tjohnson

I am at a loss to understand what you are getting at. You seem to be saying that we can legitimately expect things to work as they normally do, which is fine, but it this remarkable in any way? It seems so obvious that one wonders why you would mention it at all.

What is a "causal theory"?

Let me rephrase. One cannot say with certainty what something is but one can say with certainty what something is not. For example, I can say with certainty that the earth is not a sphere but I cannot say exactly what shape it is.

I agree, all science relies on assumptions and as science progresses it makes less and simpler assumptions. The behaviour of instruments is not the kind of assumption I am referring to here, however, since it possible to verify if instruments are working properly. I was thinking more like, for example, Newton assumed that space and time were independent and absolute and built a system of dynamics based on that assumption.

OK, it's far more than an assumption, what is it then? A very strong assumption? So there is a scale of assumptions going from very weak to very strong? I can live with that.

LOL, you mean like my partial denture? I did my degree in Honours Mathematics with a lot of Physics thrown in for good measure. My career, however, has been mostly in surveying and computer programming. And you?

I don't know if it's "wrong" to make these kind of assumptions but there is always a risk. We are free to make all kinds of assumptions but they are still assumptions and often we are reminded that this is so when things don't work out as we expect. It is precisely when this happens that encourages us to have a closer look and thus our knowledge increases.

Whether or not someone broke the law is decided by other people and so is a matter of opinion. Also, nothing in biological research can falsify that Adam and Eve were created - it only makes it highly unlikely. If I said God exists but he only allows certain people to see him (like me then how can you falsify that?

But these "relevant attributes and powers" are what? In order to explain what you mean you will necessarily be moving towards a physical explanation, ie. physics. Even if it something as simple as "humans cannot generate enough lift with their arms because they lack the wing structure that birds have".

Out of curiosity I checked into this and it turns out (as Phil stated) that you can indeed use partial derivatives to help solve this. Using the equation S = xy + 512/y + 512/x and taking partial derivatives with respect to x and y and setting to zero, we find that this only happens when x = y = 8. Then z = 256/64 = 4.

From the above article; We will never know "exactly what the fate of the Universe will be". To say things like this is to confuse science with omniscience.

I agree with Ellen, that a theory of some sort is implied. If not, then the only reason you have for your belief that humans cannot fly is that you have never seen one fly. If I ask you "why not?", you will have to come up with some "theory" about why this is the case. I believe the theory is hidden in this phrase "assessed the attributes of human beings and their corresponding powers".

Yes, Merlin also made an assumption, which I think is necessary to use differential calculus to minimize the surface function. Without an assumption you have 3 unknowns and 2 equations.

There is a difference between a positive assertion and a negative assertion. If I say humans cannot fly by flapping their arms then to falsify this assertion you must produce one human who can fly this way. But If I say it is possible that a human can fly this way then we can never falsify this for sure since there is always the possibility that we might discover one that can. So? I was addressing Popper's argument that inductive reasoning is never valid. Moreover, your second statement is positively verifiable. All you need do is produce one human who can fly by flapping his arms. But before you expect others to take this hypothesis seriously (in the absence of positive verification), you would need to present reasons for supposing that it is possible for a human being to fly by flapping his arms. The fact that something may be "logically possible" doesn't count for diddly-squat in this matter. As Kant pointed out, logical possibility pertains to meaning; to say that x is logically possible is merely to assert that x is not self-contradictory. This by itself is no reason to believe that x may actually be the case. This requires specific reasons or evidence that pertain to this particular case. (Kant called this "material possibility.") Ghs Sorry, I am not familiar with Popper's ideas about inductive reasoning, I just threw that into the mix. People can have many reasons about why they believe something is possible, which is why you can't falsify a positive assertion. You may not like or agree with their reasons but that is not the point. The same applies to the existence of God. I can say God doesn't exist with certainty because to disprove me you have to produce God in a way I can see. On the other hand if you say God exists and you have seen him I can't deny that because I can't be in your head.

Prove it.

There is a difference between a positive assertion and a negative assertion. If I say humans cannot fly by flapping their arms then to falsify this assertion you must produce one human who can fly this way. But If I say it is possible that a human can fly this way then we can never falsify this for sure since there is always the possibility that we might discover one that can.

I don't think you have enough information to calculate that. If we knew the sides were 2 ft high, for example, then you would have the surface area, S=xy+4x+4y and 2xy=256. Then y=128/x and substituting you get S=4x + 496/x + 128. Taking the derivative, dS/dx = 4 - 496/x^2 and setting to 0 yields that x=sqrt(128), or around 11.31 ft. Then y=11.31 also.

That's an interesting formulation, "I may know p, but p may be false", mentioned in this thread, although I'm not sure who wrote it. I would reword it slightly after Korzybski; "I may know p, but my knowledge of p will always be incomplete". We can never know all about something because we only get limited information with our senses and our instruments. This does not stop us from knowing a great deal and using this knowledge to our advantage.

Wow, you've been through hell.

No, there is nothing incorrect in that definition. That we can expand the definition to include the fact that such an animal plays a role in mythology is not relevant. It just doesn't exist in reality - as far as we know. Perhaps we'll discover one day such an animal. Does the "incorrect" definition then suddenly become "correct"? Of course not, we've then only discovered that the set of entities conforming in reality to that definition is not empty, as we thought at first. LOL, now we are getting into the realm of which characteristics are the defining ones. Is whether or not the thing is observable an important characteristic? Hmmm.

Yes, until such time as there is a unicorn to observe.

A unicorn is a horse with a horn on its forehead (and some other characteristics). Is that definition incorrect? After all, there is no such thing! So your definition 3 is not incorrect, it only doesn't correspond to an entity in real life (as far as we know, have we looked in the Andromeda galaxy yet?). Of course as a statement about the already defined concept "man" it would be incorrect, but then it's not a definition. Personally, I don't think in terms of 'correct' vs. 'incorrect' definitions, I am only trying to understand what Rand was getting at.

Here are 3 definitions of 'man'. 1. Man is an animal with rationality 2. Man is an animal with the ability to pass knowledge from one generation to the next using complex symbolic schemes and various media 3. Man is an animal with rationality and wings Possibly the first is more general and the second more specific in its description about how this "rationality" is used. Neither of these is incorrect but they are different and they lead to different points of view of, or concepts of man. But the 3rd one is just plain "incorrect" in the sense that there is no such thing.

What you imagine is irrelevant. Nobody can know what you're imagining, people can only judge what you define on its own terms. You might for example give a generally accepted definition of a horse, while you're imagining a cow or a unicorn. Your definition might also be unconventional, i.e. you define a horse with the attributes of a cow, which would be impractical due to communication difficulties, but it wouldn't be incorrect, you'd only choose a different and possibly confusing term. In general it's advisable to use generally accepted definitions to avoid communication problems, but sometimes a new and different definition may be useful, as long as you clearly state what your new definition is and why you use it. Like I said in another post, if I observe a class of animals with 3 legs, yet a describe (define) them as having 4, then that is incorrect. If my definition does not match I am imagining/conceiving then this is what I imagine Rand is talking about with respect to definitions. I don't at present, however, understand the part about the essential characteristic that makes all the others (or the greatest possible number) possible.

Does not match what concept? You'll have to define that concept first, so you're back to square one. One definition may be more practical than another one, but as long as a definition is not contradictory in itself, there is no "incorrect" definition. That a definition may not correspond to something in real life is not relevant, you can very well define gnomes, unicorns and circles. You can't define a concept, you can only imagine it. If I imagine a horse, but define 'horse' as a cow then it is an incorrect definition.