Discussions about the nature of essence and about the inference problem for non-Humean theories of nomic modality have largely proceeded independently of each other. In this article I argue that the right conclusions to draw about the inference problem actually depend significantly on how best to understand the nature of essence. In particular, I argue that this conclusion holds for the version of the inference problem developed and defended by Alexander Bird. I argue that (...) Bird’s own argument that this problem is fatal for David Armstrong’s influential theory of the laws of nature but not for dispositional essentialism is seriously flawed. In place of this argument, I develop an argument that whether Bird’s inference problem raises serious difficulties for Armstrong’s theory depends on the answers to substantial questions about how best to understand essence. The key consequence is that considerations about the nature of essence have significant, underappreciated implications for Armstrong’s theory. (shrink)

While the inference problem is widely thought to be one of the most serious problems facing non-Humean accounts of laws, Jonathan Schaffer has argued that a primitivist response straightforwardly dissolves the problem. On this basis, he claims that the inference problem is really a pseudo-problem. Here I clarify the prospects of a primitivist response to the inference problem and their implications for the philosophical significance of the problem. I argue both that (...) it is a substantial question whether this sort of response ought to be accepted and that the inference problem, contra Schaffer, remains a significant problem with important implications for the non-Humean position. I also argue that this discussion indicates grounds to be wary about applying the Schaffer-style strategy of straightforwardly dissolving problems by stipulation to other philosophical problems. (shrink)

The difficulties facing Humean regularity accounts of laws have led some philosophers to a theory that takes laws to be necessitation relations between universals. In this paper I evaluate David Armstrong's version of this theory by considering two of its key elements: its solution to the so-called “Inference Problem” and its denial of uninstantiated universals. After considering some potential problems with each of these elements on their own, I argue that Armstrong's solution to the Inference Problem (...) and his denial of uninstantiated universals are not two independent aspects of his view. His solution to the Inference Problem depends upon his denial of uninstantiated universals. (shrink)

How do non-Humean laws govern regularities in nature? According to the Inference Problem, non-Humean accounts of governing face a central problem: it is not clear how such laws do perform their governing function. Recently, Jonathan Schaffer has argued that the introduction of a law-to-regularity axiom is sufficient to solve the Inference Problem. The authors argue that Schaffer’s solution faces a devastating dilemma: either the required axiom cannot, on its own, differentiate the non-Humean account from a (...) Humean account of laws or, if more content is added to the primitive governing posit, it should be shown how and why the ‘outfitted’ posit obtains in the world. Furthermore, the authors show that those cases that Schaffer presents to motivate his approach are not analogous to the case of lawhood and so they cannot provide justification for his axiomatic solution. (shrink)

A well-known difficulty that affects all accounts of laws of nature according to which the latter are higher-order facts involving relations between universals (the so-called DTA accounts, from Dretske in Philosophy of Science 44:248–268, 1977; Tooley in Canadian Journal of Philosophy 7:667–698, 1977 and Armstrong (What is a Law of Nature?, Cambridge University Press, Cambridge, 1983)) is the Inference Problem: how can laws construed in that way determine the first-order regularities that we find in the actual world? Bird (...) (Analysis 65:147–55, 2005) has argued that there is no solution to the Inference Problem which is consistent with both categorical monism (that is, the view that all natural properties are categorical) and basic tenets of Armstrong’s account of the laws of nature. This paper shows that, given Armstrong’s view about laws as first-order structural universals whose instantiation ‘produce’ nomic regularities and under specific plausible metaphysical assumptions concerning nomic relations which are consistent with a broadly construed DTA approach to laws, there is no extra difficulty regarding the Inference Problem in a categorical monistic context besides the ones that beset structural universals in general. (shrink)

In this article I intend to show that the inference problem, one of the main objections raised against the anti-Humean theory of natural laws defended by Dretske, Tooley and Armstrong (?DTA theory? for short), can be successfully answered. First, I argue that a proper solution should meet two essential requirements that the proposals made by the DTA theorists do not satisfy. Then I state a solution to the inference problem that assumes a local immanentistic view of (...) universals, a partial definition of the nomic necessitation relation as a relation of existential dependence, and a principle constraining multiple occupancy. I also argue that my solution meets the two requirements. Finally, I deal with non-standard laws such as exclusion laws, causal laws and laws involving spatiotemporal parameters. (shrink)

