Knowledge in archaeology is necessarily inferential and empirical in its foundation. This, if for no better reason, is why archaeology can call itself a genuine science. Archaeology must build its mansions of knowledge from the ground up, quite literally so. It is quite the case, as Einstein wrote, that conceptual systems remain fair game until and unless they become contradicted by the factual evidence. The hard evidence in an on the ground provides the touchstone for scientific validity and truth in Archaeology, no matter how wild the speculation may become. It provides the anchor that prevents the archaeological superstructure, the ship of archaeology, from drifting away upon uncertain seas of understanding.

Factual evidence is always context-bound and context-driven. This entails always that any particular artifact or other kind of archaeological fact (archifact) will tend on average to be relatively silent about itself and its significance. Context driven facts carry little internalized information that is relevant to its significance in the context. This of course is a relative statement to make, but this sets a fundamental kind of constraint to the informational value and flexibility of our fundamental archifacts. We cannot simply remove a fact from the provenience of its "discovery" and the context of its understanding and apply it willy-nilly to any unrelated truth that we wish. We cannot interpret it in any decontextualized way, nor can we cast it down into any other context and reinterpret it in another way. The fact that one group of people made black pottery in one corner of the world has nothing directly to do with the fact that some other group made red pottery in some other corner of the world.

Analogical convergence is always possible. We must speculate that the greater the likelihood of correspondences, the greater the affinity of characteristics in form, function and even in construction, between two otherwise unrelatable objects, then the greater the claim can be made to some kind of nonanalogous, or rather homologous relationship existing between the two.

Analogy and homology are not necessarily mutually exclusive in their meaning. There are possible intermediate or hybrid sets that share both analogical and homological relationships. Complete or perfect analogy implies similarity without any other direct relationship. In fact, for a perfect analogy, direct relationship would spoil the analogical relationship based upon similarity, and hence cannot be permitted. This leads to the opposite conclusion, that two remarkably different or non-identical things, even in a sense contrastive things, may in fact share a direct homological relationship.

Archaeology's reference universe remains always unknown. It can be said to be finite, but of unknowable size and dimensionality. This can be called the total possible sample universe of archifacts that are discoverable by archaeologists in the world. This entails a paradoxical and inherently ambiguous state of archaeology's knowledge, that is always de facto a subset of this larger universe. Whatever archaeology may know, this knowledge is always a referential to a larger but unknown context. This is true of course of any science, but it is especially acute in a peculiar manner in archaeology. This is because archaeological evidence is always partial and particularly incomplete

Historical information patterning demonstrates a tremendous inherent complexity of an epi-phenomenal landscape. Numerous instantiations in countless and countlessly complex contexts defy simple causal determinations and straight-forward cause-effect relationships. As the father of American anthropology would have said, the natural history of the evolutionary records is cosmographic in its descriptive empiricism. A boulder rolling down the side of a hill, perchance dislodged by lizard crawling within a crevice where the boulder attaches to the hill, rolls down the hill in an underdetermined manner. All that we know is that gravity demands its descent in willy-nilly fashion. Perhaps it will hit a smaller rock below, and its trajectory of descent shift ever so slightly that it impacts against a tree, tipping the tree and dislodging even more rocks. An avalanche ensues that destroys an entire village at the base of a hill, where another instance of a dislodged rock of similar proportions might of found a state of stable rest upon a ledge below.

In terms of the natural history record of evolutionary process, and understanding the mechanical and dynamic aspects of evolutionary speciation, it must be said at the outset that any "rules" or principles derived from an analysis of its patterning must be at best "general" and descriptively paradigmatic in their application. They are like the Indirect approach in military strategy derived from an analysis of military history. They appear to be robust, to apply to most cases in a general sort of way, and yet they lack the "predictive" outcomes kind of validity we expect especially from our physical theories. In systems theory, the most we can come to expect are general ratios or formulas of "expectability" of different kinds of outcomes. The classic example in nature is the prediction of earthquakes. Scientists may expect with a very reasonable chance of success that an earthquake of major magnitude will strike in a given region, but they cannot predict exactly when or where such an event will actually take place. Thus, historical sciences lack the precision and degree of accuracy we come to expect of "pure science."

