What’s the difference between natural law and a law of nature?

Natural law is a legal philosophy that deals with questions of how human beings ought to behave and how they should treat each other. In contrast, scientists use laws of nature describe how living and nonliving things in the universe actually do behave. In other words, the difference is between the legal and ethical concept of should do as opposed to a scientific concept of does. This difference is really a difference in the mood of the verb to do.

The mood of a verb means the attitude that the speaker or writer has about the action described in the sentence. There are five basic moods in English.

Indicative Expresses facts and truth.
Interrogative Asks questions.
Imperative Gives commands or makes requests.
Conditional Expresses what could or would happen if some condition is met.
Subjunctive Express some idea that is contrary to fact (if I were king of the forest…).

Verbs can express actions or states of being. The tense of a verb expresses whether the action or state of being is in the past, present, or future (was, is, or will be). The aspect of a verb expresses other features of the timing, such as whether the action or state of being is completed or ongoing, and whether it is repeated. In English, we generally use the present tense and the indicative mood to express actions and relationships that are usually or always true in the present, as well as to express actions and relationships that are usually or always true for all time. Mathematicians and scientists sometimes use mathematical symbols to express these ideas. In mathematics, the equals sign (=) expresses a state of being. The equals sign means the same thing as is or are, which are indicative forms of the verb to be.

What is a mathematical theorem?

A mathematical theorem is a sentence that expresses a fundamental relationship between purely abstract concepts. Since these sentences deal with concepts that have no physical reality, their truth can be proven mathematically.

  • The infinity of primes: There is an infinite number of prime numbers.
  • The Pythagorean theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
pythagorean theorem photo
A geometrical proof of the Pythagorean theorem. Photo by tobo

The truth of those theorems has been proven mathematically. You do not have to rely on observation to prove that they are true. In other words, you do not have to measure triangles or count prime numbers to test the truth of those statements.

What is a law of nature?

Unlike a mathematical theorem, a law of nature is a sentence that expresses a fundamental relationship between things that do have some sort of physical reality. Even though a law of nature may be expressed mathematically (e.g., E=mc2), you cannot prove it mathematically. All you can do is try to disprove it by finding cases in which it does not hold. Thus, when scientists talk about laws of nature, they mean the important fundamental rules that every physical entity in the universe always seems to follow. Here are some examples:

  • The First Law of Thermodynamics (law of nature): the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed
  • The Second Law of Biology: The cell is the fundamental unit of life.

Nobody has ever found a way to create or destroy energy. Einstein figured out that you can convert energy into matter and matter into energy, in the ratio expressed by E=mc2, where E is the amount of energy, m is the amount of mass, and c is the speed of light. However, the total amount of mass-energy in a closed system is constant. Nobody has ever found a situation in which the First Law of Thermodynamics does not hold. Of course, this raises the baffling question of how the universe began. If mass-energy cannot be created, how did it come to be? Perhaps the First Law of Thermodynamics applies only when the observable universe is in its current state. (Scientists in the field of cosmology are trying to answer that question.)

The Second Law of Biology also deals with objects with physical reality. As a result, you cannot prove it mathematically. You could disprove it by finding some living thing that does not consist of one or more cells. But so far, nobody has. (Viruses are not cells, but they are not considered to be living things because they do not have a metabolism.)

What is natural law?

Natural law is an ethical and legal concept, not a scientific concept. Natural law deals with the ethical questions of what ought to be done, not the scientific question of what happens. Grammatically, expressions of natural law are phrased as commands, which means that the verb is in the imperative mood. In English, we have several ways of expressing commands and requests. We can use the stem of the verb, or we can use a modal auxiliary (such as shall, should, ought, or must). When we phrase a negative command, we need to use do as an auxiliary, along with the adverb not. We can also phrase the command or request as a question, to be polite.

  • Clean your room!
  • Do not close the window.
  • Thou shalt not kill.
  • Could I have a glass of water?

In most commands in English, the subject (you) is implied but not directly stated. Also, the identity of the person who is issuing the command is usually implied. If the command is being given verbally and in person, there is no need to identify the commander. However, if the command has been written down or passed from one person to another, the identity of the person who issued the command may be unclear.

Several important philosophers have argued that ethical statements are mainly either expressions of emotion or attempts to influence other people’s behavior. These attempts to influence other people’s behavior are essentially commands or requests. Yet the commands and requests are often phrased in a way that obscures the identity of the commander. Instead of expressing that you want a person to do something, you may say that God wants them to do it. If you put the fear of God into them, they may do as you ask. Yet the Third Commandment (do not take the Lord’s name in vain) warns you not to do this lightly.

Many commandments have an “or else” clause. In some cases, the “or else” clause is a warning of the natural consequences that will result if you fail to take good advice. In other cases, the “or else” clause is a threat of what will be done to you if you disobey. Powerful people have always told other people what they should and should not do. These commands have always been backed up with a threat. In medieval times, the king was believed to rule by divine right. Thus, he had the God-given authority to make commands and to punish those who fail to follow them. In contrast, modern societies have laws that were passed by a legislature. Either way, a government’s laws are not mere suggestions. The government has the power to punish people who refuse to obey.

police photo
Photo by G20Voice

The concept of natural law as a universal system grew out of imperialism. When kingdoms conquered other kingdoms, the conquerors realized that some kinds of laws varied from place to place, often for good, practical reasons. Nevertheless, they started to look for some higher type of law that could be applied everywhere. Monotheists felt that this type of law would come from divine commandment. In contrast, some pagan philosophers, such as Cicero, felt that this type of law would be shaped by the nature of the universe and the nature of humankind. The Founding Fathers of the United States were more impressed by pagan political philosophers than by the Bible, which is why the Declaration of Independence mentions “Nature’s God” but does not mention Christianity or the Bible. The Constitution does not make any mention of any God, or of the Bible or Christianity. Instead, the First Amendment forbids Congress from establishing a religion for the nation.

universal declaration of human rights photo
John Trumbull’s painting of the signing of the Declaration of Independence. Photo by conservativemajority
Former US First Lady Eleanor Roosevelt chaired the committee that drafted The Universal Declaration of Human Rights, a statement about the kinds of laws that should be passed everywhere.
Former US First Lady Eleanor Roosevelt chaired the committee that drafted The Universal Declaration of Human Rights, a statement about the kinds of laws that should be passed everywhere.

After World War II, the United Nations passed a Universal Declaration of Human Rights, which described the kinds of laws that needed to be passed everywhere, in order to promote freedom, justice, and peace in the world.  This document expresses a Ciceronian type of natural law:  basic principles of human rights that have been proved through long and painful experience to be  essential underpinnings of a just society. It was ratified by countries with a wide range of religious backgrounds.

 

Hume’s Guillotine

david hume photo
Photo by Stifts- och landsbiblioteket i Skara

The Scottish philosopher David Hume taught us an important lesson that has come to be known as Hume’s Guillotine: you cannot derive moral principles (ought-statements) purely from statements about facts about the world (is-statements).  You always have to take some sort of feeling into consideration. For example, you cannot decide whether you would rather be paid $1 per hour or $100 per hour for the same work, unless you feel that getting more money would be better.

To make wise decisions, you must know the relevant facts about the world. You must also be good at figuring out the if-then statements that apply in your situation. This knowledge and skill will enable you to figure out what your options are. Yet to choose from among those options,  you must also rely on your feelings of what would be best.

Photo by www.brevestoriadelcinema.org

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