Logic

Logic (from the Greek λογική logikē) encompasses the guiding principles of reasoning and is integral to philosophy and science. There is also a philological and philosophical aspect to the English word logic finding itself within the Greek word logos. Logos depending on contextual considerations can mean "the Word", or "what is spoken", in the philosophical theology of John or "thought" and "reason" in Greco-Roman philosophy of classical antiquity. Traditionally in the modern academic setting logic is studied as a branch of philosophy and can be defined as the correct way to reason from premises to conclusions. Logic provides an underlying framework for correct thought, no matter the subject being studied. Since the nineteenth century logic has also been commonly studied in the field of mathematics and even more recently in the twenty-first century computer science. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialist analyses of reasoning such as probability and arguments involving causality.

Formal logic encompasses a wide variety of logical systems. There are various systems of logic captured in this framework such as term logic, predicate logic and modal logic. Formal systems are indispensable in all branches of mathematical logic. The table of logic symbols describes various widely used notations in symbolic logic.

History
History's greatest scientists, from Aristotle to Galileo to Newton, all held to the former view, namely that logic is absolute and objective. They viewed the universe as having objective, logical principles, or what is sometimes referred to as the prior condition for intelligible rationality. This view is a philosophy of science since logic must be established before even conducting any part of the scientific method. Utilizing the scientific method by logic then allows man to grasp the nature of the universe to a more specific degree. Great scientists who were also creationists believed that God designed the universe as intelligible or logical, so that logic is what we have in common with the mind of God revealed to us by special creation in His image.

Ontological grounding of logical laws and mathematical truths of the created world within, not the physical brain of human beings, but the immaterial mind of God as divine archetypes is a particular historical mindset that was very influential in forming natural philosophy (considered a precursor to modern science). The archetypal view is found in the work of the early modern philosopher Marin Mersenne (1588 to 1648). Although the main thrust of Mersenne and his work was from within the context of medieval European society, he held that mathematical truths found in nature exist as, "archetypes in the mind of the Creator". Modern day creationists, either of the YEC or OEC variety find common ground as they think along the same lines as well. Mersenne conceded that mathematics is not concerned with the essences of things, but held that the eternal truths of mathematics exist as archetypes in the mind of the Creator, employed in the creation of a harmonious universe. Human reason is created in the image of divine reason, allowing us to achieve some understanding of the universal harmony through the “mixed mathematics” of such sciences as optics, astronomy, and mechanics, not to speak of harmonics itself.

Nature of Logic
Creationists assert and believe in a transcendent or objective origin and nature of logic. Logic is not a result of human biological evolution and is not contingent upon humanity or natural laws for its existence in any way. Logic in the creationist worldview consists of metaphysical objects called propositions, like numbers and sets. Logical laws are expressed as propositions, and because of this, they are not located in physical space and time, rather being dealt with by human beings in the mind. Logic, and even mathematics as they do share an intimate relationship, according to the creationist are natural representations of the way God thinks.

The nature of logic, if it is material or immaterial, or how logic exists within the classical definition of the term within a strict materialist worldview, cannot be coherently accounted for by atheism, as it can be within theism. Theism supports existence of a supernatural and metaphysical, non-contingent being, that is personal, and exists outside of space and time. Attributes like these fall within the tradition of classical theism, and describe what is called God. A personal creator and designer of the cosmos, with the resulting intelligibility of nature, articulating the mind of the designer. Theism provides, on philosophical grounds, reason to a transcendent grounding in a being which has a logical nature. This lends to a consistent overall worldview for theistic religions such as Christianity when dealing with the existence of logic. Christianity makes sense of the intelligibility of nature through logical laws because of the intelligible nature of the creator. The intelligibility of nature is a concept which has to be presupposed, taken for granted within materialistic science of the 21st century.

Atheism is the belief that there is no God or any spiritual or supernatural being that exists. There is only the physical universe. Reality is what is experienced by the senses (See: Sensory system), and so is physical and natural, with no immateriality. This in turn reduces the propositions of logic, and eventually mere thoughts about anything (what are called mental states), down to electro-chemical reactions in the brain. (See: Reductionism).

The dominant views regarding the nature of logic are then as follows:
 * Logical objectivity: Logic encompasses the guiding principles that organize the universe itself; they exist whether we believe in them or not.
 * Logical subjectivity: Logic originates in the brain through social construction or biological evolution and are used to explain what we see in the universe. The laws of logic exist because humans over time essentially invented them, and are not fundamental principles found outside of the universe itself.

