’m not sure that I understand what Liberal is talking about, but in real science in the real world observation always overrules “logic”.

Well, the thread in which he posted that (and which I started) is about economics.

Whether economics is “real science” is debatable.