If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.

The Metaphysics of Knowledge presents the thesis that knowledge is an absolutely fundamental relation, with an indispensable role to play in metaphysics, philosophical logic, and philosophy of mind and language. Knowledge has been generally assumed to be a propositional attitude like belief. But Keith Hossack argues that knowledge is not a relation to a content; rather, it a relation to a fact. This point of view allows us to explain many of the concepts of philosophical logic in terms of knowledge. Hossack provides a theory of facts as structured combinations of particulars and universals, and presents a theory of content as the property of a mental act that determines its value for getting knowledge. He also defends a theory of representation in which the conceptual structure of a content is taken to picture the fact it represents. This permits definitions to be given of reference, truth, and necessity in terms of knowledge. Turning to the metaphysics of mind and language, Hossack argues that a conscious state is one that is identical with knowledge of its own occurrence. This allows us to characterise subjectivity, and, by illuminating the 'I'-concept, allows us to gain a better understanding of the concept of a person. Language is then explained in terms of knowledge, as a device used by a community of persons for exchanging knowledge by testimony. The Metaphysics of Knowledge concludes that knowledge is too fundamental to be constituted by something else, such as one's functional or physical state; other things may cause knowledge, but do not constitute it.

The Metaphysics of Knowledge presents the thesis that knowledge is an absolutely fundamental relation, with an indispensable role to play in metaphysics, philosophical logic, and philosophy of mind and language.
Knowledge has been generally assumed to be a propositional attitude like belief. But Keith Hossack argues that knowledge is not a relation to a content; rather, it a relation to a fact. This point of view allows us to explain many of the concepts of philosophical logic in terms of knowledge. Hossack provides a theory of facts as structured combinations of particulars and universals, and presents a theory of content as the property of a mental act that determines its value for getting knowledge. He also defends a theory of representation in which the conceptual structure of a content is taken to picture the fact it represents. This permits definitions to be given of reference, truth, and necessity in terms of knowledge.
Turning to the metaphysics of mind and language, Hossack argues that a conscious state is one that is identical with knowledge of its own occurrence. This allows us to characterize subjectivity, and, by illuminating the "I"-concept, allows us to gain a better understanding of the concept of a person. Language is then explained in terms of knowledge, as a device used by a community of persons for exchanging knowledge by testimony. The Metaphysics of Knowledge concludes that knowledge is too fundamental to be constituted by something else, such as one's functional or physical state; other things may cause knowledge, but do not constitute it.

If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.