• Contractarian ethics claims that all right and wrong comes from promises, both explicit and implicit, and our keeping those promises.  If you keep your promises, you’re a good person.  If you don’t, you’re not.  People who argue from this standpoint often claim there is an implicit contract inherent to everyone, such as “I won’t kill people.”  Thus, murder is wrong by universal implicit contract.
• Rights theory claims that every person has some inherent rights that extend until they conflict with the rights of another.  The exact list of rights varies from theorist to theorist, but usually includes the right to life, property, and choice of lifestyle.  Thus, it’s wrong to kill someone because it denies them their right to life.
• Consequentialist ethics claims that the effects of an action are the sole evidence of whether that action was right or wrong.  These ethical systems tend to include lists of what consequences are good and bad.  Thus, murder is wrong because it results in a person’s death and death is bad.
• Aretaic ethics claims that right and wrong are determined by the effect on the actor’s personal character or identity.  That which makes you a better, stronger, saner, more skillful person is good; that which makes you a worse, weaker, madder, clumsier person is bad.  Thus, murder is wrong because it makes you a murderer.
• Deontological ethics claims that everyone has a duty to act and not act in certain ways and to abandon that duty is wrong.  We have an inherent duty not to murder, so murder is inherently wrong.

All of these sources of right and wrong are really more of ways of thinking about right and wrong rather than actual conclusions.  The conclusions can be altered and manipulated based on the rights you have, duties you must adhere to, character traits that you must seek, or whatever such thing.  Also, any of them can include or exclude God or spirituality as the source for those rights or duties, determiner of consequences, party to your implicit contracts, etc.

• Mathematical Logic is the philosophical basis and reasoning that determines how arithmetic relates to reality or hypothetical concepts.  Mathematical logic includes proofs (postulates, correlaries, theorems), set theory, and several areas and theories that blur between mathematics itself and philosophy in a more general sense.  An understanding of mathematical logic turns all other mathematical knowledge into a problem solving tool and makes obvious math’s role in understanding relationships and connections in reality.  It’s the philosophy that proves math worthwhile.
• Arithmetic is the manipulation of numerical values and relationships between numbers.  It consists of numerical values (digits, number bases), addition (subtraction), multiplication (division), exponentiation (powers and roots),  integration (derivatives), and the symbolic language used to represent all these things (signs, algebraic variables, order of operations).  Arithmetic is concerned with definitive answers based on deductive logic but without any obvious implication or call to action.  Two plus two equals four, but there’s no indication of what to do about it.
• Measurement is the means by which arithmetic is made relevant to the real world.  It provides numbers to reflect the amount of some trait of reality, giving it a numerical value that can be manipulated arithmetically.  There are two types of measurement, counting (3 eggs) and quantifying (1.2 deciliters of egg whites), as well as an entire science concerned with the design of useful, accurate measuring devices.  No measuring device can ever be exactly perfect, so we are forced to choose some degree of “close enough” measurement.  Statistics is the field of measurement that tries to determine the nature of a whole by analyzing a smaller sample.  It, among measuring systems, is often singled out as “lying with numbers”.  Statistics are not inherently lies or untrustworthy, but are inductive measurements:  that is, a proper statistical study provides a trustworthy measurement of the sample and makes likely (but not definitive) conclusions about the whole from these samples.  A good statistical analysis will include a range of values the truth probably resides within, a “best guess” value somewhere within that range, and a “confidence interval” measurement of the probability that the true value lies between that range.  Without knowledge of the range and confidence interval, the “best guess” value quoted by itself is uninformative.  Reporting of statistical results in that manner is the lie, not mathematical statistics itself.
• Calculus is the mathematical field concerned with attributing a mathematical description to a hypothetical or real-world event.  Calculus derives relationships between measured occurrences in reality, allowing for a mathematical explanation of the event to be developed, usually in the form of a function.  The location and speed of a car can be measured, but the apparent location of the car at some point in time is calculated.
• Applied Mathematics is the use of mathematics to determine the answer to a real-world problem. Measurement describes specific points in reality, calculus determines relationships and fills in the story, but applied mathematics allows one to creatively manipulate those relationships to empower human action.  You can measure the size of a boulder you can’t move, calculate details of gravity and the force necessary to move the boulder, but it takes creative application of mathematics to design a device (a lever, perhaps, or a wench) that makes moving the boulder possible.  This is where mathematics becomes a creative expression, where you can pursue one of thousands of possible solutions and succeed or fail on your own innovative thinking.
• Numerology is the belief in spiritual connections between seeming coincidental occurrences of numbers.  The three flight numbers for the jets hijacked on Sept 11th, 2001 that successfully struck their targets  (in no particular order) are AA11, United 175, and AA77.  If you add the digits from these flights together (1+1=2, 1+7+5=13, 7+7=14) then add the digits from the answers together (2+1+3+1+4) you get 11, the same as the date of the attack.  The digits from the month and date (9+1+1) also add together to 11.  The number of letters in George W. Bush’s name is also 11.  Some people believe that a sufficient number of such arithmetic connections constitutes evidence of divine will or other spiritual connection between events.  Unlike arithmetic and applied mathematics, there is little mathematical logic defending this view.  For that reason, many (myself included) consider this to be arithmetic-based superstition that fails to demonstrate anything about the actual reality.