The view a person has upon the origin and nature of logic usually falls into the above two broad categories. Being of the philosophical domain if logic is not thought of on the abstract level, but reduced down to the physical brain and biological evolution, there is impact on views regarding science. Michael Ruse, a philosopher of science, goes so far to actually concede that moral objectivity is illusory with no reality to it. Moral language is scientific, solely created by biological evolution and accompanying processes. Essentially human beings evolved through socio-economic pressures, a way to survive that exceeds other competing creatures. However, if morality, or logical concepts for that matter exist subjectively and only objectively within an illusion of the individuals brain for survival, logic and morality become reduced to the random configurations of the neurophysiology of the brain. There is no justifiable reason that is outside of human subjective experience that coheres well with a completely materialistic worldview of reality such as atheism.

A scientific atheist commits to circular reasoning when trying to prove the authoritative and universal truths of logical laws. Science is the only truly meaningful knowledge (See: Scientism) within their worldview. Therefore to prove the existence of logic not only must it have a material nature and origin but logical laws must be used, so inevitably an argument is created which commits a logical fallacy. Essentially logic has to be used to prove logic. Science, and so the foundation of knowledge of the atheist worldview must presuppose without scientific investigation the past and future operation of the continuity of logic.

Laws of Logic
The fundamental laws of logic are the starting presupposition of all discourse and thinking by human persons. Since persons must apply the laws of logic to everyday life and any type of challenge or study, science itself also has to presuppose the laws of logic for it to even function. A coherent creationist philosophy of science includes transcendence thus accepting the laws of logic as absolute and objective. Logical laws are metaphysical in nature, not physical and thus not scientific, coming even before the application of the scientific method.
 * 1) The law of non-contradiction. A cannot be A and not A at the same time.
 * 2) The law of identity. A is A. A is not B.
 * 3) The law of excluded middle. There is either A or not A.
 * 4) The law of rational inference or what is called transitive cause in metaphysics. If A = B and B = C then A = C. The passing of judgment as true from one believed premise to another.

Logical fallacies

 * Main Article: Logical fallacies

A logical fallacy is an error in logical argumentation. It is a flaw in the structure of an argument, which is said to invalidate the argument, as opposed to representing an error in its premises. A fallacy within an argument is independent of the truth, and does not necessarily imply anything about the argument's premises or its conclusion. It is simply an error which violates the rules of logic. Nevertheless, arguments that are derived from a logical fallacy often lead to an incorrect conclusion due to faulty reasoning.

Branches of Logic
Branches of logic include:
 * Informal logic: The reasoning that occurs in daily life, in the course of decision-making and debate. Informal logic is the broadest of all the forms: it encompasses all the issues of reasonableness, of evidence, and of logical fallacy that we address in daily life. It also knows by "common sense" the things that formal logic only knows by rules. One doesn't need to know what the word "syllogism" means to know that if all humans are mortal and Socrates is a human, then Socrates is mortal. It's common sense.
 * Formal logic: A set of formal "rules of logic". Formal logic and its symbolic counterpart are more secure and certain than informal logic. Their rules can be named, tested, and verified. However, they only operate within a limited realm: the realm in which the parties agree on their premises. They have nothing to say when it comes to questions of whether premises are reasonable or not. Further, they are, for the most part, simply a codification of informal logic: putting names on things we all know by common sense.
 * Symbolic logic: A system of symbols reducing formal logic to formulae similar to mathematics.

Modes of Logic
Raw data derived by scientific experimentation needs presentation in an unbiased manner. What should be encouraged in the scientific sphere, or what inductive observation is, is explanation of natural observation absent of what can be called a meta-narrative. If philosophical deduction must be articulated because of implications some observation upon a natural phenomena has on the origin of life question for example, the goal should be to show an accurate trace from inductive and deductive modes of the argument and from which the ultimate conclusive claims are derived.

Inductive observation
Inductive observation is the investigation into what the observation of nature really is and why it works. A complex pursuit crossing many disciplines becoming so successful since its conception that inductive observation or the inductive method is sometimes used interchangeably with the scientific method. Inductive observation adopts a position placing experimentation and observation as the authority for obtaining knowledge about the natural world.

Deductive reasoning
Deductive reasoning is philosophically fertile, meaning that its defined terms are conceived by assumptions called axioms which are particular self-evident truths. A logical formulation of undefined terms, definitions and axioms enables a coherent argument for a particular truth claim like the existence of God to articulate grand meta-narratives. Meta-narratives spawn from inductive observation but become crafted into a philosophy of science, and there can be what is sometimes unreasonable deduction or false meta-narrative. Deductive reasoning with its various elements and logical flow is used to illuminate further the ultimate extended outcomes of nature. Questions like why is there something rather than nothing, and what created the universe and cosmos as a whole are important deductive thoughts from the observed natural world. On this conception, then, philosophy is distinguished by the kinds of considerations and arguments it employs. It does not consider a world apart from that of the various sciences. Rather it considers just that world, but from the standpoint of what can be established about it by a priori argument, where it takes as its premises generally recognized activities as conceptualized in experience. But neither does it compete with science. For its task is to show what must be the case for the ensemble of scientific activities to be possible.