Alethic pluralists argue truth is a metaphysically robust higher-order property that is multiply realized by a set of diverse and domain-specific subvening alethic properties. The higher-order truth property legitimizes mixed inferences and accounts for a univocal truth predicate. Absent of this higher-order property, pluralists lack an account of the validity of mixed inferences and an adequate semantics for the truth predicate and thereby appear forced to abandon the central tenets of alethic pluralism. I argue the use of many-valued logics to (...) support pluralism fails to address the pluralist’s metaphysical problem regarding mixed inferences and mixed truth functional connectives. The high degree of heterogeneity of the alethic realizers challenges the plausibility of a single higher-order functional property. A functional property with such a heterogeneous base cannot be projectable at a theoretically significant level. The problem with mixed inferences and truth functions is but one symptom of the deeper projectability problem. (shrink)

In this article I intend to show that the inference problem, one of the main objections raised against the anti-Humean theory of natural laws defended by Dretske, Tooley and Armstrong (“DTA theory” for short), can be successfully answered. First, I argue that a proper solution should meet two essential requirements that the proposals made by the DTA theorists do not satisfy. Then I state a solution to the inference problem that assumes a local immanentistic view of (...) universals, a partial definition of the nomic necessitation relation as a relation of existential dependence, and a principle constraining multiple occupancy. I also argue that my solution meets the two requirements. Finally, I deal with non-standard laws such as exclusion laws, causal laws and laws involving spatiotemporal parameters. (shrink)

In response to various shortcomings of regularity theories of natural law, some philosophers of a realist bent have recently been drawn to the view that a law of nature is a relation between universals. Heading this group are Michael Tooley and D. M. Armstrong.

In this article I intend to show that the inference problem, one of the main objections raised against the anti-Humean theory of natural laws defended by Dretske, Tooley and Armstrong ("DTA theory" for short), can be successfully answered. First, I argue that a proper solution should meet two essential requirements that the proposals made by the DTA theorists do not satisfy. Then I state a solution to the inference problem that assumes a local immanentistic view of (...) universals, a partial definition of the nomic necessitation relation as a relation of existential dependence, and a principle constraining multiple occupancy. I also argue that my solution meets the two requirements. Finally, I deal with non-standard laws such as exclusion laws, causal laws and laws involving spatiotemporal parameters. (shrink)

This article is an attempt to use the insights of objective probability theory to solve the Sleeping Beauty problem. The approach is to develop a partial theory of direct inference and then apply that partial theory to the problem. One of the crucial components of the partial theory is the thesis that expected indefinite probabilities provide a reliable basis for direct inference. The article relies heavily on recent work by Paul D. Thorn to defend that thesis. (...) The article’s primary conclusion is that Beauty can by way of a justifiable direct inference from a statement of expected indefinite probability reach the conclusion that the epistemic probability that the relevant coin toss lands heads is 1/3. The article also provides an account of why the self-locating information that Beauty acquires on Monday is evidentially relevant to the question of whether the coin toss lands heads or tails. (shrink)

The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. (...) Past theories of direct inference have postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability . I address the lacuna in past theories by introducing criteria for being a relevant statistic . The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories. (shrink)

In reply to Geach's objection against expressivism, some have claimed that there is a plurality of truth predicates. I raise a difficulty for this claim: valid inferences can involve sentences assessable by any truth predicate, corresponding to 'lightweight' truth as well as to 'heavyweight' truth. To account for this, some unique truth predicate must apply to all sentences that can appear in inferences. Mixed inferences remind us of a central platitude about truth: truth is what is preserved in valid inferences. (...) The question is why we should postulate truth predicates that do not satisfy this platitude. (shrink)