All of these views (except perhaps numerology) deserve to be explored in the classroom, with logic and especially application being absolutely essential.  It’s no wonder that mathematics bores so many students when it’s purpose for existence isn’t presented!  But, at least in my experience, mathematics only appeals to those who discover the logic and creative aspects of mathematics for themselves, outside of classroom influence.  It’s a deep, resounding shame.

“Hi, Psudo.”

To demonstrate what I mean, I’ll provide an example: I’ll classify terms for artificiality in beings, intended to be compatible with reality and useful in science fiction writing.

• A natural person is a being entirely formed by natural phenomenon (or perhaps divine intervention) with no intentional design by engineering by any other type of being from this list. The definition includes that of a biological makeup organized entirely without technological manipulation of composition and a maximum of self-determination. (The controversy over whether free will exists at all is not addressed here.) Artificial insemination or incubation do not alter the “natural” status as defined because they do not alter the composition of the being.
• A creature is anything created by design. It literally means “that which was created.” Originally coined to refer to naturally occurring beings on the premise of their having been created by God, it is less controversially used in a sci fi setting to refer to that which is created by mortals or automations. After all, while the existence of God and creation ex nihilo continues to be debated, the evidence is quite clear that natural people make (build) things. However, it does carry with it the connotation of at least the kind of living response that animals have, if not the full maximum of free will attributed to humans. (I do not mean to address whether animals have free will; I merely state here that animals are widely agreed to have equal or less free will, not more, than humans.)
• An automation is any tool that, after being initially put into operation, will continue to perform some task without outside intervention. A wind-up clock is an automation since it works until it runs out of energy without human interference, but a sun dial is not since it requires intervention from the sun. By definition, an automation has no self-determining will whatsoever. It operates with mechanical predictability if not mechanical form. One reason people often take offense when referred by the pronoun “it” is the connotation of mindless automation therein.
• A robot is an artificial automation designed to perform work. The word comes from Czech word for “slave” used as an ideal of the perfectly obedient and perfectly effective slave-worker. This hard perfection is not possible with natural, flexible life, thus explaining the artificial and abiotic construction. In this sense, the term “robot” also carries a connotation of practical usefulness. The term should be applied, as it so often is, to every mechanical toy that ever comes along. A mechanical toy is an amusement rather than a useful worker.
• An android is an automation in human form. The connotation of mechanical response remains in common with robots, but the definitions differ in that androids are neither necessarily designed to perform work nor necessarily lacking a biological structure. If you’re going to tell the story of the robot that defies it’s programming, a biological android is probably best. More biological elements make the flexibility of mechanical response more believable.
• A cyborg is a natural person combined with machines to artificially stabilize their biological systems, perhaps even in environments that would otherwise kill the natural person. The definition does not include any restraint on free will; in fact, it’s original usage in 1960 was part of a plan to free humans to travel to the stars. In a broad sense this may include people kept artificially alive by medical machines, but the more common, narrower sense requires that the machines be required for the survival of even a healthy cyborg. A person with a pacemaker is not inherently a cyborg even in it’s broadest sense except when the pacemaker is actively altering the heartbeat; the rest of the time, the pacemaker is not actually regulating anything, but merely detecting whether regulation is necessary.
• A clone is an artificial but biological being identical to natural people in physical makeup but not necessarily in matters of self-determining will. The question of whether two beings, absolutely identical in physical structure but different in means of construction, will have equal capability for self-determination is tied to speculation about the mind, the spirit, or other metaphysical properties. The argument goes: “Just because you build an identical telephone doesn’t mean the call is the same.” And the rebuttal: “Neither is it required to be different.”
• A replicant is an artificial, biological being designed to imitate a specific species without imitating any specific individual. All the same connotations apply to replicants as apply to clones, except without the identical natural counterpart. The term was coined by the book Do Androids Dream of Electric Sheep? which was made into the movie Blade Runner.
• A synthetic (as a noun) is a term useful for referring to any artificial or partly artificial being (as in the movie Aliens), but is especially useful to refer to those that escape other classification (the Aliens instance could also be classified replicants). Personally, I think it best applies to purely artificial, purely biological beings. Not mere copies (clones or replicants), but biological beings of an entirely engineered species. I’d like to see more science fiction written about such beings, and frankly that’s my main motivation for promoting this term.
• A golem is an artificial creature produced by magical or paranormal means rather than technological. Traditionally, the golem is made of earth animated by a paler, arguably corrupt version of the same process by which God created Adam in the Book of Genesis. Frankenstein’s monster and similar creatures built from reanimated remains are sometimes referred to as “flesh golems”, being an artificial being of flesh once animated by natural life. In both these cases, and thus in the definition of golem itself, technology is insufficient to entirely construct the animate being, requiring paranormal means to finish the job.

Emotions are not addressed in this list at all. I see no reason why emotion would be inherently required or denied by any of the definitions in this list.

“Animal” is not listed here because I do not wish to address the questions of whether animals are people (eg, have free will), which terms apply equally to animals as to human people, and whether agricultural technologies have altered the “natural” state of animals.

Don’t be reluctant to comment on some point just because I’ve explicitly avoided commenting above. I don’t want the definitions to be dependent on the outcome of philosophical question, but I’m perfectly happy to see some philosophical debate.