Occam’s sword explained by the laws of matter and energy and applied to philosophy and science.
Laws of Matter and Energy, Albert P. Carpenter, Eliminative Materialism, Eliminative and Multiplicative Materialism, Philosophy, Philosophy of Science
by Albert P. Carpenter
The first principle of Occam’s sword is Occam’s razor verbatim, while the second is based on Chatton’s anti-razor while modeled on the first. The third and fourth are novel and give rise to two novel conservation laws; the Conservation of Properties. The reason, then, that entities and their properties are not to be multiplied or eliminated quantitatively is that matter and energy and their properties cannot be created or destroyed. On the other hand, entities can be created and destroyed qualitatively which gives rise to the second variant of Occam’s sword. So that entities and their properties can be multiplied and eliminated as matter and energy is qualitatively created and destroyed.
The First Formulation of Occam’s sword:
There are two variants of Occam’s sword based on either of two sets of laws of matter and energy (the quantitative and qualitative laws) that serve as their explanatory basis. Thus for the quantitative laws of matter and energy, Occam’s sword assumes the following form:
1) Entities are not to be multiplied beyond necessity.
2) Entities are not to be eliminated beyond necessity.
3) Properties of entities are not to be multiplied beyond necessity.
4) Properties of entities are not to be eliminated beyond necessity.
(Properties are to be understood as the behavior of matter and energy under varying conditions.)
The Second Formulation of Occam’s sword:
The second variant is based on the qualitative laws of matter and energy and assumes the following form:
1) Entities are to be multiplied as necessary.
2) Entities are to be eliminated as necessary.
3) Properties of entities to be multiplied as entities are multiplied.
4) Properties of entities are to be eliminated as entities are eliminated.
The Explanatory Basis for Both Variants of Occam’s sword
As mentioned in the introduction, the physical explanation for both is based on the distinction between the quantitative and qualitative laws of matter and energy. These are expressed quantitatively as:
1) Matter and energy cannot be quantitatively created.
2) Matter and energy cannot be quantitatively destroyed.
3) The properties of matter and energy cannot be quantitatively created.
4) The properties of matter and energy cannot be quantitatively destroyed.
and qualitatively as:
1) Matter and energy can be qualitatively created.
2) Matter and energy can be qualitatively destroyed.
3) The properties of matter and energy can be qualitatively created as matter and energy are qualitatively created,.
4) The properties of matter and energy can be qualitatively destroyed as matter and energy are qualitatively destroyed.
Quantitatively will be understood as the amount of matter and energy.
Qualitatively will be understood as the kinds or forms that matter and energy assumes as a result of the transformation.
There are numerous applications for Occam’s sword in Philosophy, Science, the Philosophy of Science and the Philosophy of Religion. The most significant application for Occam’s sword is perhaps in its capacity to subsume Eliminative and Multiplicative Materialism which while these theses originate in the Philosophy of Mind they extend into ontology and epistemology and establish the reciprocal relationship that holds between the two.
Occam’s sword and the Laws of Matter and Energy in Philosophy
Eliminative and Multiplicative Materialism: analyzed, subsumed and explained
by Albert P. Carpenter
In the first of two parts, Paul Churchland’s thesis of Eliminative Materialism in the Philosophy of Mind will be introduced, analyzed and discussed leading to the identification of two theses embedded in one: Eliminative and Multiplicative Materialism. These will be subsumed by Occam’s sword. In part two, a second sense of Eliminative and Multiplicative Materialism will be presented based on the distinction between the quantitative and qualitative laws of matter and energy. These theses will, also, be subsumed by a second variant of Occam’s sword. Finally, Eliminative and Multiplicative Materialism will be interpreted as epistemological theses with a metaphysical explanation to be found in the laws of matter and energy.
Eliminative Materialism in the Philosophy of Mind
It is not the purpose here to provide an overview of the origins or history of Eliminative Materialism (see the entry for ‘Eliminative Materialism’ at wikipedia and the article by the same name at the Stanford Encyclopedia of Philosophy) nor will its merits be debated. Rather, it will be stated as formulated by Paul Churchland, analyzed and discussed. Further, the evidence in support of each will be provided and evaluated.
