iSoul In the beginning is reality

Category Archives: Science

Science particularly as related to creation and the creation-evolution controversy

Logic as arithmetic

George Boole wrote on “the laws of thought,” now known as Boolean Algebra, and started the discipline known as Symbolic Logic. A different George, George Spencer Brown, wrote on “the laws of form,” which presented an arithmetic system underlying logic. Below are two symbolic logics equivalent to Boolean algebra that resemble ordinary arithmetic in some respects. To resemble arithmetic in other respects, use the Galois field of order 2, GF(2). Zero is taken as representing false, and one as true.

LOGIC OF SUBTRACTION

Subtraction

A – 0 = 1 – A = 1

A – 1 = A

Definitions

– A is defined as 0 – A (and so 0 is ”  “, ground, false)

A + B is defined as  A – (– B)

Tables

A 0 − A A − B 0 1 A + B 0 1
0 1 0 1 0 0 0 1
1 0 1 1 1 1 1 1

Consequences

– (– A) = A

A − B = A ← B

A + B = A ∨ B

A + B = B + A

– is not distributive

 

DIVISION LOGIC

0 / A = A / 1 = 0

A / 0 = A

Definitions

/ A is defined as 1 / A (and so 1 is ”  “, ground, true)

A • B is defined as  A / (1 / B)

Consequences

1 / (1 / A) = A

A / B = – (A → B)

A • B = A ∧ B

A • B = B • A

/ is not distributive

Tables

A 1 / A A / B 0 1 A • B 0 1
0 1 0 0 0 0 0 0
1 0 1 1 0 1 0 1

 

Physics and theology

The 19th century physicist Ernst Mach is known for his view that all motion is relative, which influenced Albert Einstein. Mach is also known for his book The Science of Mechanics (1883 in German, 1893 in translation), from which the following excerpts about physics and theology are taken (Open Court edition, 1960):

Consolation, [Pascal] used to say, he could find nowhere but in the teachings of Christianity; and all the wisdom of the world availed him not a whit. p.543

Every unbiased mind must admit that the age in which the chief development of the science of mechanics took place, was an age of predominantly theological cast. Theological questions were excited by everything, and modified everything. No wonder, then, that mechanics is colored thereby. p.546

In Leibniz’s correspondence with John Bernoulli, theological questions are repeatedly discussed in the very midst of mathematical disquisitions. Their language is not unfrequently couched in biblical pictures. p.549

Maupertuis, the famous president of the Berlin Academy, and a friend of Frederick the Great, gave a new impulse to the theologizing bent of physics by the enunciation of his principle of least action. In the treatise which formulated this obscure principle … the author declared his principle to be the one which best accorded with the wisdom of the Creator. p.549

Euler magnanimously left the principle [of least action] its name, Maupertuis the glory of the invention, and converted it into something new and really serviceable. … The theological point of view, Euler retained. He claims it is possible to explain phenomena, not only from their physical causes, but also from their purposes. “As the construction of the universe is the most perfect possible, being the handiwork of an all-wise Maker, nothing can be met with in the world in which some maximal or minimal property is not displayed. There is, consequently, no doubt that that all the effects of the world can be derived by the method of maxima and minima from their final causes as well as from their efficient ones.” p.550

Similarly, the notions of the constancy of the quantity of matter, of the constancy of the quantity of motion, of the indestructibility of work or energy, conceptions which completely dominate modern physics, all arose under the influence of theological ideas. The notions in question had their origin in an utterance of Descartes, before mentioned, in the Principles of Philosophy, agreeably to which the quantity of matter and motion originally created in the world–such being the only course compatible with the constancy of the Creator–is always preserved unchanged. The conception of the manner in which this quantity of motion should be calculated was very considerably modified in the progress of the idea from Descartes to Leibniz, and to their successors, and as the outcome of these modifications the doctrine gradually and slowly arose which is now called the “law of the conservation of energy.” But the theological background of these ideas only slowly vanished. p.551

During the entire sixteenth and seventeenth centuries, down to the close of the eighteenth, the prevailing inclination of inquirers was, to find in all physical laws some particular disposition of the Creator. But a gradual transformation of these views must strike the attentive observer. Whereas with Descartes and Leibniz physics and theology were still greatly intermingled, in the subsequent period a distinct endeavor is noticeable, not indeed wholly to discard theology, yet to separate it from purely physical questions. Theological disquisitions were put at the beginning or relegated to the end of physical treatises. Theological speculations were restricted, as much as possible, to the question of creation, that, from this point onward, the way might be cleared for physics. p.551-552

