Deductive-nomological
Encyclopedia
The deductive-nomological model (or D-N model) is a formalized
view of scientific
explanation
in natural language
. It characterizes scientific explanations primarily as deductive arguments
with at least one natural law
statement among its premises. "Nomological" comes from the Greek word "νόμος
" (nomos), i.e., "law."
The D-N model is taught implicitly in schools, and approximates our pre-theoretical conception of science, which many non-experts hold. It was initially formalized by Carl Hempel and Paul Oppenheim
in their article Studies in the Logic of Explanation (1948). A sketch of it can be found in Karl Popper
's Logic of Scientific Discovery (1934).
In the D-N model, at least one of the statements si must be a "law-like" statement—a problematic concept, but initially thought to be captured by universal affirmatives
, i.e., statements of the form "all X are Y." The explanans must be appropriately testable or observable—they must have "empirical content." If the premises are all true and if the argument is deductively valid
, then the following constitutes a correct deductive-nomological explanation of p:
s1. . . sn, therefore, p
As a very simple illustration, consider the following: we observe that a piece of chalk falls when released. Why does the chalk fall? A D-N explanation might look like this (without attending to all subtleties in the precisely correct statement of the premises and conclusion):
The model is influenced by logical positivism
in its tone and implication, devised as a prescriptive form for scientific explanations. Due to the way that the model eschews any account of causality
, scientific modelling
, or simplification—and the general rejection of logical positivism
—it is no longer accepted by most current philosophers of science.
Formal science
The formal sciences are the branches of knowledge that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics, and some aspects of linguistics....
view of scientific
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
explanation
Explanation
An explanation is a set of statements constructed to describe a set of facts which clarifies the causes, context, and consequencesof those facts....
in natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
. It characterizes scientific explanations primarily as deductive arguments
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
with at least one natural law
Natural law
Natural law, or the law of nature , is any system of law which is purportedly determined by nature, and thus universal. Classically, natural law refers to the use of reason to analyze human nature and deduce binding rules of moral behavior. Natural law is contrasted with the positive law Natural...
statement among its premises. "Nomological" comes from the Greek word "νόμος
Nomos
Nomos or Nomoi may refer to:* Nome , a subdivisions of Ancient Egypt* Nome , the administrative division immediately below the peripheries of Greece * law...
" (nomos), i.e., "law."
Background
The D-N model is known by many names, including the covering law model, the subsumption theory, Hempel's model, the Hempel-Oppenheim model, and the Popper-Hempel model of explanation (Niiniluoto, 1995). Its introduction in the philosophical literature is part of a broad general discussion about the nature of scientific explanation (i.e., what it is, what it should be, etc.).The D-N model is taught implicitly in schools, and approximates our pre-theoretical conception of science, which many non-experts hold. It was initially formalized by Carl Hempel and Paul Oppenheim
Paul Oppenheim
Paul Oppenheim was a German chemist, philosopher, independent scholar and industrialist....
in their article Studies in the Logic of Explanation (1948). A sketch of it can be found in Karl Popper
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
's Logic of Scientific Discovery (1934).
Formalization
The model offers the following account of scientific explanation, where an explanation is set out as a formalized argument:- Let p be the explanandum - the statement that describes the phenomenon or phenomena to be explained.
- Let s1. . . sn be the explanans - the statements that "explain" the statement P.
In the D-N model, at least one of the statements si must be a "law-like" statement—a problematic concept, but initially thought to be captured by universal affirmatives
Term logic
In philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...
, i.e., statements of the form "all X are Y." The explanans must be appropriately testable or observable—they must have "empirical content." If the premises are all true and if the argument is deductively valid
Validity
In logic, argument is valid if and only if its conclusion is entailed by its premises, a formula is valid if and only if it is true under every interpretation, and an argument form is valid if and only if every argument of that logical form is valid....
, then the following constitutes a correct deductive-nomological explanation of p:
s1. . . sn, therefore, p
As a very simple illustration, consider the following: we observe that a piece of chalk falls when released. Why does the chalk fall? A D-N explanation might look like this (without attending to all subtleties in the precisely correct statement of the premises and conclusion):
- Massive objects attract each other with a force proportional to their masses and inversely proportional to the square of their distance apart.
- The chalk and Earth are massive objects.
- Holding the chalk overcomes the force of attraction between it and Earth
- Therefore, the chalk falls when released
The model is influenced by logical positivism
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...
in its tone and implication, devised as a prescriptive form for scientific explanations. Due to the way that the model eschews any account of causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
, scientific modelling
Scientific modelling
Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling...
, or simplification—and the general rejection of logical positivism
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...
—it is no longer accepted by most current philosophers of science.
Related subjects
- Explanandum and explanansExplanandumAn explanandum is a phenomenon that needs to be explained and its explanans is the explanation of that phenomenon. For example, one person may pose an explanandum by asking "Why is there smoke?", and another may provide an explanans by responding "Because there is a fire"...
- Hypothetico-deductive modelHypothetico-deductive modelThe hypothetico-deductive model or method, first so-named by William Whewell, is a proposed description of scientific method. According to it, scientific inquiry proceeds by formulating a hypothesis in a form that could conceivably be falsified by a test on observable data...
- Models of scientific inquiryModels of scientific inquiryIn the philosophy of science, models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at...
- Philosophy of sciencePhilosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
- Scientific methodScientific methodScientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of...
Types of inference
- Abductive reasoningAbductive reasoningAbduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...
- Deductive reasoningDeductive reasoningDeductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
- Inductive reasoningInductive reasoningInductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...