As espoused by Paul Churchland, Eliminative Materialism is the thesis that Psychology is a theory of ours and others mental phenomena and one that is so flawed that it and its ontology of pain, fear, and joy, etc. will be replaced by a completed Neuroscience (and [presumably] its ontology of neurons, …etc.) (Churchland, 1981).
There are actually two theses embedded in Eliminative Materialism as stated above. The first is that Psychology will be eliminated (negative thesis) and second that Neuroscience will replace it (positive thesis). The first is called Eliminative Materialism because it subtracts from scientific ontology by making discoveries of entities that do not exist. The second will be term Multiplicative Materialism because it adds to scientific ontology by making positive discoveries in the Neurosciences of entities that actually exist.
In a subsequent article, Paul and Patricia Churchland cite the following cases in support of Eliminative Materialism of other theoretical and ontological eliminations from the history of science:
1) ” The phlogiston and the phlogiston theory of combustion
2) The caloric fluid and the caloric theory of heat
3) The rotating crystal spheres of Ptolemaic astronomy
4) The four humors of medieval medicine
5) The vital spirits of premodern biology
6) The luminiferous aether of pre-Einsteinian mechanics [electromagnetism?]”
(Churchland and Churchland, 1998).
Each instance above constitutes a case of negative discovery, where (and though never discerned with absolute certitude we nonetheless in practice decide that entities do not exist) we found and determined that each entity in question above does not exist (consider also the negative results of the Michelson-Morely experiment with regards to the aether). They were subsequently subtracted from the ontology of scientific discourse. Note, also, that this is an epistemological change not an ontological one in the sense that nothing has been subtracted from the world.
In an analogous way there is considerable evidence from the history of science in support of Multiplicative Materialism. Consider the following discoveries:
1) The four moons of Jupiter by Galileo Galilei in 1610
2) Microorganisms by Anton van Leeuwenhoek in 1675
3) Uranus by William Hershel in 1781
4) X-rays by Wilhelm Conrad Rontgen in 1895
5) Electron by J. J. Thomson 1897
6) DNA by Crick and Watson in 1953
(Hellemans and Bunch, 1988).
Each instance above constitutes a positive discovery, where it was found that an entity does exist. It was subsequently added to our collective scientific ontology. Here again this is an epistemological change not an ontological one. Nothing has been added to the world.
Eliminative and Multiplicative Materialism in Ontology and Epistemology
While Paul Churchland sees Eliminative (and Multiplicative) Materialism as thesis (es) in the Philosophy of Mind the evidence in its (their) support suggests that it (they) reach beyond the scope of that field and extend more generally into the relationship between epistemology and ontology.
In both cases, (Eliminative and Multiplicative Materialism’s) nothing has been created or destroyed (in keeping with the explanation for Occam’s sword that the conservation laws represent). There is in this sense a zero sum ontological net loss/gain in the above instances of discovery (both negative and positive). This gives the erroneous impression that ontology is static and merely to be cataloged. Part 2 will be concerned to provide evidence of ontological net gain (positive) and loss (negative) when the qualitative laws of matter and energy are applied to Eliminative and Multiplicative Materialism. This will give rise to a dynamic ontology and as in Part 1 a dynamic epistemology as well.
When the two senses of Eliminative and Multiplicative Materialism are subsumed by the two variants of Occam’s sword, then the relationship between ontology and epistemology will become clearer because at that point the quantitative and qualitative laws will be identified as the explanatory basis for the epistemological principles of Occam’s sword. This will result in the complimentary relationship that holds between epistemology and metaphysics.
The Subsumption of Eliminative and Multiplicative Materialism (in the first sense)
It is possible to bring Eliminative and Multiplicative Materialism under two principles:
1) Unnecessary entities are to be eliminated.
2) Necessary entities are to be multiplied.
The term ‘necessity’ will be understood to mean not ‘explanatory necessity’ in a theory, but rather as evidential necessity by discovery. Thus entities are to be necessarily eliminated for which there is no empirical evidence and entities are to be necessarily multiplied for which there is empirical evidence.
It will be noted that the formulation of these two principles is based on the rhetorical distinction between exhortation and dehortation. Therefore, the above principles are the exhortive version of the dehortative principles that:
1) Entities are not to be multiplied beyond necessity.
2) Entities are not to be eliminated beyond necessity.