Historical sciences, like evolutionary theory, are therefore fundamentally "epiphenomenal" as systems theory. They exhibit patterns that cannot be reductionistically described in terms of physical causal relations alone. As precise as we have become in our molecular analysis of organic life-forms, we are still no closer to a kind of theoretical understanding of Evolution that has the kind of predictive/descriptive precision found in the physical sciences. To rely upon such organic analysis alone is to miss the basic point of biological systems theory, and to be over-reductionistic in our explanatory models. We must yield certainty, precision, accuracy and prediction, for greater explanatory power in our general models.

In this way, going back to the formulas of evolution above, I will state that in general, it is appropriate to substitute some kinds of analytical processes found in the physical sciences for others. The result is that a sense of systematicity is retained in our ability to simplify our understanding of extremely complex phenomena, but at the sacrifice of the kind of "certainty" and hence "control" we would like our sciences to otherwise have.

In this regard, based on previous research in the human sciences, I will suggest the following kinds of substitutions that I will seek to apply to my models of biological and human systems theory. These are the following:

1. Where possible, ordinal values of measurement are substituted by "cardinal values" of "relative measurement" and if this is not possible then by "nonparametric" values of "comparative measurement" or "concrete description" (i.e., one rabbit, two rabbit, three rabbit, four...)

In such descriptive measurement, a direct "one-to-one" correspondence between the descriptive term and the thing(s) it describes can no longer be deduced, without disguising a great deal of instantive variability and non-categorical values.

In other words, one biological organism is not just like another similar biological organism, in the same way that we might say that one hydrogen proton is just like the next, and both have the same discrete values.

2. Where possible, inferred causal relationships are substituted by "causal correlations" as implied by the first regression formula above, and if this is not possible then by "correlational" values that assume some kind of indirect or hidden set of relationships.

3. Where possible, basic principles and laws found in the physical sciences, leading to mathematically precise and predictive theoretical formulas, that are judged essentially "correct" as finite puzzle-solutions to specific problems, are substituted by general descriptive rules and paradigmatic statements that are held to govern similar situations and hold true for most sets of circumstances. These general rules and paradigmatic statements do not lack uncertainty and are not unexceptionally applied to all similar situations in the exact same way.

4. The kind of rigorous and faultless logic that can be ascribed to cosmological and physical theories and statements, for instance in the statement of Equivalence, Symmetry and Conservation, does not apply in the same way in the historical sciences and is instead substituted by a kind of alternative and historical logic that is related closely to what is called practical logic and rhetoric. Underlying this logic is a looser kind of three-value non-dichotomization, and of necessity a kind of modus tollens rationalization of deriving an antecedent from a consequent. There is also implicit a form of deriving an "is" (or at least a "was" ) from an "ought." Informing this kind of logical rationalization is also a form of universal common sense that is based on a theory of natural sets, compared to classical exclusive categories. Thus, theoretical descriptions lack exactly the same kind of parsimony of explanation expected in the physical sciences. Instead, simplification of explanation rests on working and heuristic values of achieved realism in succinct descriptive (nonmathematical) explanation.

5. Finally, going back to the language of description, replacing implied one-to-one correspondences inferable from solid physical descriptions with a kind of one-to-one correlation expected and common place in historical descriptions, with all the implications of analogy and homology, metaphor and interpretivism, we are left with a basic challenge of comparing apples and oranges. This kind of challenge is obvious in evolutionary history, especially when it comes to alternative taxonomic reconstructions.

Where possible, I have sought to replace direct physical comparison and "identity" with a form of statistically based system of assumable "similarity," based on arbitrary but explicit decision rules, and if not possible, with a kind of metaphorical similitude or "likeness" that includes the possibility of statistically estimated "likelihood."

This leads into a form of statistical description and decision making that I call possibilistic statistics, and is beyond the purview of this text to explicate fully. I only broach the issue here with the point of emphasizing the ways that we can approach the problem of description and explanation in the historical sciences with at least one eye to being systematically self-explanatory, reliable and consistent.

