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In Levinas' philosophy, alterity is the concept of 'otherness', central to understanding ethics as the primacy of the Other's needs over one's own. It challenges the egoism inherent in Western philosophy and prompts a responsibility for the Other that is unconditional.

In Levinas' philosophy, the 'saying' is the act of communication that expresses openness and responsibility before it is solidified into the 'said', which is the content or fixed meaning of what has been expressed. Levinas emphasizes the ethical significance of this process.

The face-to-face encounter is key in Levinas' ethics, where the 'face' of the other demands a response and represents the infinite obligation to the Other. It signifies a personal connection that is ethical in nature and not reducible to knowledge or systems.

Levinas describes the self as a 'hostage' to the Other's needs, highlighting the vulnerability and passive dimension of ethical subjectivity. This imagery serves to stress the deep ethical commitment to the Other that Levinas sees as fundamental to being.

Levinas' book 'Totality and Infinity' explores the limits of totality (knowledge, society, being) and the concept of infinity (ethical relation with the Other). It's his philosophical work that lays out his critique of Western philosophy and his own ethical framework.

The concept of 'the Third' introduces the social dimension into Levinas' ethics, where others are not encountered in isolation but within a community. This complicates the direct responsibility to the Other by considering justice and our obligations to all others.

Levinas uses the term 'infinity' to describe the experience of the Other that transcends the finite categories of thought. It is a direct relationship with the Other that always exceeds our capacity to comprehend or contain.

Substitution is the phenomenological process in Levinas' philosophy where one finds oneself in the position of the Other, bearing their responsibility. It's the basis for the radical altruism that Levinas proposes, where the self is hostage to the Other's needs.

Levinas uses the term 'an-archy' to convey an ethical relationship that is without beginning or principled foundation, but arises from the encounter with the face of the Other. It disrupts the hierarchical and structured order of being and knowledge.

Illeity refers to the unassailable and irreducible dimension of the Other in Levinas' philosophy, the part that always escapes our attempts to know or categorize. It guides us to an ethical relationship that respects the mystery and sanctity of the Other.

Proximity in Levinas' thought is not merely a spatial concept but an ethical relation where the closeness to the Other entails a responsibility that is not chosen but thrust upon us. It emphasizes the immediate and compelling nature of ethical obligations.