These latter are readily identifiable as the first two principles of Occam’s sword. Thus, Occam’s sword (as a set of epistemological principles) subsumes Eliminative and Multiplicative Materialism (in the first sense).
These principles could be restated as:
1) Entities are not to be multiplied for which there is no empirical evidence.
2) Entities are not to be eliminated for which there is empirical evidence.
1) Entities are to be multiplied as they are discovered.
2) Entities are to be eliminated as they are not discovered.
Eliminative and Multiplicative Materialism (in the second sense)
As stated above and as thus far conceived both Eliminative and Multiplicative Materialism conform to the conservation laws of matter and energy (in the quantitative sense). We will now consider cases where entities are created and destroyed.
Ontology is not static. Consider the following list of entities:
1) Dell Inspirion 1570 (computer)
2) Apple iOS (smart phone)
3) Nissan Leaf (electric car)
4) Sousa chinensis (Indo-Pacific dolphin)
5) Taodium distichum (bald cypress)
6) Panthera Parduc (panther)
These are all entities that exist now but did not at one time or another exist in the past.
Now consider this list:
1) Tyrannosaurus Rex (dinosaur)
2) Pteranodon Stenbergi (pterodactyl)
3) Utasusaurus hataii (Ichthyosaur)
4) Aelipile by Heron of Alexandria approximately A.D. 100 (steam power)
5) Su Sung’s “Cosmic Engine” built at Khaifeng in A.D. 1090 (water clock)
6) Antikythera computer 1st century B.C.
(James and Thorpe, 1994)
These are all examples of entities that existed in the past but do not now exist.
In each instance above there is/was a net gain/loss in our ontology as matter and energy is transformed from one form into another.
There are laws that explain this ontological dynamism. They are the Qualitative Laws of Matter and Energy (see the qualitative and quantitative distinction in Nolan, 1997).
1) Matter and energy can be qualitatively created.
2) Matter and energy can be qualitatively destroyed.
Here the term ‘qualitative’ refers to the kinds and forms that matter and energy assumes as a function of its transformations.
In this sense, while it is empirically verifiable that matter and energy cannot be created or destroyed quantitatively it is equally empirically verifiable that matter and energy can be created and destroyed qualitatively.
This gives rise to Eliminative and Multiplicative Materialism in the second sense in which entities are eliminated from the ontology of science as they are destroyed and multiplied as they are created.
The Subsumption of Eliminative and Multiplicative Materialism (in the second sense)
As with the first sense of Eliminative and Multiplicative Materialism there are principles that subsume the second sense as well. The exhortative version is:
1) Entities are to be multiplied as they are created.
2) Entities are to be eliminated as they are destroyed.
Or in the dehortative version:
1) Entities are not to be eliminated that have not been destroyed.
2) Entities are not to be multiplied that have not been created.
There is much that is novel in this article and it may take some time to get used to it. Among the original ideas expressed here are:
1) Multiplicative Materialism and its complimentary role with Eliminative Materialism
2) Occam’s sword and its introduction into the discussion on Eliminative and Multiplicative Materialism
3) The subsumptive role Occam’s sword plays in in regard to Eliminative and Multiplicative Materialism
4) The Qualitative and Quantittative distinction and its application to;
a) Occam’s sword
b) Eliminative and Multiplicative Materialism.
In addition, all of the subsumtive principles (i.e. Occam’s sword) stated above for both senses of Eliminative and Multiplicative Materialism are epistemological principles, while the laws of matter and energy both quantitative and qualitative serve as their explanatory basis and are thus their ontological counterparts.
This has the effect of integrating epistemology and metaphysics such that the first principles of each are interdependent in a complementary relationship.
It should also be stated that the second set of entities that have been discovered i.e. the moons of Jupiter etc. could have just as easily been incorporated into the latter list of entities that have been created through the processes of the transformation of matter and energy. The distinction is merely meant to be illustrative.
1) Carpenter, Albert; P. (2012); Occam’s sword URL=http://occamsword.wordpress.com
2) Churchland, Paul (February 1981); Eliminative Materialism and the Propositional Attitudes, Journal of Philosophy 78, no. (pp. 67-90).
3) Churchland, Patricia and Paul Churchland (1998); Intertheoretic Reduction: A Neuroscientist’s Field Guide in On the Contrary: Critical Essays 1987-1997, The MIT Press, Cambridge.