Towards the close of the eighteenth century a remarkable change took place,–a change which was apparently an abrupt departure from the current trend of thought, but in reality was the logical outcome of the development indicated. After an attempt in a youthful work to found mechanics on Euler’s principle of least action, Lagrange, in a subsequent treatment of the subject, declared his intention of utterly disregarding theological and metaphysical speculations, as in their nature precarious and foreign to science. He erected a new mechanical system on entirely different foundations, and no one conversant with the subject will dispute its excellencies. All subsequent scientists of eminence accepted Lagrange’s view, and the present attitude of physics to theology was thus substantially determined. p.552 [Lagrange’s Mécanique analytique was published in 1788.]

Newton never, despite his profound religiosity, mingled theology with the questions of science. … The same may be said of Galileo and Huygens. p.552

It stands to reason that in a stage of civilization in which religion is almost the sole education, and the only theory of the world, people would naturally look at things from a theological point of view, and that they would believe that this view was possessed of competency in all fields of research. p.553 #

… the theological conception of nature itself owes its origin to an endeavor to obtain a more comprehensive view of the world;–the very same endeavor that is at the bottom of physical science.  p.556

In fact, science can accomplish nothing by the consideration of individual facts; from time to time it must cast its glance at the world as a whole. p.556

But now, after a century has elapsed, after our judgment has grown more sober, the world-conception of the encyclopaedists appears to us as a mechanical mythology in contrast to the animistic of the old religions. p.559

Physical science does not pretend to be a complete view of the world; it simply claims that it is working toward such a complete view in the future. The highest philosophy of the scientific investigator is precisely this toleration of an incomplete conception of the world and the preference for it rather than an apparently perfect, but inadequate conception. p.559

# One might update this sentence as follows: It stands to reason that in a stage of civilization in which science is almost the sole education, and the only theory of the world, people would naturally look at things from a scientific point of view, and that they would believe that this view was possessed of competency in all fields of research.

Design illustrated

This post continues thoughts about design, last posted here.

Here is a description of how cement is made from the Portland Cement Association:

In its simplest form, concrete is a mixture of paste and aggregates, or rocks. The paste, composed of portland cement and water, coats the surface of the fine (small) and coarse (larger) aggregates. Through a chemical reaction called hydration, the paste hardens and gains strength to form the rock-like mass known as concrete.

The key to achieving a strong, durable concrete rests in the careful proportioning and mixing of the ingredients. A mixture that does not have enough paste to fill all the voids between the aggregates will be difficult to place and will produce rough surfaces and porous concrete. A mixture with an excess of cement paste will be easy to place and will produce a smooth surface; however, the resulting concrete is not cost-effective and can more easily crack.

The design in this case is the proportion of ingredients in the mixture. It might happen that the ingredients formed naturally but they would be in the correct proportion only by design. That is, the particular application entails a goal, which the design meets.

Certainly concrete can and does happen naturally in aggregate rock formations. But it does not meet a need without a design. And that doesn’t happen naturally. Roads built with concrete only happen because engineers and construction crews built them. There’s nothing natural about that.

Design and entropy

A carrier is the baseline transmission (such as a wave) that is modulated for a signal. Carriers have minimum entropy. Their opposite, noise, has maximum entropy. A signal conveys a message between a sender and a receiver. The entropy of signals is between that of the carrier and noise.

Carriers are the canvas for the artist. The canvas starts out blank. Then paint is added, which is the signal for the viewer. Noise would be like splotches of paint that somehow got put on the canvas. If the canvas were all noise, the signal would be completely covered with random bits of paint. The signal is designed to be between these extremes.

The closer a signal is to looking like the carrier, the lower the entropy and the simpler the message. The closer a signal is to looking like noise, the higher the entropy and the less the complexity of a message that can be transmitted. With the carrier alone or noise alone there is no message.

Design works the same way. A carrier alone or noise alone exhibit no design. A simple design would be similar to a carrier or to noise. A more complex design would be between the extremes of all carrier and all noise.