What implications does this have for our formulations above? However refined I may make them, they are just that, generalistic formulations, and not "mathematical formulas" as are found in the physical sciences. If systematicity is introduced to the elaboration and applications of their variables and relationships, this systematicity comes from the five caveats about historical science listed above, and not from a hidden presumption of these being physical science-type equations.

The object of this brief essay is to demonstrate that a form of relatively objective and unbiased interpretation can be developed relative to a site and its arrangement of artifacts and its provenience within a larger archaeological system of information. By objective and unbiased I am referring to the relative lack of influence of preconceived relations or ideas that shape the interpretation and distort it in a form that is arbitrary and alien to the natural relational patterns evidenced originally by the site. I must emphasize the term "relative" because at no time, in the archaeological relativity of our knowledge, can we assume that we are being in some absolute sense "objective." I argue that it is possible to develop scientific standards suitable to archaeological interpretation that fall within what can be considered to be a reasonably objective range. We accomplish this by several means:

1. We allow the artifactual evidence of a site to "speak for itself" in terms of its relationships at multiple levels. We describe what we see in the most basic terms that we see it, without necesssarily typing or "labeling" it by some other standard.

2. We restrict our descriptive language by means of the use of various scales of objective measurement and various denotative definitions of standard forms and kinds of relationships possible.

3. We coordinate the interpretation of evidence, directly and indirectly, upon multiple levels of analysis and synthesis within the larger framework of the site context.

4. We impose what can be considered to be a reasonable model for describing relationships between things found at the sight, in terms that infer and imply a mechanical and efficient relationship of a system.

5. We defer broader interpretation of evidence, model building, until we have accumulated and developed a substantial body of information in reference to a sight.

a. We do not infer relationships or events for which there is no direct or indirect supporting evidence.

b. We rule out relationships or event structures in the case that there is counterfactual or contradictory evidence.

All of this would be based upon an exhaustive and detailed analysis of the data and artifacts associated with a site, its stratigraphy and other physical associations, as well as its context to other sites and a broader contemporaneous framework. If we have only one site that pertains to only one time period, then that site can be said to be the sole representative of that time period and exists in isolation from any other site that may be more distantly related by time, place or form. The hominid fossil record is typically of this nature, especially as we go deeper and deeper back into time. In this case, it is extremely difficult to draw inferences that span large periods of time and large areas.

There is a set of rules of thumb that may help to determine degree of similarity between sites:

a. If sites are closely related in time, they may be of similar or related origin.

b. If sites are closely related in space, they may be of similar or related origin.

c. If sites are closely related in form, on a statistical basis, they may be of similar or related origin.

d. If sites are closely related in more than one or all of the above, they may be more similar or of related origin.

In any case, even if we an establish similarity of time, space and form, it is still almost impossible to rule out the question of chance analogy versus historical homology of type. What comes to our rescue is that there is a given likelihood that can be attached to similar forms or traits that are human-made or artifactual, versus traits that are natural. Paleontological evidence of skulls, if they are very similar in form and distinctive features, even if they are widely separated in place and time, make a strong case for the long term and widespread continuity of fossil type, as for instance is found with Homo erectus fossils both in Africa and in Asia as well as in a few intermediate regions. We know that these similarities are probably not the result of evolutionary convergence, and are probably the result of vertical evolutionary transmission. On the other hand, if we find similar forms of pottery, in almost every detail, both in sites in the New World and in the Old World, with no obvious connections between them, and with different time-frames for each, it is difficult to rule out the possibility of analogical convergence, or alternatively, horizontal transmission of either the artifact or the ideational form of the artifact, as for instance what has been found with porcelain trade between China and Europe that lead to an emulation of Chinese styles.

In this kind of decision-making, there is a kind of relational logic that must be followed, as well as a kind of possibilistic statistics that can be applied that would allow us to make some kinds of informed decisions regarding the inferences we draw from our samples. We can apply certain significance and certainty factors, depending on how loose or strict we wish to make our interpretation. We must always work with a fundamental proviso in the development of our interpretation:

No matter how remote the chances, there is always at least a residual possibility that we may be wrong.

The challenge from a statistical standpoint is how wrong are we willing to risk ourselves being. We can also apply a looser form of heuristics that will assist us in our decision making.

