# 'Proof'

From what I understand, this is pretty much what I've been trying to say. Of course, mathematics isn't the only example of a field in which all variables are known. In tautology, one eliminates all variables by creating a self-definition; it's essentially the same, although a broader category of sorts.

Quite correct.

My 2 cents:

Some would like to argue that:
1) A statement MUST be empirically verifiable for it to be meaningful as well as scientific (verificationism).
2) A positive statement carries the burden of proof.

Number one is easily refuted. It is impossible to empirically verify the statement that "the interior angles of triangles on an Euclidean plane will ALWAYS add up to two right angles". Yet this is true and meaningful as there are various ways to prove it and is quite useful. However there is zero empirical evidence (Euclidean 2D planes do not physically exist, they are intellectual abstractions) and yet it is scientific (science of logic and mathematics).

Number two is more interesting.
Let's look at the following positive statements:
1) The universe is composed of elementary indivisible and indestructible particles and all phenomena is explained in terms of the arrangement and rearrangement of these particles.
2) The universe began to exist.

Both these statements carry the burden of proof. Both statements are falsifiable. A common mistake to make is to try and use empirical science to try and prove or disprove these statements. It has to be understood that empirical scientific hypotheses and theories rely on evidence to accept or reject a hypothesis and not prove or disprove it. For example, there is certainly a lot of evidence to suggest that the big bang theory is true and that it is certainly reasonable to accept the theory. It can be argued that the theory that the universe has been in a steady state for infinity has been falsified through observation and that it is reasonable to reject that theory.

But the large amount of evidence does not prove statement two to be true. In order to formally prove or disprove a statement, one has to rely on a formal system of logic, for example deductive logic. The above two statements do not seem to be able to be formally proven or disproven (even though the evidence supports 2 and is against 1), they still carry the burden of proof, but one can still decide to accept or reject them based on evidence.

So what about formally proven statements such as "the interior angles of triangles on an Euclidean plane will ALWAYS add up to two right angles". The statement is still falsifiable and can be shown to be false if there is something wrong with the logic of the proofs of the statement. The statement does not rely on empirical evidence to be true, thus empirical evidence is irrelevant with regards to the truth of the statement. Of course the empirical observation that humans are capable of logically proving things to be true and that there exist physical things that approximate (in some sense) to something like 2D triangles on Euclidean planes e.g. a triangular piece of paper (a 3D object existing in space-time if you want).

With regards to religious debates and proof, some ID and creationist people (and others) keep insisting that the existence of God is some sort of scientific hypothesis or theory. For example, in the case of ID is is argued certain arrangements of matter (here the mechanistic view of matter seems to be assumed) are too improbable to exist without the interference of some intelligence. The problem is, while they may argue that there is empirical evidence to suggest it is reasonable to accept the theory, they will never be able to prove it to be true. I suppose the opposite is also true since they can claim it is falsifiable, but that is hardly a convincing argument for it.

The traditional, classical theistic arguments for the existence of God are not empirical scientific hypotheses or theories but rather resemble formal and logic proofs (e.g. Thomistic proofs) that rely on certain empirical observations/evidence (e.g. change happens). While the proofs are falsifiable, it relies on either denying the empirical observations as axioms (again, e.g. change happens) or showing that there is something wrong with the logic and/or the underlying metaphysics of the proofs.

So the debate between IDers, creationists and those who argue against them seem entirely irrelevant and even silly from a classical theistic view since none of these groups interact with the logic and rationality of the traditional proofs or the underlying metaphysics that support the arguments.

An extra cent or two :

So what is the scope of philosophy?

The terms philosophus and philosophia were first employed by Pythagoras (in Cicero’s Tusculan Disputations) and roughly meant to Pythogoras as the pursuit of wisdom. The term philosophy then in turn changed to signify wisdom and the love of it, which was seen as the highest kind of knowledge. There are various kinds of knowledge, for example knowledge we gain via our everyday experience of reality for example historical, literary, knowledge about the physical world, knowledge about art etc. There are also other forms of knowledge that we gain by making use of our intellect and capability to reason in order to classify, analyze, and interpret etc. the knowledge we gain from everyday experience.

We try to explain knowledge gained from our senses in order to understand and gain insight about their causes and reasons. Knowledge from our capability to reason in turn yield systemized truths which we call sciences. For example, knowledge about the physical world gained from our senses are in turn intellectually analyzed to yield certain truths about the physical world and thus rightly called the empirical physical sciences (e.g. physics and biology).

Knowledge about certain geometrical structures gained via sense experience is reasoned and analyzed and in turn yield certain truths about them and rightly called the mathematical sciences (e.g. algebra geometry in this case etc.). There is also knowledge from our sense experience of our social enterprises as humans and from these we analyze, reason etc. and from it the social sciences emerge (e.g. economy, psychology, political etc.). These are called special sciences since they deal with whatever relevant causes of the particular topic they are concerned about.

There are also more general sciences whose domains are much more extensive than the special sciences. For example, we are also moral beings that are capable reasoning and from this moral and ethical science arise that need to incorporate understanding from physical sciences and social sciences.

In this sense, philosophy is seen as a general science and its main aim is to answer deeper and more extensive questions and in order to do so, rational enquiry and reasoning needs to be employed to understand the more ultimate reasons and causes of things. Here it is important to distinguish between philosophy and theology. Theology tries to answer and reason about ultimate questions by making use of reason that is aided and enlightened by Divine revelation (For example Christian theology is enlightened by Jesus, or Islamic theology by Mohammed etc.). Philosophy, properly understood, is thus different from theology and different from the special sciences and properly defined as: the science of all things through their ultimate reasons and causes as discovered by the unaided capabilities of the human intellect and human reason (See Coffey's, Ontology, Theory of Being).

Philosophy can be divided into practical (e.g. ethics, Logic, Philosophy of science, mind etc.) and speculative (e.g. metaphysics).

A few things about the philosophy of logic, metaphysics, the special sciences and especially the empirical physical sciences needs to be said to further distinguish between what kinds of sciences they are.

The empirical physical sciences studies things such as objects, substances, processes, organisms etc. and may be referred to as “real sciences” or “scientiae reales” as the Scholastics described it. Philosophy of logic studies thought as a process capable of attaining certain proofs and truths. The study of logic can thus be referred to as a “rational science” or what the Scholastics called “scientia rationalis”. Metaphysics in turn is concerned with real being and its attributes. In other words it is concerned with the very nature of a thing, with being itself, with the root principle and operations of existing things. Aristotle referred to it as philosophia prima, i.e. the first philosophy that deals with the most fundamental and deepest aspects of reality. Metaphysics (traditionally viewed as the queen of the sciences), while called a speculative philosophy and a general science, is informed by the findings of the special sciences as well as logic. Also, metaphysical arguments and views can only be successful if the overall metaphysical view is coherent and interprets the facts logically and consistently.