Entropy is a way to determine the presence of design. The more that entropy is in-between zero and the maximum, the more likely it is a result of design. A simple measure of design may be constructed from entropy as follows:

Define a design index, Ξ (xi) from the entropy, H, as

Ξ := (HHmin) / (HmaxHmin),

which ranges from zero if H = Hmin to one if H = Hmax. If the design index is one-half, then H is the mid entropy. The closer the value of Ξ is to one-half, the more likely the distribution is the result of design.

2015, updated

Knowledge and repetition

Consider the distinction between repeatable events from unrepeatable events. Repeatable events includes events that have repeated or may be repeated at will (as in a laboratory) or may possibly repeat in the future. Unrepeatable events are events that are very unlikely to repeat or are impossible to repeat. It is said that science only studies repeatable events, and it can be argued that history is the study (science) of unrepeatable events – not that it excludes repeatable events but that it focuses on unrepeatable events.

“Nature” could be defined as the realm of repeatable events. Then natural science would be the study of nature or repeatable events. Those events that are unrepeatable would be left to historians but ignored by natural scientists. But could such scientists rightly study the past while ignoring unrepeatable events? Ignorance of unrepeatable events would be a limitation and a defect. We would not expect historians to ignore repeatable events, so why expect scientists to ignore unrepeatable events?

We may well expect events that only involve inanimate nature are repeatable in some way. But are all events with living beings repeatable? The position of naturalism says, Yes. But at some point we need to say, No, at least some living beings have free will (or whatever you want to call it) so that their actions may be unrepeatable, and thus beyond the purview of a science of repeatable events.

Knowledge of repeatable and unrepeatable events may need different methodologies to address both kinds of events but it could not ignore either kind without bias. We need both the study of history, with its unrepeatable events, and the study of science, and its repeatable events, as independent disciplines. The synthesis of science and history would require a different discipline, perhaps called “scihistory” or “histence”, that would balance the input of each discipline with the other.

Science in the center

There are many different musical temperaments that have been used to tune musical instruments over the centuries. They all have their advantages and disadvantages. But there is one musical temperament that is optimally acceptable: the equal temperament method in which the frequency interval between every pair of adjacent notes has the same ratio. This produces a temperament that is a compromise between what is possible and what is agreeable to hear.

Science faces many situations such as the challenge of musical temperament. Conventions and methods need to be adopted and there are multiple options, each with their advantages and disadvantages. There are those who promote one method and those who promote another method, often the opposite method. Should science pick one and force everyone to conform? Or should science find a compromise of some sort?

There is a way in the middle that is a compromise between extremes and alternatives. It is a conscious attempt to avoid extremes and biases, and seek a solution that is the most acceptable to all. This is science in the center, a science that minimizes bias. Although it might be called “objective,” that obscures the fact that it is a conscious choice.

I previously wrote about the need for a convention on the one-way speed of light. Science of the center would avoid the bias toward one direction of light and choose a one-way speed that is in the middle between all the possible speed conventions. This is the Einstein convention, which is part of his synchronization method.

Science in the center includes not biasing classifications either toward “lumping” or “splitting.” Nor should explanations of behavior be biased toward “nature” or “nurture.” The particulars of each case should determine the outcome, not a preference for one side or the other. If there’s any default answer, it’s in the center between such extremes.

Occam’s razor is understood to prescribe qualitative parsimony but allow quantitative excess. This is as biased as its opposite would be: to prescribe quantitative parsimony but allow qualitative excess. Science in the center would avoid the bias that each of these has by prescribing a compromise: there should be a balance between the qualitative and the quantitative. Neither should be made more parsimonious than the other. All explanatory resources should be treated alike; none should be more abundant or parsimonious than any other. I’ve called this the New Occam’s Razor, and it is an example of science in the center.

Reality and conventions #4

This post continues a series of posts. The previous one is here.

Modern natural science attempts a systematic account of the causes of change in the physical world, and is willing to go against the appearance of the physical world if that will further its goals. This differs from the ancient Platonic attempt to “save the appearances” at all costs by placing appearances within an ad-hoc but meaningful system.

