This is often combined with the argument that if the brain had fixed views and the arguments were mere after-constructs with no causal effect on the conclusions, science would have been impossible and the use of arguments would have been a meaningless waste of energy with no persuasive effect on brains with fixed views. Mathematical models
Many mathematical models of physical systems are deterministic. This is true of most models involving differential equations (notably, those measuring rate of change over time). Mathematical models that are not deterministic because they involve randomness are called stochastic. Because of sensitive dependence on initial conditions, some deterministic models may appear to behave non-deterministically; in such cases, a deterministic interpretation of the model may not be useful due to numerical instability and a finite amount of precision in measurement. Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations. Quantum and classical mechanics
Day-to-day physics
Since the beginning of the 20th century, quantum mechanics—the physics of the extremely small—has revealed previously concealed aspects of events. Before that, Newtonian physics—the physics of everyday life—dominated. Taken in isolation (rather than as an approximation to quantum mechanics), Newtonian physics depicts a universe in which objects move in perfectly determined ways. At the scale where humans exist and interact with the universe, Newtonian mechanics remain useful, and make relatively accurate predictions (e.g. calculating the trajectory of a bullet).
In the case of nomological determinism, these conditions are considered events also, implying that the future is determined completely by preceding events—a combination of prior states of the universe and the laws of nature. Yet they can also be considered metaphysical of origin (such as in the case of theological determinism). Nomological
Nomological determinism, generally synonymous with physical determinism (its opposite being physical indeterminism), the most common form of causal determinism, is the notion that the past and the present dictate the future entirely and necessarily by rigid natural laws, that every occurrence results inevitably from prior events. Nomological determinism is sometimes illustrated by the thought experiment of Laplaces demon. Nomological determinism is sometimes called scientific determinism, although that is a misnomer. Necessitarianism
Necessitarianism is closely related to the causal determinism described above. It is a metaphysical principle that denies all mere possibility; there is exactly one way for the world to be. Leucippus claimed there were no uncaused events, and that everything occurs for a reason and by necessity. Predeterminism
Predeterminism is the idea that all events are determined in advance. The concept is often argued by invoking causal determinism, implying that there is an unbroken chain of prior occurrences stretching back to the origin of the universe. In the case of predeterminism, this chain of events has been pre-established, and human actions cannot interfere with the outcomes of this pre-established chain. Predeterminism can be used to mean such pre-established causal determinism, in which case it is categorized as a specific type of determinism.