1. Develop alternative interpretive models, independently, and test for best all round fit to the data.

2. The greater the agreement between different, disparate or distant sites or samples, the stronger the case can be made for direct homology, if analogy can be ruled unlikely.

3. Rule out interpretations that do not fit or square with the known data, or that impose unlikely models without supporting evidence.

4. Search for discrete clues within the data or site that may point in the right direction.

5. Do not ignore counter-evidence or clues that do not point in the right direction.

6. If there is evidence that is not accounted for or remains contradictory to one's interpretation, then change the interpretation to better fit the evidence, and not the evidence to fit the interpretation.

The basis for the argument for objective interpretation in data analysis and evaluation, and the possibility of building from sufficient informational bases a more general model of a system represented by archaeological site complexes, stems from the fact that relational patterns found within and between sites that can be considered proximate or affinal in time, space, and form, will tend to exhibit a certain degree of minimal order exhibited in terms of spatial arrangement, function, recurrence, etc., which patterning suggests underlying or implicit rule structures. This kind of patterning is to be expected for instance, from systems that are known to be of human origin. We can see this even in the regular geometricity of forms as well as in the regular pattern of shape, size, etc. associated with forms. Ancient paleolithic stone tools bear out these kinds of systematic patterns quite effectively. The basis for objective interpretation stems from the hypothesis that human systems exhibit typical and regular ordered patterns of relationship, and these kinds of patterns will be transferred within a transformational or translational system to archaeological site complexes.

Of course, how much information we may thus distill from objective relations found in sites may be nonetheless severely limited and insufficient in any general and larger symbolic sense. They may prove to be quite unsatisfactory from the standpoint of developing larger models of human systems that can be considered to be fleshed out and as large as life itself.

Only the discovery of new data is likely to lead to improved interpretation.

Data can be discovered through new means of site excavation, survey, analysis and relational determination.

The kind of model I have imposed upon archaeological inquiry is a kind of empirical, ground up, inductive theory construction. This model is slow and clumsy at best, and as with all inductive work, remains always vulnerable to the discovery of the next "Black Swan." Such theory is said to be data dependent, and this is in contradistinction to hypothetico-deductive theory construction that is relatively data-independent. The theory of evolution has been the most successful hypothetico-deductive theory, followed perhaps only by Einstein's general theory of relativity. It leads to a kind of belief that all great theory must of necessity be independent of the data and hypothetico-deductive in orientation. Great theory is not off-limits to archaeological constructions, and in fact, archaeologists should be encouraged to develop grand theories of systems that serve to frame the facts that they normally work with.

It is interesting in this regard, and something of an operational paradox, that the approved approach for ground up theory building that rests upon analytical rigor and attention to detail and relation, is precisely the opposite of the preferred approach in objective theory construction from the top-down. There is an inherent heuristic advantage in top-down theory building to be as initially open and dialectically neutral as possible in the elaboration of alternative frameworks. This entails a willingness to constrain received data in ways it does not obviously or logically seem to fit. I am not suggesting by this statement that a theory of cosmic origins of the Egyptians is more viable than a theory of their native sui generis origins in the deserts of Egypt itself. Eventually, it should be possible to rule out the former kind of theory in lieu of the latter, on rational and evidentiary grounds alone, without having any direct proof. What is necessary in such a case is a relative degree of open-mindedness to see patterns that may not exist in the data, not because they are impossible or not there, but because we superimpose patterned order on the data ourselves. We are trying, in other words, to move past and beyond our own paradigmatic preconceptions about how the data is construed in a more general context.

What we know is always probabilistically conditioned by what we do not know. This relationship between the known and the unknown is not one of a simple dichotomous complementarity--"not known" is not synonymous with the unknown. Rather the complementariness between known/unknown can be said to be complex and governed by dynamic relations of conditional equivalence. This non-dichotomous relationship underlying our information systems permits us the flexibility to search, construct, simulate and test alternative hypothetical frameworks from the standpoint of a variable calculus of confidence.

