The necessitarian states that there are metaphysical connections of necessity in the world that ground and explain the most fundamental regularities. Necessitarian theorists usually use the word must to express this connection.[1] Thus, NT maintains must-statements are not adequately captured by is-statements (must ≠ is, or certain facts are unaccounted for).[2] Nomic necessity claims that it is difficult for mere regularity to account for certain counterfactual claims because what happens in the actual world do not themselves imply anything about what would have happened had things been different.[3] If it is now true that Q occurs if P causally precedes Q then the necessitarian can adequately account for counterfactual claims. Given the present antecedent condition of P at tn and P implies Q at tn and it was true that P implied Q at tn-1 then using P as an antecedent for R at hypothetical tn-1’ then R is true if P was a sufficient condition R at tn-1’. Thus, there is certainty in the truth of counterfactual claims. However, counterfactuals allow for conflict between truth functional interpretation and ordinary language. For instance, any counterfactual claim with the necessary condition having a false truth-value and the sufficient condition obtaining a truth-value that is true then the counterfactual claim will be invalid.
Why is supporting counterfactual conditionals a symptom of nomic necessity? I would ague that there must be a connection or relationship between the conditions. Consider the argument, as modus ponens, that if the moon’s core is made of cheese then my desk is made from mahogany. What relationship do these two conditions have? The truth-value is valid (F-T-T). However, I recognize that this is merely a preference, which is, at times, convenient. When making a novel explanans and prediction the relationship between the conditions may not be epistemically evident. This is one of the reasons why I prefer the I-S model over the D-N model for the sake of being modest in explanatory scope and the epistemic range of data in the explanandum.
There may be reasons for rejecting the necessitarian claims by underdetermination. Neither non-local quantum correlations nor (in light of non-localizability) the nature of the fundamental constituents of material reality can be explained or understood if the explanatory constraints of naturalism, or necessitarianism, are preserved. These quantum phenomena require an explanation. The failure of material identity/individuality in the quantum realm not only undermines the ontology of naturalism, it also renders necessitarian theories of natural law untenable. This leads to the conclusion that the empirical regularities of quantum theory are mere regularities unsupported by any natural nomological structure.[4]
Historically, logical positivism dropped the philosophical contributions and had gotten closer to nomic necessity. This had entailments for property dispositions. How do you test an empirical property? When appealing to properties it is referring to realism, something that happens to the entities but particularly the properties. For the anti-realist dispositions are most fundamental aspects of reality. One cannot get more reductive than dispositions and necessity. Unless a necessitarian is prepared to say that the relation of necessity is actually observed in the instances of some law or describing certain properties, the inference to a necessary law creates the problem of inductive reasoning.[5] Likewise, unless the appropriate necessary connections are postulated the fixed premises for deductive reasoning are not as firm as the logical positivist would like them to be. Then, logical positivists have sought to avoid nomic necessity due to the metaphysical problems imported with such explanations and causation. Thus, instrumentalism enters the scene. Since it seems nearly impossible to get to nomic necessity the positives adopted the instrumentalist or anti-realist position and considered that the next best option. If you have an adequate explanation that approximates the world then you have the conditions that bring an event about. The logical positivist breaks explanations down by conditions because they do not necessarily know what causality is metaphysically.
[1] Robin Collins, “God and the Laws of Nature,” Philo Vol. 12 No. 2 (2009): 2-3. (Preprint).
[2] Bernard Berofsky, “The Regularity Theory,” Nous Vol. 2 No. 4 (1968): 316.
[3] Collins, 4.
[4] Bruce Gordon, “A Quantum-Theoretic Argument against Naturalism,” in The Nature of Nature. Eds. Bruce Gordon and William Dembksi (Wilmington, DE: ISI Books, 2011), 181.
[5] Berofsky, 325-26.