In one sense, philosophy is the helpmeet of science. It aids in the task of putting our conceptual household in order: tidying up arguments, discarding unjustified claims. But in another sense, philosophy peeks over the shoulder of science to a world that science in principle cannot countenance. As Professor Scruton put it elsewhere, “The search for meaning and the search for explanation are two different enterprises.” Science offers us an explanation of the world; it may start out as an attempt to explain appearances, “but it rapidly begins to replace them.” Philosophy seen as the search for meaning must in the end endorse the world of appearance. The New Criterion, vol. 12, no. 10

Saving the appearances famously led to tweaking Ptolemaic astronomy despite its inability to explain why celestial bodies should move in epicycles. The Newtonian system didn’t give ultimate explanations but at least it gave laws that applied on Earth and skyward.

Yet there is nothing “wrong” with saving appearances such as the motion of the Sun relative to the Earth. In that sense, geocentrism was never wrong despite generations of people being taught so. Whether saving the appearances or saving the system is a goal, both must accept some conventions that include things such as the celestial body of reference – or lack thereof.

One may legitimately pursue a phenomenal science that saves appearances by sacrificing some consistency in conventions. For example, the Moon is in orbit relative to the Earth and the Sun is in a different kind of orbit relative to the Earth. In order to save both of these appearances, one would have to use a gravitational dynamics for the Earth-Moon system and a levitational dynamics for the Earth-Sun system. Awkward, perhaps, but legitimate.

Reality and conventions #2

This post continues the topic of the previous post here.

Every pair of contrary opposites may have one or more conventions associated with it. That is because there is a symmetry between the two that can be reversed. Note this is not the case with contradictory opposites: they are not symmetric. Note also that terms may be symmetric without the references of the terms being exactly symmetric.

I’ll start with the latter point. A common example is the terms for male and female. In some respects they are symmetric opposites but in other respects they are not. The language can mislead on this point. Males and females have some similarities, some contrary (or complementary) differences, as well as differences that are not contraries, just different. Some aspects of male-female relations are conventions but not every aspect is.

The deconstructionists associated binary opposites with power structures (not unlike Hegel). They would reverse the meaning in order to undermine them. That assumes pairs are complete contraries, which is not as common as they thought. Deconstructionism works mostly on texts, in which the language of contrary opposites is deconstructed. The conventions associated with contrary opposites can be reversed but not all binary opposites are genuine contraries.

Contradictory opposites such as good and evil or true and false are not symmetric, contrary to the language that is often used. Not-evil is not necessarily good and not-false is not necessarily true. What is a matter of goodness or truth are not mere conventions.

There is a reality independent of us (or of our minds) but some things are conventions that are dependent on us. Motion is real but all motion is relative so it is a convention as to what motion is relative to. Galileo and the Scholastic philosophers (and their supporters) were wrong to think of the Earth as either only at rest or only in motion. Whether or not the Earth moves is a convention.

Reality and conventions #1

This post relates to the previous post here, as well as posts on light conventions here and here.

There comes a point in science in which a convention needs to be adopted in order to avoid confusion and ensure consistency. The tendency, however, is to think that the convention adopted is real, that is, that reality uniquely matches the convention. But that is an illusion since a different convention can legitimately be adopted.

This happens more often that we might realize. I have not tried to catalog all the conventions of science but here are some:

  1. Units of measure. These are all conventions, and there are variations such as the inch-pound units.
  2. Statistical significance. A p-value of 0.05 is often used, but it is a convention, not statistics.
  3. Negative charge of the electron. The current and the flow of electrons are in opposite directions.
  4. “A rod is undergoing tension. Is this negative or positive? In steel and concrete studies, tension is positive. In soil studies, tension is negative.”

Some of these conventions are a matter of choosing a value as the standard, others involve selecting a positive and a negative type (direction, charge). The positive type would seem to be the main or default one, as with arithmetic, but this may not be the case.

The conventions on the one-way speed of light show that the question relates to the status of the observer. Is the observer always right? That leads to one convention, in which the incoming speed of light is instantaneous. Is there an average that is right? That leads to Einstein’s convention, in which light travels at the average of the two-way speed of light.

Scientifically the latter is more straightforward but the problem is that it entails that some observations need to be corrected. The former may be more awkward but it has the advantage that “the observer is always right.” This accords with a common-sense realism and empiricism.

Consider optical illusions. They are something that appears one way but under further investigation are another way, such as the horizontal lines in this cafe wall illusion that appear to be sloped:

cafe wall illusion

But what about refraction? When we see a stick in water, it appears to bend but when we put our hand in the water, there is no bend. Yet we do not call this an illusion. We call it refraction. That is, it is an optical phenomenon and the appearance of a bend is real.

