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A-theories (dynamic theories) hold that temporal distinctions of past, present, and future are fundamental and objective, and that time genuinely passes — events become present and then recede into the past. Presentism (only the present exists) and the growing block (past and present exist, future does not) are major A-theory variants. B-theories (static theories) hold that all times exist equally in a four-dimensional spacetime manifold, and the only genuine temporal relations are tenseless earlier-than/later-than; 'now' is an indexical like 'here' with no ontologically privileged status. The debate turns on arguments from special relativity, the experience of temporal passage, and the truthmakers for tensed statements.
Read Sider's Four-Dimensionalism Chapter 2 for the B-theory and Crisp's 'Presentism' for the A-theory. Evaluate the Einstein/relativity argument against presentism: does the relativity of simultaneity refute it, or can presenters relativize the present to a reference frame?
The A-theory/B-theory distinction is about what is metaphysically fundamental in our description of time. Ordinary temporal language includes two very different kinds of expression: tense (past, present, future) and relational order (earlier than, simultaneous with, later than). The debate is about which of these is more fundamental — or whether one can be reduced to the other. From your study of philosophy of time, you know that time is not obviously simple; the A/B debate sharpens that intuition into a precise philosophical question.
B-theory (the static, tenseless view) holds that all genuine temporal facts are relational: events are ordered by earlier-than/later-than, and this is the complete story. The word "now" is an indexical — it refers to whatever time the utterance is made, just as "here" refers to the speaker's location. There is nothing metaphysically special about the present moment; it is simply the time of this utterance. All times exist equally in a four-dimensional spacetime block. What we experience as "temporal passage" — the felt sense that time flows — is a feature of how we experience time, not a feature of time itself. B-theory finds natural support in special relativity: since the theory eliminates absolute simultaneity (two events can be simultaneous in one frame and non-simultaneous in another), "the present" cannot be a frame-independent objective feature of reality.
A-theory (the dynamic view) insists that the distinction between past, present, and future is genuine and metaphysically fundamental — not reducible to mere relational ordering. The world has a dynamic structure: events are first future, then present, then past. "Now" doesn't just pick out a time indexically; the present is the ontologically privileged moment. This intuition is hard to resist phenomenologically: the future feels genuinely open, the present feels vivid and immediate, and the past feels fixed. A-theorists argue that the phenomenology of temporal passage is veridical — it accurately reflects a real feature of the world. Presentism (only the present exists) and the growing block (past and present exist; future does not) are the major A-theory variants.
The debate crystallizes around concrete puzzles that connect to your temporal logic background. For the B-theorist: how do we formalize A-theoretic language without smuggling in absolute simultaneity? For the A-theorist: what are the truthmakers for past-tensed statements? If "Caesar was murdered" is true now, what in the world makes it true? The presentist says only present entities exist — Caesar doesn't exist — yet we make apparently true claims about him. Proposed solutions include ersatz past times (abstract objects representing past states) or primitive temporal operators that don't require past entities to exist. Neither is free of cost. These pressures make the A/B debate one of the most technically demanding and metaphysically consequential in contemporary philosophy.
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