4) Clark, Andy (1997); Being There: putting brain, body and world together again, The MIT Press, Cambridge.
4) Hellemans, Alexander and Bryan Bunch (1988); The Time Tables of Science, Simon and Schuster, New York.
5) James, Peter and Nick Thorpe (1994); Ancient Inventions, Ballentine Books. New York.
6) Johnson, Mark and George Lakoff (1999); Philosophy in the Flesh, Basic Books, New York.
7) Nolan, Daniel (1997); Quantitative Parsimony, British Journal for the Philosophy of Science 48 (3): (pp.329-343).
8) Reddy, Michael, J. (1979); The Conduit Metaphor in Metaphor and Thought, ed. Andrew Ortony. Cambridge University Press. Cambridge.
9) Wilson, Robert A.and Lucia Foglia; Embodied Cognition, The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.). URL=
The Laws of Matter and Energy in Ontology
Physicalism/Materialism is the dominant metaphysic in the 21st century and as philosophers and scientists progress further into it, the quantitaive and qualitative laws of matter and energy will assume an ever expanding and significant role as their implications for Science, Philosophy and Religion are more fully articulated. In fact, it is predicted that what the Churchland’s did in the Philosophy of Mind, introduce empirical evidence from Neurobiology to answer traditional problems in Philosophy, the laws of matter and energy will also do for Metaphysics by introducing empirical evidence from physics to answer traditional problems in Philosophy. This is to be welcomed because Metaphysics should be informed by and share with Physics the same first principles in anticipation of a physicalist philosophy of the future.
This has the effect of inserting the most empirically tested and verified laws of nature into the core of ontology. Thus, the laws of matter and energy are the laws of ontology. These are the laws that govern existence. They say nothing of the kinds of entities that exist, but only the rules by which that which does exist must conform.
The Status of Ontological Arguments:
The discussion of the application of the laws of matter and energy to Ontology, naturally, lends itself to the status of ontological arguments. There is no causal relationship between such arguments and existence. Their status is strictly rhetorical which is to say they have only the capacity to inform, exhort or dehort. Therefore, it is not possible to instantiate by virtue of argument alone such entities as god. Such arguments may or may not influence “belief”, but have no causal efficacy. However, there are cases wherein it is possible to influence ontology rhetorically. In instances of artifacts, arguments for their existence may lead to an expansion of our ontology. Case in point, Nichola Tesla argued for the possible existence of a previously thought to be impossible entity known to us today as the A/C motor. It was subsequently built based on his theory and design, but only after considerable expenditure (the transformation of matter and energy) of effort.
Occam’s sword in Epistemology
As we have seen in the section of this article on the Subsumption of Eliminative and Multiplicative Materialism, Occam’s sword, in both it’s variants, serves as epistemological laws. They place profound constraints and define freedoms on and for knowledge in the sense of what is and is not possible.
Occam’s sword in Logic
Reification: the thingification of abstract entities as if they were concrete ones. For example, justice is often treated as though it were a concrete entity on par with people. Thus, one finds such phrases as “blind justice” suggesting as it does that justice has human qualitites or characteristics. This is fallacious because, while matter and energy can be transformed from one form into another there is no energy pathway by which it is physically possible to transform abstract entities into concrete ones.
Occam’s sword in Aesthetics
The Pathetic Fallacy:
The attribution of human emotions to inanimate objects or phenomena. For example, the angry wind swept down and blew away the mir. There is no neurology to wind that would support affect. Therefore, it would require the instantiation of such a nervous system in the wind in order for such a possibility to exist. There is no energy pathway by which this is physically possible.
Occam’s sword in the Philosophy of Science/Metascience
Occam’s sword as Methodological Principles in Theory Construction:
As currently conceived Occam’s razor has been seen as a methodological (epistemological)principle by which to adjudicate between competing scientific theories, the ontologically simpler being deemed preferable for reasons that philosopher and scientist have struggled to find (see Sober et. al.). Since Occam’s sword subsumes Occam’s razor that tradition is reinforced and explained as we have seen in the section on Eliminative and Multiplicative Materialism which are applicable here.
The reason then that theorists employ Occam’s razor and now Occam’s sword is that we have no capacity to instantiate hypothetical entities such as the phlogiston, aether or caloric fluid in the first place. Neither can theorists uninstantiate entities such as the four moons of Jupiter, atoms or DNA simply because it is physically impossible to do so (as discussed in the conclusion).