Knowledge can be transmitted by a valid deductive inference. If I know that p, and I know that if p then q, then I can infer that q, and I can thereby come to know that q. What feature of a valid deductive inference enables it to transmit knowledge? In some cases, it is a proof of validity that grounds the transmission of knowledge. If the subject can prove that her inference follows a valid rule, then her (...) inference transmits knowledge. However, this only pushes the question back to the inference that was made in this proof. What feature of that inference enables it to transmit knowledge? A vicious regress looms here. Every proof requires a valid inference, and every valid inference must follow at least one rule of inference. So every proof must follow at least one rule of inference. Therefore not every valid inference that transmits knowledge can acquire this power through a proof, on pain of vicious infinite regress. So it must be possible to transmit knowledge by making an inference that follows an underived rule. A deductive inference that follows an underived rule is what I will call a basic deductive inference. It must be possible to transmit knowledge by making a basic deductive inference. But how is this possible? What feature of a basic deductive inference gives it this power to transmit knowledge? (shrink)

This paper develops a means–end analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce (...) hidden particles. Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions—including prescriptions for when exactly to introduce hidden particles. (shrink)

Probability and inverse inference; Neyman-Pearson theory; Fisherian significance testing; The fiducial argument: one parameter; The fiducial argument: several parameters; Ian hacking's theory; Henry Kyburg's theory; Relevance and experimental design.

If one investigates a process that has several causes but assumes that it has only one cause, one risks ruling out important causal factors. Three mechanisms account for this mistake: either the significance of the single cause under test is masked by noise contributed by the unsuspected and uncontrolled factors, or the process appears only when two or more causes interact, or the process appears when there are present any of a number of sufficient causes which are not mutally exclusive. (...) In ecology and evolutionary biology, experiments usually test single factor hypotheses, and many scientists apparently believe that hypotheses incorporating several factors are so much more difficult to test that to do so would not be practical. We discuss several areas in ecology and evolutionary biology in which the presupposition of simple causation has apparently impeded progress. We also examine a more mature field, the study of atherosclerosis, in which single factor studies did significantly delay progress towards understanding what now appears to be a multifactor process. The problem has three solutions: either factorial experiments, dynamic models that make quantitative predictions, response-surface methods, or all three. In choosing a definition for ‘cause’, we make a presupposition that profoundly influences subsequent observations and experimental designs. Alternative definitions of causation should be considered as contributing to potential cures for research problems. (shrink)

The hypothesis that God supernaturally raised Jesus from the dead is argued by William Lane Craig to be the best explanation for the empty tomb and postmortem appearances of Jesus because it satisfies seven criteria of adequacy better than rival naturalistic hypotheses. We identify problems with Craig’s criteria-based approach and show, most significantly, that the Resurrection hypothesis fails to fulfill any but the first of his criteria—especially explanatory scope and plausibility.

It would be difficult to overestimate the influence Hume’s problem of induction exercises on contemporary epistemology. At the same time, the problem of induction has not perceptibly slowed the progress of mathematics and science. This ironic state of affairs, immortalized by C. D. Broad’s description of induction as “the glory of science” and “the scandal of philosophy,” ought in all fairness to give both sides some pause. And on occasion, it does: the mathematicians stop to concede that Hume (...) has not yet been answered, the scientists worry about randomization of experiments, and inductive skeptics stir uneasily in their chairs at the mention of certain mathematical theorems that seem palpably to have bearing on the problem. (shrink)

A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and (...) plausible definition, given here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature. (shrink)

This paper aims to solve a potential problem for the methodology of constitutive inference offered by Harbecke. The methodology is ultimately based on Mill’s “method of difference”, which requires a complete variation of factors in a given frame. In constitutive contexts, such a complete variation is often impossible. The offered solution utilizes the notion of a “mechanism slice”. In a first step, an example of a currently accepted explanation in neuroscience is reconstructed, which serves as a reference point (...) of the subsequent discussion. The regularity theory of mechanistic constitution and the corresponding methodology of constitutive inference are then introduced. Eventually, it is argued that the proposed solution accommodates well all schematic situations in which the impossibility of varying all test factors could be expected either to lead to false inferences or to preclude the establishment of correct constitutive claims. (shrink)