The known and the unknown are not mutually exclusive subsets of the total range of possible knowledge--rather they are intersecting sets with overlapping complementariness and fuzzy edges. Thus there is a chaotic interaction between knowledge and the unknown, and there is a prototypicality effect of both the known and the unknown such that some kinds of knowledge are 'better known' and less conditioned by the unknown that others.

A lower level of significance for one set of data may lead to higher corroboration with other sets of data, thus an cumulative optimization and reduction of the net differences between data sets, while a higher level of significance may actually decrease the corroboration with other data sets.

If subsequent trials tend to randomly skew the known sample, this will be an indication of conceptual bias, or symbolic reification of the data. In a random sample, the least likely in a normal curve will be as likely as the most likely. This is because all knowledge is known and must therefore follow a normal curve of distribution. The failure of such data to do so will reflect a bias in the primary dimensions of relation rather than in the sample itself.

The presumption of the system of calculating confidence in the corroboration of fundamentally incommensurable data sets presented in this paper rests upon several premises. 1) The subset of the known tends to fall into a normal curve of distribution of variation. 2) The subset of the unknown is a complex set composed of the noise of the unknowable that is totally random and follows no normal distribution, and a subset of the knowable "unknown" that will tend to fall into a range of normal distribution--one that tends to be proportionately complementary and skewing of the curve of the known.

The gaps in our record of knowledge, and how we deal with these gaps, have a critical influence upon how we inter-relate our information and construct our hypothesis. There is a biased tendency to deal with such gaps in a "mythological" manner, which will have an affect upon how we conceptually frame and interpret our knowledge. The larger the gaps the more "random" the unknowable and the more skewed the likely relation between the known and the unknown. These gaps between knowledge points can be evaluated as relative "distances" in hypothetical, multidimensional space, upon which we can construct an operator-goal difference table. Plausible alternative hypothesis should work to reduce these differences in a complex, multidimensional way--the most probable set of hypothetical inferences being the optimal composite value that minimizes this distance.

This is offered as a viable, systematic substitute to the loose application of Occam's Razor. The discovery of subsequent data should work to confirm or disconfirm alternative hypothesis by predictably or unpredictably increasing/reducing this net distance. The greater the "skewing" effect of subsequent data, the less plausible the original hypothesis. The smaller the sub-sample, the higher the limits of confidence must be set and the lower the level of significance obtainable.

Corroboration in the lack of empirical evidence does not have to depend upon the researcher's own biased preconceptions, philosophical premises and rationalizations based upon the application of Occam's razor--human history has rarely taken the most direct course in its development. When multiple sources of information are available, even if the net cumulative information is insufficient, then a systematic approach based upon the relative distance between cumulative data points for each source will allow a less biased means for the construction and selection of alternative hypothesis.

It is apparent that we must separate the issue of the relative arbitrariness and non-arbitrariness and relative/absoluteness of data of data from the related issue of discrete/continuous or qualitative/quantitative scales of description. In general we may say that an arbitrary category is necessarily a relative or non-absolute category, but is not necessarily a qualitative as opposed to quantitative category. In general, quantitative categories may be relatively arbitrary and qualitatively categories may be relatively non-arbitrary.

Though this systematic quality suggests that the complexity of the problem of commensurable quantification of alternative sources of data may even be entered into a computer, the problems of counting, sampling, statistical description, and comparability, remains essentially qualitative problems of "confidence" in the normative decision-making and judgment involved in the assignment of discrete, absolute values to continuous, relative data sources. At some point in the decision-making process, a trade-off must be made between the empirical accuracy of the data and the reduction in the inherent complexity of the problem.

This point may be reached when the etic grid of arbitrary "tesserae" of measurement cross-cut the "natural" or basic boundaries of the aggregation of data in a minimally random manner, and this can be represented by a proportional ratio of fit between the grid and the data set. This "measure of confidence" can be used to combine and compare alternative sources of data by means of weighted and ranked averages.

The weighting and ranking of these proportional ratios of confidence may be done paradigmatically and alternatively, and sets up a systematic search-solution space for the comparison of different data sets, by means of the multi-dimensional scaling of the different ratios of confidence--the best choice being the solution set with the minimal net distance, or the maximal proximity, between combined data points, and the range of variation being the best boundary of plausibility for alternative solutions.

