When considering what kinds of things exist (a central question of ontology), an immediate distinction one can draw is between objects and properties. Roughly, the distinction corresponds to grammatical subjects and predicates within a sentence. For instance, the sentence “Paco is short” has grammatical subject “Paco” and predicate “is short”, and is about the object *Paco* and the property of *being short*. The sentence states that the object *Paco* possesses the property of *being short*.

Although this is a rough distinction, it is nonetheless useful. However, it is also useful to introduce some more technical terminology concerning objects, properties, and relations, and I will do so with the help of information from the American Philosophical Association.

**Objects**

When considering physical, concrete, sensible things of our experience that causally interact with other things (such as houses, rocks, chairs, trees, dogs, planets, etc), the distinction between objects and properties seems obvious. But are there non-physical, non-spatial, and atemporal objects? For instance, many philosophers believe that numbers are objects. Numbers, however, lack causal efficacy. They do not cause anything and are not caused by anything. Rather, they are thought to be **abstract** objects, which are neither located in space nor time.

The grammatical distinction previously articulated, although useful, begins to break down in other respects. For example, take the following two sentences: “Roses are red”, but also “Red is a color”. For in the first sentence “red” occurs as part of the predicate, and in the second it occurs as the subject. So is *red* an object or a property?

Philosophers have attempted to resolve this problem by delineating between **universals and particulars**. “*Red* is a property of individual, physical objects, and such objects are said to *possess* the property, or alternatively the property is said to *inhere* in them. These objects are called *particulars*. Furthermore, we can talk about the property itself, in abstraction from any particular instantiation of it. When we talk of the property in this way, we are discussing a *universal*. Some philosophers believe that universals have a distinct existence, distinct that is from any particular instantiation. In such a case, universals would themselves be (rather confusingly) objects, although objects of a quite different ontological category to the particulars which instantiate the universal. That is there would be the particular objects which possess the property *red*, and the universal object *redness” (*American Philosophical Association*).*

It’s important to note that the proper conception of abstract objects, universals, mathematical objects, propositions, and so on is a matter of immense philosophical debate. This debate, however, extends beyond the purposes of the present post.

Another important, related distinction is that between **tokens and types**. A particular blue object, for example, is a *token* of the *type* “blue objects”. This is very useful when it is unclear whether one is referring to a particular instance of something or the general class or type to which it belongs. Take, for instance, the question “How many letter are there in the word ‘popcorn’?”. If we mean *token* letters, then there are seven. But if we mean letter *types* then there are five: “p”, “o”, “c”, “r” and “n”. We say that the two “p”s in “popcorn” are two tokens of the same type.

**Properties**

There are a lot of distinctions to be drawn in philosophy, and sometimes it can get overwhelming. But, there’s a good reason for it. Distinguishing between concepts helps with precision, clarity, coherence, and so much more. And this philosophical love for distinctions applies just as much to properties as it does to so many other considerations I have covered thus far.

Perhaps one of the most important distinctions to be drawn is that between an object’s **essential and accidental** properties. Metaphysics is the study of (or, rather, a quest to find) the fundamental nature of things. We want to know what it is about something that makes it the thing it is. An object’s essential properties are those properties which it could not lack. If you take away these properties, the object itself ceases to be the same object. For instance, imagine a glass of milk. This milk could easily have been in a jug, carton, or mug instead of a glass. It might have been at a different spatio-temporal location. It could have been a different temperature to the temperature it actually is. But it could not have been made up of anything other than water molecules and the various proteins that essentially characterize milk. For that is precisely what milk *is*. Being composed of water molecules and the proteins is an *essential property* of milk, it is what it is for something to *be* milk. Being a particular temperature, or in one container or another, or one location or another, are accidental properties of the sample of milk. It could have lacked those properties without ceasing to be what it is.

Another useful distinction is between **intrinsic and extrinsic** properties. Consider a golden retriever, Max. Let us say that Max is two feet tall, that he weighs 35 pounds, has brown eyes and golden hair, and is loved by his owner, Sophia. In addition, Max is taller than his Chihuahua buddy, Jimmy, and is the neighbor of a cat. Then his *intrinsic properties* include being two feet tall, weighing 35 pounds, and having brown eyes and golden hair. His *extrinsic properties* include being loved by Sophia, being taller than Jimmy, and being the cat’s neighbor. The reason the former are intrinsic properties of Max’s is that they are dependent solely upon his nature, upon his make-up. The latter are extrinsic properties of Max’s because they are determined *partially* by other objects, people, or states of affairs, such as Sophia, Jimmy, and the state of affairs involving the neighboring house having a cat, *and* Max’s relation to them. For example, whether or not Max has the extrinsic property of being taller than Jimmy depends not only on one of Max’s intrinsic properties, but also on one of Jimmy’s intrinsic properties. Extrinsic properties generally consist in **relations** holding between two or more particular objects.

**Relations**

While this whole series has been *guided* by the American Philosophical Association page previously linked, the following passage regarding relations is directly quoted.

Consider the different categories of relations, and their logical properties:

*Transitivity*

A relation *R* is **transitive** if and only if (henceforth abbreviated “iff”):

if *x* is related by *R* to *y*, and *y* is related by *R* to *z*, then *x* is related by *R* to *z*.

For example, “being taller than” is a transitive relation: if John is taller than Bill, and Bill is taller than Fred, then it is a logical consequence that John is taller than Fred.

