Empirical models have an advantage in that standard procedures for data collection and model construction can often be automated, so that less application development time and engineering analysis are needed. But training of the application developers is still needed, so that they understand and recognize the occurrence of pitfalls and limitations for the particular methods used. Empirical models should be limited within the ranges of data used in their development, unlike first principles models that may extrapolate well beyond the range of test data. For instance a first principles model may state that the total flow into a unit equals the total flow out of a unit.
That model is a straight line on a graph when plotting flow in vs. But the measurement errors captured in the empirical model will lead to huge errors when that curve is extrapolated outside the range of the training data. RBFN can provide these warnings. Empirical models typically have a disadvantage that they need to be rebuilt when there are changes in the monitored system configuration or operating modes.
They also typically require more data analysis for re-use on instances of similar equipment than first principles models. And in no case can we satisfy ourselves that they are so by looking merely at the relations of one part of the train of thought with another. We must ascend to the original sources, the presentations of experience, and examine the train of thought in relation to these.
Merrill's First Principles of Instruction
Little as the modern representatives of the Schoolmen are satisfied, either with the spirit of Mr. Mill's demand, or with the mode of his own response to it, they have deemed it well worth while, not indeed to change the old Logic, but to add to it a new book. Pure Logic remains substantially what it was, and is justified in its position. It assumes, as all other sciences do and must, that human thought has, in general, objective reality; and on this most legitimate assumption it proceeds to lay down the laws of orderly, consistent thinking.
The newly added part of Logic, often called Material, Applied or Critical, takes for its special purpose to defend the objective reality of thought. Because to so characterize the world would itself be an appeal to uniformity. A uniformly non-uniform world is a contradiction in terms. Therefore, we must admit some uniformity to exist in the world. The world need not be uniform throughout, for the principle of uniformity to apply.
It suffices that some uniformity occurs. Given this degree of uniformity, however small, we logically can and must talk about generalization and particularization. The principle of uniformity is thus not a wacky notion, as Hume seems to imply. The uniformity principle is not a generalization of generalization; it is not a statement guilty of circularity, as some critics contend.
So what is it? Simply this: when we come upon some uniformity in our experience or thought, we may readily assume that uniformity to continue onward until and unless we find some evidence or reason that sets a limit to it. Because in such case the assumption of uniformity already has a basis, whereas the contrary assumption of difference has not or not yet been found to have any. The generalization has some justification; whereas the particularization has none at all, it is an arbitrary assertion.
It cannot be argued that we may equally assume the contrary assumption i. If we follow such sober inductive logic, devoid of irrational acts, we can be confident to have the best available conclusions in the present context of knowledge. We generalize when the facts allow it, and particularize when the facts necessitate it.
We do not particularize out of context, or generalize against the evidence or when this would give rise to contradictions. So, by strict logic, SOME uniformity must exist in the world, the issue is to confidently identify reliable cases, however provisionally. Where, this is surprisingly strong, as it is in fact an inductive generalisation.
It is also a self-referential claim which brings to bear a whole panoply of logic; as, if it is assumed false, it would in fact have exemplified itself as true. It is an undeniably true claim AND it is arrived at by induction so it shows that induction can lead us to discover conclusions that are undeniably true! Therefore, at minimum, there must be at least one inductive generalisation which is universally true. But in fact, the world of Science is a world of so-far successful models, the best of which are reliable enough to put to work in Engineering, on potential risk of being found guilty of tort in court.
How is such the case? Because, observing the reliability of a principle is itself an observation, which lends confidence in the context of a world that shows a stable identity and a coherent, orderly pattern of behaviour. Or, we may quantify. Suppose an individual observation O1 is Convergent, multiplied credibly independent observations are mutually, cumulatively reinforcing, much as how the comparatively short, relatively weak fibres in a rope can be twisted and counter-twisted together to form a long, strong, trustworthy rope.
So, we have reason to believe there are uniformities in the world that we may observe in action and credibly albeit provisionally infer to. This is the heart of the sciences. That is where we are well-advised to rely on the uniformity principle and so also the principle of identity. We would be well-advised to control arbitrary speculation and ideological imposition by insisting that if an event or phenomenon V is to be explained on some cause or process E, the causal mechanism at work C should be something we observe as reliably able to produce the like effect.
For relevant example, complex, functionally specific alphanumerical text language used as messages or as statements of algorithms has but one known cause, intelligently directed configuration.
There just are not enough atoms and time in the observed cosmos to make such a blind needle in haystack search a plausible explanation. The ratio of possible search to possible configurations trends to zero. So, yes, on its face, DNA in life forms is a sign of intelligently directed configuration as most plausible cause. Unsurprisingly, random text generation exercises [infinite monkeys theorem] fall far short, giving so far 19 — 24 ASCII characters, far short of the 72 — for the threshold. DNA in the genome is far, far beyond that threshold, by any reasonable measure of functional information content.
