Universal (metaphysics) in the context of Logical inference

Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of human understanding. Some philosophers, including Aristotle, designate metaphysics as first philosophy to suggest that it is more fundamental than other forms of philosophical inquiry.

Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every entity within it. To articulate the basic structure of being, ontology examines the commonalities among all things and investigates their classification into basic types, such as the categories of particulars and universals. Particulars are unique, non-repeatable entities, such as the person Socrates, whereas universals are general, repeatable entities, like the color green. Another distinction exists between concrete objects existing in space and time, such as a tree, and abstract objects existing outside space and time, like the number 7. Systems of categories aim to provide a comprehensive inventory of reality by employing categories such as substance, property, relation, state of affairs, and event.

Ontologists disagree regarding which entities exist at the most basic level. Platonic realism asserts that universals have objective existence, while conceptualism maintains that universals exist only in the mind, and nominalism denies their existence altogether. Similar disputes pertain to mathematical objects, unobservable objects assumed by scientific theories, and moral facts. Materialism posits that fundamentally only matter exists, whereas dualism asserts that mind and matter are independent principles. According to some ontologists, objective answers to ontological questions do not exist, with perspectives shaped by differing linguistic practices.

In metaphysics, particulars or individuals are usually contrasted with universals. Universals concern features that can be exemplified by various different particulars. Particulars are often seen as concrete, spatiotemporal entities as opposed to abstract entities, such as properties or numbers. There are, however, theories of abstract particulars or tropes. For example, Socrates is a particular (there's only one Socrates-the-teacher-of-Plato and one cannot make copies of him, e.g., by cloning him, without introducing new, distinct particulars). Redness, by contrast, is not a particular, because it is abstract and multiply instantiated (for example a bicycle, an apple, and a particular woman's hair can all be red).In the nominalist view, everything is particular. A universal at each moment in time, from the point of view of an observer, is a set of particulars.

In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind. Intermediate between nominalism and realism, the conceptualist view approaches the metaphysical concept of universals from a perspective that denies their presence in particulars outside the mind's perception of them. Conceptualism is anti-realist about abstract objects, just like immanent realism is (their difference being that immanent realism accepts there are mind-independent facts about whether universals are instantiated).

In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects as such—objects that do not exist in space and time.

Most nominalists have held that only physical particulars in space and time are real, and that universals exist only post res, that is, subsequent to particular things. However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), whilst others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, and bananas). Nominalism is primarily a position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars, and to the hylomorphic substance theory of Aristotle, which asserts that universals are immanently real within them; however, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus.

Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BC). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.

Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference uses mathematics to draw conclusions in the presence of uncertainty. This generalizes deterministic reasoning, with the absence of uncertainty as a special case. Statistical inference uses quantitative or qualitative (categorical) data which may be subject to random variations.

Universalism is the philosophical and theological concept that some ideas have universal application or applicability.

A belief in one fundamental truth is another important tenet in universalism. The living truth is seen as more far-reaching than the national, cultural, or religious boundaries or interpretations of that one truth. A community that calls itself universalist may emphasize the universal principles of most religions, and accept others in an inclusive manner.

A class is a collection whose members either fall under a predicate or are classified by a rule. Hence, while a set can be extensionally defined only by its elements, a class has also an intensional dimension that unites its members. When the term 'class' is applied so that it includes those sets whose elements are intended to be collected without a common predicate or rule, the distinction can be indicated by calling such sets "improper class."

Philosophers sometimes distinguish classes from types and kinds. The class of human beings is discussed, as well as the type (or natural kind), human being, or humanity. While both are typically treated as abstract objects and not different categories of being, types not classes are usually treated as universals. Whether natural kinds ought to be considered universals is vexed; see natural kind.

Philosophical realism—usually not treated as a position of its own but as a stance towards other subject matters—is the view that a certain kind of thing (ranging widely from abstract objects like numbers to moral statements to the physical world itself) has mind-independent existence, i.e. that it exists even in the absence of any mind perceiving it or that its existence is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality altogether.

Realism can also be a view about the properties of reality in general, holding that reality exists independent of the mind, as opposed to non-realist views (like some forms of skepticism and solipsism) which question the certainty of anything beyond one's own mind. Philosophers who profess realism often claim that truth consists in a correspondence between cognitive representations and reality.

The instantiation principle or principle of instantiation or principle of exemplification is the concept in metaphysics and logic (first put forward by David Malet Armstrong) that there can be no uninstantiated or unexemplified properties (or universals). In other words, it is impossible for a property to exist which is not had by some object.

The existence of properties or universals is not tied to their actual existence now, but to their existence in space-time considered as a whole. Thus, any property which is, has been, or will be instantiated exists. The property of being red would exist even if all red things were to be destroyed, because it has been instantiated. This broadens the range of properties which exist if the principle is true.

Moderate realism (also called immanent realism) is a position in the debate on the metaphysics of universals which holds that there is no realm in which universals exist (in opposition to Platonic realism, which asserts the existence of abstract objects), nor do they really exist within particulars as universals, but rather universals really exist within particulars as particularised, and multiplied.

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into work in a cyclic process." These are informal definitions, however; more formal definitions appear below.

The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter. The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.