A relation *R* is **intransitive** iff,

if *x* is related by *R* to *y*, and *y* is related by *R* to *z*, then *x* is not related by *R* to *z*.

For example, “being next in line to” is an intransitive relation: if John is next in line to Bill, and Bill is next in line to Fred, then it is a logical consequence that John is **not** next in line to Fred.

A relation *R* is **non-transitive** iff it is neither transitive nor intransitive.

For example, “likes” is a non-transitive relation: if John likes Bill, and Bill likes Fred, there is no logical consequence concerning John liking Fred.

*Symmetricity*

A relation *R* is **symmetric** iff,

if *x* is related by *R* to *y*, then *y* is related by *R* to *x*.

For example, “being a cousin of” is a symmetric relation: if John is a cousin of Bill, then it is a logical consequence that Bill is a cousin of John.

A relation *R* is **asymmetric** iff,

if *x* is related by *R* to *y*, then *y* is not related by *R* to *x*.

For example, “being the father of” is an asymmetric relation: if John is the father of Bill, then it is a logical consequence that Bill is **not** the father of John.

A relation *R* is **non-symmetric** iff it is neither symmetric nor asymmetric.

For example, “loves” is a non-symmetric relation: if John loves Mary, then, alas, there is no logical consequence concerning Mary loving John.

*Reflexivity*

A relation *R* is **reflexive** iff,

everything bears *R* to itself.

For example, “being the same height as” is a reflexive relation: everything is the same height as itself.

A relation *R* is **irreflexive** iff,

nothing bears *R* to itself.

For example, “being taller than” is an irreflexive relation: nothing is taller than itself.

A relation *R* is **non-reflexive** iff it is neither reflexive nor irreflexive.

For example, “loves” is a non-reflexive relation: there is no logical reason to infer that somebody loves themselves or does not love themselves.

*Equivalence*

A relation *R* is an **equivalence relation** or a **congruence relation** iff *R* is transitive, symmetric and reflexive.

For example, “identical” is an equivalence relation: if *x* is identical to *y*, and *y* is identical to *z*, then *x *is identical to *z*; if *x* is identical to *y* then *y* is identical to *x*; and *x* is identical to *x*.

**Three Classical Laws of Logic**

(1) The Law of the Excluded Middle

- Every proposition is either true or false
- Either p or ∼p must be true
- Symbolically: p ∨ ∼p, in which ∨ means “or”

(2) The Law of Non-Contradiction

- For all propositions p, it is impossible for both p and not p to be true in the same respect and at the same time
- Symbolically: ∼(p ^ ∼p), in which ~ means “not” and ^ means “and”
- For example, nothing can be both a square and not a square in the same respect and at the same time

(3) The Law of Identity

- Everything is identical with itself
- (∀x) (x = x), in which ∀ means “for every” or “for all”
- x is x

**Conditionals**

“A *conditional* is a statement of the form “If *A* then *B*“, which asserts that something (*B*) is, or will be, the case, provided that some other situation (*A*) obtains. *A* is known as the **antecedent** of the conditional, and *B* is known as the **consequent** of the conditional” (American Philosophical Association).

Examples of conditional statements include:

If divine command theory is true, then morality is either arbitrary or independent of God.

If Jimmy eats the moldy bread, (then) he will get sick.

**Necessary and Sufficient Conditions**

Understanding these concepts is crucial for one’s progression in the study of philosophy.

*B* is a necessary condition of *A* if *A* could not be the case without *B* being the case (however, B’s being the case does not guarantee that A will be the case). *A* is a sufficient condition of *B* if, when A obtains (or is true), that is enough to make B obtain (or true).

If A, then B.

In the above conditional A is a sufficient condition for B, and B is a necessary condition for A. Let’s look at some examples.

*If you roll a 3, you roll a prime number.*

In the above example, 3 is a sufficient condition for rolling a prime number, since, if you indeed get a three, that is enough to make it the case that you got a prime number. But rolling a three is not a necessary condition for getting a prime number. After all, you could also roll a 2, or a 5, and those would be sufficient for rolling a prime number. Thus, since you do not *have* to roll a 3 in order to roll a prime number, rolling a 3 is not a necessary condition for rolling a prime number.

But it is certainly true that rolling a prime number is a necessary condition for rolling a 3. You *have* to meet the condition of “rolling a prime number” if you are going to roll a three. But, note, rolling a prime number is not *sufficient* for rolling a 3. All by itself, the obtainment of “rolling a prime number” does not guarantee (suffice for) the obtainment of “rolling a 3”.

If it is raining outside, the sidewalk will be wet.

Of course, the sidewalk being wet is a necessary condition of it raining outside, but from the mere fact that the sidewalk is wet, that is obviously not sufficient for it to be raining. After all, someone could have been using a sprinkler, or dumped out some of their water! However, it raining outside *is* sufficient to guarantee that the sidewalk will be wet.

That concludes my series on philosophical terminology. I hope that this series can provide the necessary foundations that are required for the further engagement with my posts, as they will begin to get much more complex as they delve into the actual philosophy. But up next is a very exciting series on critical thinking… Hope to see you there!

Author: Joe

Email: NaturalisticallyInclined@gmail.com

Source: http://cas2.umkc.edu/philosophy/vade-mecum/

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