The laws, parameters and initial circumstances of the cosmos turn out to form a complex mathematical structure, with many factors that seem to be quite specific. Where, mathematics is an exploration of logic model worlds, their structures and quantities. Surprise, we seem to be at a deeply isolated operating point for a viable cosmos capable of supporting C-Chemistry, cell-based, aqueous medium, terrestrial planet based life. Equally surprising, our home planet seems to be quire privileged too. And, if we instead posit that there are as yet undiscovered super-laws that force the parameters to a life supporting structure, that then raises the issue, where did such super-laws come from; level-two fine tuning, aka front loading.
There is a lot of information caught up in the relevant configurations, and so we are looking again at functionally specific complex organisation and associated information. Pick any reasonable index of configuration-sensitive function and of information tied to such specific functionality, that is a secondary debate, where it is not plausible that say the amount of information in DNA and proteins or in the cluster of cosmological factors is extremely low.
AKA, design. It also points to certain features of our world of life and the wider world of the physical cosmos being best explained on design, not blind chance and mechanical necessity. Those are inductively arrived at inferences, but induction is not to be discarded at whim, and there is a relevant body of evidence.
Logic and First Principles: How could Induction ever work? Identity and universality in action. Another timely refreshing review of fundamental concepts that are imprescindible for serious discussions. Jawa, it seems logic and its first principles are at steep discount nowadays. I have felt strongly impressed that we need to look at key facets of argument which are antecedent to specifics of the case.
It turns out that analogy is acknowledged as foundational to reasoning and so to the warranting of knowledge , and that it is rooted in the principle of identity. Now, we see that induction — which, despite dismissive talk-points to the contrary is fundamental to science — is also similarly rooted. It seems like if we take this principle to a logical conclusion, then a completely random sequence should contain uniformity that we can generalize from, but that is false. EMH, Avi Sion speaks to the logical import of suggesting a world with no universal uniformities.
Compiled vs. First Principles Models
But on looking again at the suggestion; oops. It would be a case of U. Self-contradiction, so U is undeniable, the world necessarily has universal properties. BTW, this also has nothing to do with generalising on random sequences, which do not exhaust the world; a better candidate is whether apparent laws of nature arrived at by observation of several cases are in fact universal.
belgacar.com/components/espionner/localiser-mon-telephone-perdu-bouygues.php So, the onward question is, to identify at least provisionally cases of such. In the above, I suggest one: that we may make mistakes with [inductive] generalisations, M. This is also a case of arriving at a universal, undeniable property inductively as we know of the possibility of failure through actual cases.
Most famously, the breakdown of classical Newtonian Physics from to or thereabouts. KF, ok, I think I get it. However, it is unclear how this transfers to empirical modeling and prediction. For example, if I apply AS principle to a long sequence of random coinflips, then a run of heads is bound to show up.
On the other hand, if the sequence is non random, then we do lose out by not inferring order where there is some. We never actually know to any degree whether induction is valid, and the only way we lose is when it is valid and we assume it is not. EMH, pardon but the world is not a sequence, here we are speaking of observed reality extending across space and time, evidently starting with a bang some The attempt to deny the legitimacy of generalisation from a finite set of observations, on the so-called pessimistic induction turns on that generalisations have failed in some cases.
But, not all, and I put up one not vulnerable to future observations. Its direct answer is, first, that the denial of universalisability runs into logical trouble as outlined. Next, the distinct identity of a world and its content is in part observable and identifiable at least to provisional degree, with significant reliability. So, given that there is evidence of lawlike patterns and that some may indeed be universal, we should not allow ourselves to lose confidence in reliable patterns on the mere abstract possibility that they may be erroneous.
- First Principles | casulbamun.tk!
- Piano Quintet in A Major - Cello?
- Twelve Principles of Knowledge.
- Defining First Principles Thinking.
- Abababababa (Japanese Edition);
In short, science and engineering can be confident. KF, I agree your analysis works from an intuitive standpoint. But, from the strictly logical standpoint, the case is not so clear to me. However, it is tough to decouple the logical argument from the intuitive argument in these sorts of discussions. How would the AS principle apply to a run of heads in a long sequence of fair coin flips, without a priori knowledge whether the coin is fair or not?
EMH, I think the context is scientific induction regarding a real world, not any one phenomenon in it. However, even if coin flips — or better, magnetisation patterns of paramagnetic substances — were utterly flat random, they will collectively fit a binomial distribution, which is a level of universally applicable order.
This illustrates how it is really hard to avoid having some universally applicable ordering.
- Twelve Principles of Knowledge.
- Sparks from the Heart, Fire from the Soul!: A book of poetry from my Heart and Soul.
- Hot Flowers : A Diary;
- The Coach and the Play Stealer.
KF, hmm, that is a very interesting point. So even in the case of completely uniform randomness there is a generalized pattern.