According to Teilhard, Consciousness and Matter are aspects of the same reality, and are called the "Within" and the "Without" respectively. Evolution is the steady increase in the "Within" or degree of consciousness and complexity, through a number of successive stages: the various grades of inanimate matter; life or the "Biosphere"; man or thought or mind, the "Noosphere" (Teilhard's cosmology reflects the Christian anthropocentric bias in having man as the first species capable of self-reflective thought); and finally the uniting of all humans in a single Divine Christ- consciousness.
Teilhard thus follows the evolutionist understanding of an evolutionary progression from inanimate matter through primitive life and invertebrates to fish, amphibia, reptiles, mammals, and finally man; always an increase in consciousness. With man a threshhold is crossed - self-conscious thought, or mind, appears. But even humans do not represent the end-point of evolution, for this process will continue until all humans are united in a single Divine Christ-consciousness, the "Omega Point" (so-called after the last letter of the Greek alphabet - hence the Hellenistic statement attributed to Christ (but unlikely to be said by him, as he would not have known Greek - "I am the Alpha and the Omega, the beginning and the end"). Teilhardian cosmology thus revolves around the idea of an evolutionary progression towards greater and greater consciousness, culminating first in the appearance of self-conscious mind in humankind, and then in the Omega point of divinisation of humanity.
Teilhard refers to "Centeredness" as a characteristic of the universe on all levels. Each corpuscle of matter has a centre "within", its principle of organisation. The more complex the being, the greater degree of centreity. Teilhard teaches that Centreity is the true, absolute measure of being in the beings that surround us, and the only basis for a truely natural classification of the elements of the universe. The axis of evolution stretches from the lowest degree of centreity to the highest, and entities having the same degree of centreity constitute "isopheres", forming universal units of the same type of being. So pre-living entities are ordered on Earth in the lithosphere, the hydrosphere, and the atmosphere. Organic beings make up the biosphere, and thinking entities (which in Teilhard's system solely means man) the noosphere. When ranked in their natural order, the whole family of isopheres will define at the heart of the system a focus-point of universal synthesis, the Centre of centres, Omega [Activation of Energy, pp.10-13, 102; Beatrice Bruteau, Evolution towards Divinity, p.138]