Modifications of current theories of ordinal, interval and extensive measurement are presented, which aim to accomodate the empirical fact that perfectly exact measurement is not possible (which is inconsistent with current theories). The modification consists in dropping the assumption that equality (in measure) is observable, but continuing to assume that inequality (greater or lesser) can be observed. The modifications are formulated mathematically, and the central problems of formal measurement theory—the existence and uniqueness of numerical measures consistent with data—are re-examined. Some results also are given on a problem which does not arise in current theories: namely that of determining limits of accuracy attainable on the basis of observations.

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If u and ℜ are empirical and numerical relational systems, respectively, then a sig-function F is constant on u with respect to ℜ if, and only if, the value of F is the same for all numerical assignments for u with respect to ℜ. Using these notions we prove rigorously certain generalizations of Stevens's results.

Dr. Marjorie Grene has argued that criteria taken from a personalist philosophy of science have regulative force in the dispute between orthogenetic and synthetic or neo-Darwinian theories of evolution, and that these criteria commend the acceptance of the orthogenetic position. Grene's position includes two basically correct theses concerning the limitations of operationism and reductionism. However, she fails to show that personalist tenets are necessary for the validation of these two theses. Moreover, the proposed modifications of evolutionary theory depend upon additional premisses: that biology must study individuals rather than populations, and that the synthetic theory must prove that natural selection and mutation are the only possible factors for control of the direction of evolutionary change. The evidence for these premisses is called into question.

The structure of Reichenbach's pragmatic vindication of induction is analysed in detail. The argument is seen to proceed in two stages, the first being a pragmatic justification of the frequency interpretation of probability which is taken as a license for considering the aim of induction to be the discovery of limiting relative frequencies, and the second being the pragmatic justification of induction itself. Both justifications are found to contain flaws, and the arguments used to support Reichenbach's definition of the aim of induction presuppose the availability of a type of predicate which generates paradoxes closely related to Goodman's “grue-bleen” paradox.

Next, Salmon's “Criterion of Linguistic Invariance” is evaluated as a canon of inductive logic, which singles out the “straight rule” from an infinite class of convergent inductive rules. Upon close examination, its credentials are seen to be unimpressive. In connection with Salmon's work on linguistic invariance, we take a closer look at the impact of the Goodman paradox on probability estimator rules like Reichenbach's “straight rule.” We find that its undesirable consequences for such systems of inductive logic cannot be escaped by Salmon's solution, or indeed by any solution whose motivating idea is to rule “queer” predicates out of court.

Finally, the discussion of the Goodman paradox leads us to a modest methodological proposal for systems of inductive logic which incorperate probability estimator rules of the type at issue.

The conclusion urged in Mr Salmon's recent article ([1], pp. 252-261) is so remarkable that it may be worth recording some difficulties. He claims to rescue Reichenbach's notorious vindication of induction. This is essentially concerned with estimating long-run frequencies. By an estimator let us mean any rule for making estimates appropriate to various bodies of information. Reichenbach thought an estimator is sensible only if it is convergent, that is, roughly speaking, only if its estimates tend to approach the truth as more and more data is collected. Mr Salmon observes that an estimator should, in addition, be independent of the language in which the information is expressed. He contends that this criterion of linguistic invariance, when added to the rest of Reichenbach's train of thought, suffices to justify the “straight rule” for estimation: if m of the n observed A's are B, estimate the long-run frequency of B among A's as m/n.

What one is acquainted with has always been important for the rejection or acceptance of any ontological description. Yet the relevance of acquaintance to ontology has not always been clearly stated. Some philosophers have held that they were acquainted with the simple entities of ontological analysis. They also held that if they were not acquainted with such entities, their analysis would be inadequately supported. In this paper I argue that acquaintance with ontological simples cannot be a reason for accepting or rejecting any ontological analysis. At the same time, I examine what I believe to be the relevance of acquaintance to ontological description.

Consider a red circle, and suppose it is a paradigmatic thing. Some philosophers maintain that a thing is ontologically analyzable into a particular exemplifying properties, those properties truly ascribed to the thing by the customary words. Our red circle, then, consists of a particular, say a; two properties, red and circle; and exemplification, a tie tying a, red, and circle into “the red circle.” Upon this analysis, a is bare, i.e., not re-recognizable as such, whereas red and circle are natured, i.e., not bare, and, further, are universal, i.e., they may be exemplified by several particulars (or, somewhat differently, they may be in several things).

In [6] I tried to show how an objection to “the nominalist's” analysis of (a) “This is red” and (b) “That is red” on the basis of “the doctrine of common names” might be overcome. The objection is that “the nominalist,” attempting to analyze (a) and (b) by construing the pronouns in these sentences as two different proper names and “red” as a common name, is forced thereby to construe the copula in both sentences as the “is” of identity, and hence (it is claimed) this and that are identical, i.e., that there is only one red spot and not two. I attempted to show that by using Leśniewski's original axiom of ontology “the nominalist” could construe the pronouns in (a) and (b) as proper names, and “red” as a common name without taking the copula to express identity; he would not be forced to identify this with that.

Adolph Grünbaum has argued that Duhem's conventionalism is false for the case of Euclidean geometry ([6], [7], [8]). According to Duhem, any portion of a physical theory can be preserved from falsifiability by providing suitable modifications elsewhere in the theory. Grünbaum argues that physical theory is composed of two parts: A geometrical part H, and a physical part A. For his test case—Euclidean geometry—he contends that by a suitable specification of A, a falsification of H is possible; i.e., H can be rendered “accessible to experimental ascertainment in isolation from other physical regularities.”

In several recent publications, Professor Adolf Grünbaum has inveighed against the conventionalism of writers like Einstein, Poincaré, Quine and especially Duhem. Specifically, Grünbaum has assailed the view that a single hypothesis can never be conclusively falsified. Grünbaum claims that the conventionalists’ insistence on the immunity of hypotheses from falsification is neither logically valid nor scientifically sound. Directing the weight of his argument against Duhem, Grünbaum launches a two-pronged attack. He insists, first, that conclusive falsifying experiments are possible, suggesting that Duhem's denial of such experiments is a logical non-sequitur. He then proceeds to show that, more than being merely possible, crucial falsifying experiments have occurred in physics. I do not intend to make a logical point against Grünbaum's critique so much as an historical and exegetical one. Put briefly, I believe that he has misconstrued Duhem's views on falsifiability and that the logical blunder which he discusses should not be ascribed to Duhem, but rather to those who have made Duhem's conventionalism into the doctrine which Grünbaum attacks. Whether there are any writers who accept the view he imputes to Duhem, or whether he is exploiting “straw-men” to give weight to an otherwise trivial argument is an open question. For now, I simply want to suggest that his salvos are wrongly directed against Duhem.