Also, in theory construction, theorists can take advantage of the second variant of Occam’s sword because as we have seen novel entities can be created and destroyed including new life forms, Quark-Gluon Plasmas and Bose-Einstein condensates which expand both theory and ontology.
This has the effect of curbing reductive trends in science (especially with regards to theory construction) and provides a more holistic vision of the scientific enterprise because it allows for the discovery of entities both in a negative and positive sense while at the same time provides laws of nature that explain ontological dynamism.
Occam’s sword in the Philosophy of Biology/Metabiology
As one of the the antecedents of Occam’s sword, Occam’s razor has been employed, especially by the philosopher of science Elliott Sober, in the inferential reasoning when reconstructing paleontological lineages wherein simpler lines of descent are preferable to more complex ones (Sober, 1989).
The application of Occam’s sword in this context has little if any bearing on simplicity or complexity in the reconstruction of the past. Rather, the central theme of Occam’s sword here is the accurate reconstruction of the past based on the available evidence, such that where there is no or insufficient evidence, let silence be the defining and guiding virtue.
With that said, evolution can be a chaotic affair and is prone to be as simple or complex as the forces that drive it. Also, given the enormity of the evidential gaps involved in paleontological reconstructions, it is advised that the utmost caution be exercised.Perhaps then, it is advisable to err on the side of caution as Sober would have it.
A note in passing, evolutionary network theory will, if it has not already, supersede phylogenetic trees and cladograms.
Occam’s sword in the Philosophy of Chemistry/Metachemistry
Occam’s sword in the Philosophy of Physics/Metaphysics
Another application of Occam’s sword is to be found in the Philosophy of Physics and the ontological status of 4 dimensional space-time (4D S-T) and it’s elimination.
Ontological arguments that rely on logic and reason alone without physical evidence are specious and to be avoided. What then is the physical evidence for the existence of 4 dimensional space-time? The position that will be pursued here is that there isn’t any and therefore the focus of this section will be on the elimination of 4 D S-T from the ontology of science.
How to Eliminate 4 D S-T from the Ontology of Physics:
4D S-T is currently used throughout physics specifically and science more generally.One example can be found in how we gauge the speed of material bodies. For the sake of simplicity take, for instance the following scenario; a baseball is thrown from one person to another. It’s speed is determined to be 95 miles per hour. In this example, the motion of the ball is compared to a 4D S-T reference frame and defined in those terms. Unfortunately, this characterization is flawed because it is asymmetric and inconsistent.
In order to rectify this problem, it is necessary to reconceptualize our notion of time and the motion of the baseball. To do this it is important to recognize that one frame of reference is being compared to another. Once reconceived, then, the clock, as used to measure time , is to be understood as a system in motion. Thus, one 4D S-T system (the clock) is being compared to another spatio-temporal system that of the moving ball, both to be defined in terms of a 4D S-T.
The question then is how fast is the ball moving relative to the speed of the clock (time)? Such a comparison results in a cancelling of the dimensions of both systems and a dimensionless figure is left. Exactly what one would expect in a dimensionless universe. This approach is symmetric in that both inertial systems are defined in the same spatio-temporal terms. Furthermore, both systems are defined consistently.
Dimensional homogeneity (or the requirement that withing any mathematical model all entities and or processes be defined in the same dimensions and by extension the same temporal terms) is the basis for this reinterpretation as found int the Principles of Mathematical Modeling and applies to all spatio-temporal systems (Dym, 2004).
There is, however, one inconsistency remaining. In order to avoid confusion and the possibility of paradox, when comparing two spatio-temporal systems, it is necessary to compare rectilinear systems with other rectilinear systems of the same slope and curvilinear systems with other curvilinear systems of the same arc etc.
Occam’s sword in the Philosophy of Religion/Metareligion
1) The first variant of Occam’s sword and the ontological status of God and Satan
Perhaps it is best to say that in as far as Occam’s sword is to be applied to the ontic status god and satan; let the empirical evidence speak for itself.
2) The second variant of Occam’s sword and the ontological status of God and Satan
It could be argued that in as far as Occam’s sword in the second sense goes satan and god exist as Sociontological constructs. As such they are as real as we think they are.
