Ousia, Hyle, Substantia, and Materia
There are two philosophical terms related to the modern day conception of matter that are worth reviewing: Gr. hyle and Gr. ousia or L. substance (SEP).
From WP:
Hylomorphism is a philosophical doctrine developed by the Ancient Greek philosopher Aristotle, which conceives every physical entity or being (ousia) as a compound of matter (potency) and immaterial form (act), with the generic form as immanently real within the individual.2 The word is a 19th-century term formed from the Greek words ὕλη (hyle: "wood, matter") and μορφή (morphē: "form").
From SEP:
The philosophical term ‘substance’ corresponds to the Greek ousia, which means ‘being’, transmitted via the Latin substantia, which means ‘something that stands under or grounds things’. According to the generic sense, therefore, the substances in a given philosophical system are those things that, according to the system, are the foundational or fundamental entities of reality.
Philosophically, it is from these metaphysically complicated ideas that modern philosophers of physics have arrived at an understanding of matter:
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles (or combination of particles) that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or heat.
While materials and form used to serve as the basis of matter, mass in contemporary physics, that is anything that has mass and occupies space, is more than adequate for defining matter.
Aristotle's Thoughts on the Matter of Matter
We have an intuitive sense of matter in the form of touch and when we touch wood, for instance, there is something solid about it. To the some of the Pre-Socratics, the categories such as earth, wind, water, and fire were taken to be primitive, and there was much wrangling about what reality is and how to characterize things. The ancient atomists latched onto the notion the believe that it didn't seem to make sense that you could take a piece of wood and divide it forever, and hence arrived at Gr. atomos, indivisible. Aristotle articulated his four causes which to answer a series of why-questions. In it, he noted a way to understand simple circumstances:
A carpenter who wants to please a customer carves a statue of the client from wood.
In this view, the material cause, wood would answer questions regarding what we would consider physical being, such as how the chisel and wood interact to give rise to the formal, efficient, and final causes. The being of wood, then, allows us to discuss and predict situations with materials we can touch like wood, stone, bone, etc.
Matter and Modern Physics
In modern philosophy, great deference is given to the weight of the philosophical claims alleged by physicists, who have a science of matter that is quite successful in moving matter around (landing Armstrong on the moon), and predicting how atoms form compounds and behave (think material science and physical chemistry). Albert Einstein stands next to Pythagoras in terms of famed equations with his mass-energy equivalence. Besides making 'E equals mc squared' household science, he provided a theory to prove the existence of mass dilation and invoked the notion of invariant mass. Mass is an imputed property of matter, and thus modern notions of matter lean heavily upon the mathematics of mass and energy.
Thus, the concept of matter has moved from notions of being and substance of philosophical doctrines like hylomorphism and atomism, to being defined in terms of mass, and one of the earliest researchers in this conceptual project was Gallilei who is famous from dropping matter, letting roll down ramps, and letting matter collide all the while advocating measurement. Newton later wrote of quantitats materiae and provided his mathematical laws. Thus, natural philosophy moved in the direction of mathematical physics and operational definition. Today, physicists refer to these ideas and explicate them with terms like inertial mass, relativistic mass, and gravitational mass. Jammer has an excellent introduction in his Concepts of Mass in Contemporary Physics and Philosophy (which is an easy read if you've had a calculus-based introductory sequence to physics including classical mechanics, E&M, and modern courses).
Summary
So, the concept of matter has undergone notions starting with the ancient Greeks who intuitively related it to things and materials, to the natural philosophers who began to measure it as part of space and time, to the most modern notions that rely heavily on operational definitions of mass. Which is true, may be less important the question of which is most adequate for your worldview.