Abductive historical logic arguing backwards from the effects to the cause makes possible alternative plausible hypothesis that would not be possible in forward deductive logic. The selection of alternative hypothesis in historical reasoning therefore depends critically upon the estimation of likelihood and weighting of probabilities of alternative antecedent events. Though ultimately a relative procedure, the assignment of values is anchored in the relative availability/paucity of evidence, and in the degree to which alternative, and relatively independent sources reveal consensus or support one hypothesis versus another.

Abductive historical reasoning is a modified version of inductive inference. Such inference is guided by the most likely values available in a given sub-sample, and permits alternative inferences that are defined by only one basic constraint--as long as a inference is not definitely contradicted by counter evidence--the criterion of falsifiability--that all swans are white until one black swan is discovered. Hence, inductive reasoning is inherently tautological, or internally unfalsifiable. Abductive reasoning is internally false, as it involves a modus tollens fallacy of arguing from the consequent. But both modes of reasoning are very useful and indispensable in scientific and empirical research.

When given gaps in the record, and no firm idea of the total population or the relative size of the sub-sample, we tend to fall back upon internal arguments of non-contradiction and parsimony, i.e. Occam's razor, in construction of our hypothesis. But the chaotic complexity and multi-determination of historical patterns and processes tends to undermine the value of applying Occam's razor and tends to obfuscate the "mythological" filling in the gaps with arbitrary and alien frames of reference/inference. A systematic substitute for this process of accounting for the "gaps" in the record is outlined as a way of coming to terms with, rather than implicitly denying, the inherent complexity and problematical quality of the phenomena involved. This method relies upon the development of measures and a calculus of "confidence" that relies upon the relative weighting of alternative sets of data and the cumulative summation of the relative distances of alternative sources of data when plotted in multi-dimensional space.

This method relies upon the observed fact that the curve of distribution of any sub-sample tends toward a normal Gaussian distribution, whatever the overall skewing of the original population, and with the Bayesian conditionality of the relative cultural consensus of multiple data points that is robust with even a relatively small sub-sample of elements. This entails that the multidimensional correlation of different sets of data in a common space will tend to reflect the strength of interdependent historical relationship, and that the greater the clustering of these points in multidimensional space, the greater the strength of correlation between them.

Furthermore, on the basis of this kind of scaling, it becomes possible to construct a set of alternative reference/inference frames in which the probable direction of determination is based upon the relative inference strength, or confidence value, of arguing in one direction versus any other plausible direction.

It is possible to further systematize this process of inference frame construction and exploration by means of setting up a discrimination and operator-difference table based upon the probabilistic calculation of the total paradigm of alternative possibilities of inference. The most likely pathways through the resulting N-K network graph can be summarized as an inferential rule, which in turn can be used to build an inference engine for driving a computer based system of knowledge.

The conclusion to be drawn from this combination, if it can be implemented, is that inferential confidence can be probabilistically based upon systemic coherence that is in turn based upon a limited, given set of information, and that relative coherence can be based upon estimations of conditionality and consensus of alternative sets of data.

Such an approach, while complicated and ultimately arbitrary in the determination of its initial values, would permit the systematic exploration, simulation and comparison of alternative hypothetical frameworks that would clarify the process of filling in the gaps in the record and that would thus reduce the likelihood of external subjective bias in the construction of frameworks. The success of such a system would depend upon the relative weighting of the initial values, a process which itself can be anchored in empirical data and tests, and rendered systematic in a similar fashion, such that a range of alternative weightings can be calculated and compared.

Each set of initial values will generate a search space of alternative solutions, which can be narrowed to the most probable pathways based upon the presumption of a normal distribution. Alternative sets of inputs will thus generate multiple spaces. It is argued that these spaces will themselves be normally distributed, and that this distribution will constitute a basis for the estimation most plausible values.

An extension of this approach would be to "frame" the gaps and to plug in alternative "additional" evidence to generate alternative "scenarios." This would allow the investigation of the "gaps" that would allow us to make predictions, again based upon the presumption of a normal distribution, about which lines of research should be pursued and which kinds of evidence would support what kinds of hypothesis.