The Reduction of Occam’s sword to the Laws of Matter and Energy
The idea of reducing both variants of Occam’s sword to the respective quantitative and qualitative laws of matter an energy comes from a passage in Paul Churchland’s book Scientific Realism and the Plasticity of Mind (1979). “…in the case of an ideal reduction there should be not impediment to the claim that the item/properties paired in the correspondence rules are contingently identical to one another, in the fashion of light =electromagnetic waves at the .5u range…” “…temperature =mean molecular KE and so forth. The advantages of such a claim are straight forward . We thereby pair the ontology (terms) in the manner simplicity requires, and we salvage the legitimacy of a familiar idiom at the same time. For these reasons the identification option will probably be taken when ever it can be…” (Churchland, p.82).
We have only then to equate the terms of each variant of Occam’s sword with those of the quantitative and qualitative laws of matter and energy as follows:
* entities = matter and energy
*are not to be = cannot be
*multiplied = created (quantitatively)
or *eliminated = destroyed (quantitatively)
*beyond necessity =
properties of entities = properties of matter and energy
*are not to be = cannot be
*multiplied = created (quantitatively)
or eliminated = destroyed quantitatively)
beyond necessity =
The same applies for the qualitative laws of matter and energy.
In both, the phrase “beyond necessity” finds no corresponding phrase on the reducing side and is therefore eliminable. On the other hand, the principles pertaining to the properties of entities find no corresponding terms n the reducing side, we are thus free to invent them. They become two new laws of nature: The Conservation of Properties:
*Properties of matter and energy cannot be created in the quantitative sense.
*Properties of matter and energy cannot be destroyed in a quantitative sense.
*Properties of matter and energy can be created in a qualitative sense.
*Properties of matter and energy can be destroyed in a qualitative sense.
As was discussed in the section of Eliminative and Multiplicative Materialism, epistemology reduces to metaphysics in a thorough going physicalistic paradigm. This is in full evidence with the reduction of Occam’s sword to the laws of matter and energy. However, as Paul Churchland makes clear with reduction “we salvage the legitimacy of the familiar idiom ( in this case Occam’s sword in so far as they are epistemological principles) at the same time”
In the literature on and about Occam’s razor there is nothing like Occam’s sword to be found. Its novelty is derived from four things:
1) It’s incorporation of Occam’s razor and Chatton’s anti-razor and two associated principles related to the properties of entities.
2) The linking of Occam’s sword with the laws of matter and energy, both quantitative and qualitative, as its explanatory basis.
3) Occam’s sword subsumes Occam’s razor and Chatton’s anti-razor in the sense that it brings them within a set of principles.
4) Its applications, especially to Eliminative and Multiplicative Materialism.
5) The introduction of the Qualitative Laws of Matter and Energy is also novel.
One of the implication of Occam’s sword not discussed in the above article is that the quantitative laws are the laws of what is not possible while the qualitative laws of matter and energy are the laws of what is possible. Further, let it be said that as the quantitative and qualitative laws apply to us as well for in the first instance, there is no energy pathway by which it is physically possible (i.e. it would constitute a violation of the conservation laws) in virtue of (a) speech, cognitive or orthographic act (s) alone to instantiate or uninstantiate such entities as those denoted by such terms as ‘panther’ ‘brown dwarf star’ or ‘Bose-Einstein condensate’ without any further corporeal or technologically mediated action.
On the other hand, entities can and are created and destroyed qualitatively as matter and energy is transformed from one form into another. Not only can we interactively create and destroy entities as in trains, planes and automobiles evidence from Biology suggests that biological entities can create and destroy themselves. Thus ,there are energy pathways by which we can corporeally and technologically create and destroy entities both by our own interactions and also those activities of biological entities themselves as they are conceived, birthed, grow and develop and expire with the possibility of evolving at the same time.
Multiplicative Materialism has the effect of counterbalancing the tendency towards ‘greedy’ reductionism, providing in combination with Eliminative Materialism a holistic view of our planet and cosmos at all spatial and temporal scales past, present and future.
On a final note, let it be known that Occam’s sword is the sword in the stone. It is the instrument by which the message of the Grail is to be delivered: the King and the land are one; the organism and the environment are one. The same laws of matter and energy that apply to the environment apply equally to us in word, thought and deed.
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