Logical positivism is a beautiful, naturalistic philosophy that forms the foundation of my thinking.
Logical positivism can basically be summed up by the principle of verifiability:
The meaning of a proposition is its method of verification.
It's a little hard to grasp at first, but it's elegantly simple. A proposition is a statement that is either true or false. Not all statements are propositions, e.g.,
Squiggle juggles dimetrodon squared.
is neither true nor false, it is simply nonsensical. One of the primary goals of philosophy is to identify meaning. It is the central claim of logical positivism that a statement only makes sense if it says something concrete about experience. In other words, given a proposition, its meaning consists of all the experiments you might do to disprove the proposition. This does not mean that all meaningful propositions are false, it just means that it should be possible to show the proposition is false if it were indeed false.
If a proposition can never be falsified, not even in principle, then the proposition says nothing about experience, past, present or future. Such propositions are neither true nor false. They say nothing.
In natural language, we often say things that don't meet the strict requirements of logical positivism. Most of the time, our natural language is a shorthand for meaningful propositions. Unfortunately, sometimes we're simply confused. We may say something that sounds meaningful, but is really just poetic. Here are some examples:
God is good.
I have free will.
Typically, the person expressing these propositions intends them to be beyond verification (or falsification). If you ask a person who believes in traditional theology whether it is possible to falsify the proposition God is good, they will tell you that it is not possible in principle ("there is nothing you can show me that will convince me God isn't good..."). If that is the case, then we cannot even define the terms "good" or "God". If the proposition was falsifiable, at least we could deduce the effective meaning of the statement.
To a logical positivist, such propositions are intrinsically dissociated from all possible experience. As such, one can claim the exact opposite, e.g., God is evil, with equal validation from experience.
One ploy used by metaphysicians to try to escape the clutches of logical positivism is to claim that the principle of verifiability is itself not falsifiable. This is true, but irrelevant. The principle of verifiability is just a heuristic.
What is a heuristic? A heuristic is a way to identify the useful subset of solutions to a given problem. Example: if you reach the rim of a volcanic crater and realize you've dropped your Geiger counter, where do you search? Answer: on the cooler, solid rocks and not in the lava pools, for if your Geiger counter fell into a lava pool you don't really want it back. The heuristic does not tell you the solution, it only tells you which solutions are useful to you.
The heuristic principle of verifiability is just a demarcation between those propositions that do and do not relate to experience. A priori (independent of experience), we may posit that propositions that are not verifiable are allowed to have definite truth values (by our analogy, the Geiger counter fell into a lava pool). Alas, such propositions will never have anything to do with our experience.
The function of logic is to determine whether a given set of propositions can have a given set of truth values without contradiction. That is the sole function of logic: to guarantee consistency.
Mathematics is derived from a set of axioms (a set of propositions we declare to be true in order to establish a given context). In other words, mathematics is synthesized based on certain foundational assumptions. Mathematical propositions are not true independent of these assumptions. Nonetheless, mathematics turns out to be a useful for modeling the world.
Causality is the principle that events are preceded by causes. More accurately, the principle of causality is that the universe is arranged into consistent logical patterns that are constrained by laws of physics. If the universe were acausal, the universe would have no structure at all, and the cosmos would be utterly incomprehensible.
If the universe follows physical laws, then it must be possible to deduce those laws from observation. In order to understand any structure in the universe (temporal, spatial or otherwise) we need to construct a mathematical model of that structure. Yet, for any finite set of observations, there are an infinite number of possible models that will be consistent with emprical evidence. We select models based on their ability to predict future observations (and, consequently, their ability to be falsified).
Language and Mental Processes
A priori, we might expect that our ability to reason is limited by our language. This was in some sense the position of Ludwig Wittgenstein and W. V. Quine. Similarly, one might call upon similar arguments about the nature and limitations of human thought to find loopholes in logical positivist arguments.
However, a posteriori (in light of experience) we know that we are thinking machines subject to physical laws. As such, there is no longer room for speculation about language or mental processes that might give sanctuary to superstition.
There are no absolute ethical principles that can be decided a priori. In other words, life is what we make of it. Rules for ethical behavior are dependent on our goals. What we commonly define as "good" is a consequence of our goal of a safe, stable society that maximizes individual liberty and the pursuit of happiness.
Coming soon: Why is philosophy important?