在西方形上學的傳統裡，自柏拉圖和亞里斯多德起，就已經將事物具有的性質（以及事物之間的關係）理解為「共性」，這種立場甚至可說已經是「定型」了。承認共性存在的存有論稱為「實在論」，否則稱為「唯名論」。
實在論雖承認「共性」的存在，對於「共性」卻有不同的理解，亦即共性可理解為「柏拉圖式」的，也可理解為「亞里斯多德式」的。本門課會說明兩者的差異。無論如何，實在論認為，承認共性的存在可以說明以下三點：(1)承認「共性」的存在，可以解釋兩個事物如何具有相同的特徵，例如相同的顏色、相同的形狀；(2)「共性」可以作為述詞的意義，或者作為抽象單詞的指涉；(3)承認「共性」的存在，可以解釋自然法則，亦即主張自然法則是介於共性之間的關係。
唯名論是反實在論的立場。唯名論的派別很多，例如class nominalism、predicate nominalism、concept nominalism、resemblance nominalism。本門課會逐一介紹這些唯名論的立場，並說明：
(1)這些反實在論的學說如何回答上述三個問題；(2)這些學說會面臨的理論困難。在二十世紀新興起一種反實在論的立場，與傳統的唯名論有別，稱為「殊性存有論」。這套學說否認共性、主張性質是個殊的、並且對於上述三個問題提供了一套解決方式。依據阿姆斯壯的分析，這是唯一能夠與實在論相競爭的理論。本門課因此亦會對這套學說做一些介紹。
上述討論的「性質」主要都是關於事物本身擁有的特徵。本門課最後將補充介紹五個邏輯性質：等同、存在、謂述、必然、真。
The tradition of Western metaphysics, specifically the tradition established by Plato and Aristotle, understands the properties (and relations) had by individual objects as universals. One may even say that this is the default ontological position with regard to properties. The position that admits of universals is called "realism", whilest the position that denies universals is traditionally called "nominalism".
Although realism admits of universals, there are different understandings. Some realists think that universals are Platonic (or transcendent), others think that universals are Aristotelian (or immanent). This course will explain the difference.
Putting aside the difference, realism thinks that the positing of universals can explain the following three things: (1) the positing of universals can explain how two objects are the same in some respect, e.g., they have the same color, or the same shape, or the same size. (2) Universals are the meanings of predicates or are the references of abstract singular terms. (3) The positing of universals help understand the nature of natural laws, i.e., universals are the relata of nomological relations.
Nominalism is an anti-realist position. There are several versions of nominalism, e.g., class nominalism, predicate nominalism, concept nominalism, resemblance nominalism. This course will explain what these doctrines claim and explain (1) how these nominalist doctrines answer the above three questions and (2) what theoretical difficulties they have.
In the twentieth century, a new anti-realist approach, viz., the trope ontology, emerges. It denies the reality of universals, takes properties to be particulars, and offers yet another set of answers to the above questions. According to Armstrong, trope ontology is the only anti-realism that is competitive with his realism.
The above disscussions all surround ordinary properties had by objects. We shall briefly explore five logical properties near the end of the semester: Identity, Existence, Predication, Necessity, and truth.