So it is a matter of classification. Yet all classifications are a matter of convention. We cannot get away from convention. In that sense reality is ambiguous or (à la Heisenberg) uncertain.

Since Plato and Aristotle science has included an attempt to “save the phenomena”. Although they meant different things by this phrase, it does indicate the primacy of phenomena. After all, there is no science (except perhaps for mathematics) without appearances. If all appearances are illusory, then appearance is not something to be explained but to be explained away.

A common-sense realist takes appearance as reality, with the understanding that some reflection is needed to avoid mistakes.

The knowledge the realist is talking about is the lived and experienced unity of an intellect with an apprehended reality. This is why a realist philosophy has to do with the thing itself that is apprehended, and without which there would be no knowledge. (#5 in A Handbook for Beginning Realists by Étienne Gilson)

Properly apprehended, the world of appearances is the real world. The observer is always right.

Classical Model of Science

Another paper that should get wider exposure: “The Classical Model of Science: a millennia-old model of scientific rationality” by Willem R. de Jong and Arianna Betti. Synthese (2010) 174:185-203. Excerpts:

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science. p.185

The Classical Model of Science as an ideal of scientific explanation

In the following we will speak of a science according to the Classical Model of Science as a system S of propositions and concepts (or terms) which satisfies the following conditions:

(1) All propositions and all concepts (or terms) of S concern a specific set of objects or are about a certain domain of being(s).

(2a) There are in S a number of so-called fundamental concepts (or terms).

(2b) All other concepts (or terms) occurring in S are composed of (or are definable from) these fundamental concepts (or terms).

(3a) There are in S a number of so-called fundamental propositions.

(3b) All other propositions of S follow from or are grounded in (or are provable or demonstrable from) these fundamental propositions.

(4) All propositions of S are true.

(5) All propositions of S are universal and necessary in some sense or another.

(6) All propositions of S are known to be true. A non-fundamental proposition is known to be true through its proof in S.

(7) All concepts or terms of S are adequately known. A non-fundamental concept is adequately known through its composition (or definition). p.186

The Classical Model of Science is a recent reconstruction a posteriori of the way in which philosophers have traditionally thought about what a proper science and its methodology should be, and which is largely set up, as it were, by abduction. The cluster (1)-(7) is intended, thus, to sum up in a fairly precise way the ideal of scientific explanation philosophers must have had in mind for a very long time when thinking about science. p.186

A proper science according to this Model has the structure of a more or less strictly axiomatized system with a distinction between fundamental and non-fundamental elements. p.186

The history of the conceptualization Science knows three milestones: first of all, Aristotle’s Analytica posteriora, especially book 1; secondly, the very influential so-called Logic of Port-Royal (1662), especially part IV: ‘De la méthode’, written mainly by Antoine Arnaud and relying in many respects on Pascal and Descartes; and finally Bernard Bolzano’s Wissenschaftslehre (1837). p.187

The formulation coming closest to a systematization of the ideal of science we codify in the Model is perhaps the description of scientific method given in the Logic of Port-Royal, ‘The scientific method reduced to eight main rules’:

Eight rules of science

1. Two rules concerning definitions

1 . Leave no term even slightly obscure or equivocal without defining it.
2. In definitions use only terms that are perfectly known or have already been explained.

2. Two rules for axioms

3. In axioms require everything to be perfectly evident.
4. Accept as evident what needs only a little attention to be recognized as true.

3 . Two rules for demonstrations

5 . Prove all propositions that are even slightly obscure, using in their proofs only definitions that have preceded, axioms that have been granted, or propositions that have already been demonstrated.
6. Never exploit the equivocation in terms by failing to substitute mentally the definitions that restrict and explain them.

4. Two rules for method

7. Treat things as much as possible in their natural order, beginning with the most general and the simplest, and explaining everything belonging to the nature of the genus before proceeding to particular species.
8. Divide each genus as much as possible into all its species, each whole into all its parts, and each difficulty into all its cases. pp.187-188

… the Model is a fruitful analytical tool. Its influence lasted until recently; having persisted at least to Lesniewski, it in fact extended far beyond what one might expect at first glance. It is certain, however, that at a some point the Model was abandoned without being replaced by anything comparable. p. 196