Of the many proposals for inferring genetic regulatory structure from microarray measurements of mRNA transcript hybridization, several aim to estimate regulatory structure from the associations of gene expression levels measured in repeated samples. The repeated samples may be from a single experimental condition, or from several distinct experimental conditions; they may be “equilibrium” measurements or time series; the associations may be estimated by correlation coefficients or by conditional frequencies (for discretized measurements) or by some other statistic. This paper describes two (...) elementary statistical difficulties for all such procedures, no matter whether based on Bayesian updating, conditional independence testing, or other machine learning procedures such as simulated annealing or neural net pruning. One difficulty obtains if large numbers of cells are aggregated in a measurement of expression levels from a common population of cells; the other obtains if small numbers of cells are aggregated or if samples are separately aggregated over different populations of cells. (shrink)

This essay is a refutation of Hume on causal inference. The decisive point of the refutation is that Hume's argument is invalid unless it is assumed, contrary to his own relational theory of time, that mere difference in dates can affect the course of nature. In the preliminary discussion of sections II and III the words “cause,” “effect,” and “causal relation” are employed in a nontechnical sense, which is exemplified in such statements as “Fire causes heat”, “Lightning and thunder (...) are causally related”, “When one turns the steering wheel to the right, the effect is that the car moves to the right”, and so on. But in order to forestall rebuttals in defense of Hume one needs a greater precision in terminology as well as in conception of causality. Section IV aiming at precision gives a statement of the principles of causality which is in accordance with the position of modern science. An examination of this statement shows that the validity of causal inference must be accepted along with a relational theory of time. A comment on causal inference in relation to induction brings the discussion to a close. (shrink)

I.1. Two reasons for studying inference. Inference is studied for two distinct reasons: for its bearing on justification and for its bearing on learning. By and large, philosophy has focused on the role of inference in justification, leaving its role in learning to psychology and artificial intelligence. This difference of role leads to a difference of conception. An inference based theory of learning does not require a conception of inference according to which a good (...) class='Hi'>inference is one that justifies its conclusion, whereas, obviously, an inference based theory of justification does require such a conception.1 Because of its focus on normative issues of justification, philosophy has taken a retrospective approach to inference, whereas a focus on learning naturally leads to a prospective approach. A focus on learning leads us to ask, "Given what is known, what should be inferred? How can what is known lead, via inference, to new knowledge?" A focus on justification has led philosophers to concentrate instead on a retrospective question: "Given a belief, can it be validly inferred from what is known? How can what is known justify, via inference, a new belief?" Thus, for philosophy, inference can be regarded as permissive: one needn't worry about what to infer, only about whether what has been arrived at somehow or other is or can be inferentially justified. A theory of learning, on the other hand, requires a conception of inference that is directive, for the problem of inference based learning is precisely the problem of what to infer. (shrink)

The present work is an expansion of the author's doctoral dissertation, entitled "The Fiducial Argument," completed at Columbia University in 1975. Seidenfeld's principal objective, as stated in the Preface, is to "reconstruct and evaluate Fisherian statistics, with special attention to Fisher's idea of fiducial probability as it pertains to inverse inference.".

Scientists often study hypotheses that they know to be false. This creates an interpretive problem for Bayesians because the probability assigned to a hypothesis is typically interpreted as the probability that the hypothesis is true. I argue that solving the interpretive problem requires coming up with a new semantics for Bayesian inference. I present and contrast two new semantic frameworks, and I argue that both of them support the claim that there is pervasive pragmatic encroachment on whether (...) a given Bayesian probability assignment is rational. (shrink)

The problem of theory choice and model selection is hard but still important when useful truths are underdetermined, perhaps not by all kinds of data but by the kinds of data we can have access to ethically or practicably—even if we have an infinity of such data. This article addresses a crucial instance of that problem: the problem of inferring causal structures from nonexperimental, nontemporal data without assuming the so-called causal Faithfulness condition or the like. A new (...) account of epistemic evaluation is developed to solve that problem and justify a standard practice of causal inference in data science. (shrink)