Here is at least one way that the Laws of Thought are commonly stated:

*The law of identity:*Any thing that is, is.*The law of contradiction:*No thing can both be and not be.*The law of the excluded middle:*Every thing must either be or not be.

Where I deliberately use various versions of the verb ``to be''
conjoined with ``negation'', the version of these laws given by modern
logicians might use ``be true'' and ``be false'', although these are not
precisely the same thing. Truth and Non-truth are much subtler concepts
than Being and Non-Being, and the latter concept pair is subtle *enough* to cause us no little amount of difficulty.

Note well that I say ``modern logicians'' in the paragraph above. In
some very deep sense mathematicians and philosophers and
logicians^{2.13} have advanced *formal logic itself* more in the last hundred
or so years than they did in the previous indefinite interval of time
preceding the late 1800's or early 1900's. Yet historically, systematic
analysis of our *understanding* of things began with these simple
Laws of Thought as expressed by the Greeks. That's an excellent reason
to postpone until a later chapter the discussion of formal logic per se
and concern ourselves with the *existential* analysis of a Real
Universe using the Laws of Thought themselves. After all, our ultimate
concern is with knowledge of a Universe that actually exists, and the
rules of logical inference are perfectly happy establishing *abstract relationships* between *abstract symbols*, often
relationships and symbols that ``exist'' only in our *imagination*,
that shadowy realm of looped experiential reality where we can
hallucinate, dream, and think of *six impossible things before
breakfast!*^{2.14}We will therefore begin our examination of Thought with the *concrete* instead of the *abstract*.^{2.15}

We will find that the concrete (as abstractly expressed by the Laws
above) is a bit mushy and hasn't quite set yet, but that it contains a
few hard nuggets that somehow must form a foundation for all
knowledge.^{2.16} Let us begin like proper scientists, even
though we really don't know what it *means* to be a proper scientist
yet, by being very, very skeptical. I mean, like, cynical.
Mistrusting. Doubtful. We will try to understand the Laws of Thought
in some sense that doesn't require *words* or other symbols by
chopping the words themselves apart and attempting to realize the
concepts in a way that is more *existential* than *analytical*.

To put us into the proper frame of mind, let us begin by *doubting*
all of these Laws. The fact that they are usually presented as *self-evident truths* should not deter us. First of all, they are *not* self-evident truths - we haven't even figured out what they *mean* as they are expressed in English (or for that matter in Greek, or
Hindi, or Hopi).^{2.17}
Second, a point that will be relentlessly hammered in this text is that
historically, a tremendous number of advances in e.g. mathematics,
physics, psychology, sociology, and really pretty much all of human
intellectual endeavor have come about when people *rejected*
``obvious truths'' and explored the consequences of *alternative*
``truths''. Being a physicist and knowing way more than is good for me,
I can even express *why* this is so in terms of optimization theory
on a rough (non-convex) landscape.^{2.18} ``Truth'' is often
analyzed in some convex region of this ``logical landscape'' in such a
way as to effectively ``lock'' analytic conclusions in some reasonably
self-consistent way to some optimum, where making *small* changes in
some logical argument yields immediate change away from optimal *truthiness*^{2.19} , allowing proponents of the accepted optimum to assert its
obvious and unquestionable correctness.

However, then along comes an *iconoclast* who makes a ``long jump''
in the underlying propositional space on the basis of some heretical
intuition or another, and the next thing you know all of human
understanding is *reorganized* around a *new* optimum - at
least until the next brilliant iconoclast comes along. Hence the
Copernican/Galilean revolution, hence the Newtonian (classical)
revolution, hence the non-Euclidean and non-Aristotelian revolutions,
hence the ongoing Gödelian revolution, hence the Relativity
revolution, hence the Quantum revolution, hence.... you get the idea.

Interestingly, as a teacher and researcher, I have long observed that it
is *dangerous* to *know too much* about any subject if one
wishes to *advance* that subject, just as (paradoxically enough) it
is dangerous to know too *little*. For example, physics (say,
classical Newtonian non-relativistic physics) is generally presented to
impressionable young students in an *overwhelmingly logical way*. A
logical calculus of being is developed and carefully connected to
everyday observations. Objects are assigned coordinates and causality
is formalized in terms of differential equations of motion that are so
overwhelmingly *perfect* and *internally consistent* that the
observation of an incredibly strong correspondance between this system
and everyday experience seduces the mind into saying ``Aha! This is it!
Truth!''

If this isn't enough, we enlist the Brain's own biochemistry and
hormonal system, designed to help us *survive in a hostile world*
where *fight or flight* can become necessary at any moment by *punishing* and *rewarding* students to a greater or lesser extent in
the various versions of Academe around the world according to how well
they *master* this system via *conditioned learning* as *if*
it really were *Truth*.

But of course it is not, only an approximation that *appears* to
work because of the relative scale of a single constant, because of our
silly insistence on viewing time as an *independent variable
indexing causal time evolution* instead of a *spatial coordinate of
essentially static events*, because of our insistence on the *idea*
that ``objects'' exist at all at specific points in space and time with
certain *``obvious''* requirements of continuity on the underlying
functional description of that ``existence''. All of which, alas, turns
out to not be the case.^{2.20} Small wonder, then, that we have to wait
for students to come along who are *a bit lazy*, who are *rebellious*, who are too stubborn or stupid to be properly conditioned,
who are unafraid to go all the way back to the beginning and start over
making *different* basic assumptions in order to precipitate one of
these conceptual revolutions.^{2.21} That
which is imagined to be ``known'' is a trap to our imagination from
which we can escape only by dint of immense effort and a certain amount
of pain.

When it comes right down to it, Truth is pretty much *Truthiness*.
Truthiness is a quality of knowledge assigned on the basis of *intuition* or *instinct* - ``from the gut'' - instead of on the
basis of rigorous logical analysis and connection to things like facts.
Very shortly we'll have you hanging out over the existential Pit of
Despair, where we will make the true but unprovable assertion that
logical analysis and what we consider to be ``facts'' are inventions of
our intuition, possibly supported by our instincts, and hence logical
analysis itself is illogical. With that understood^{2.22} we will now
proceed to analyze the *truthiness* of the Laws of Thought.

What *kind* of beast, we might start by asking, are these Laws? No
matter how self-evidently correct you might imagine them to be,
ultimately they are *semantic assertions* in a language, and (like
thought itself) exist only in the realm of our imaginations. To ``do''
anything with them we must imagine a set of definitions and a formal
reasoning process in a symbolic language in which the Laws are assumed
to be constraints on the symbolic objects about which we wish to reason.
Ultimately, such an *imaginary* reasoning process will take a given
set of *imagined* (and hence conditionally true) premises and reason
``correctly'' according to the rules to some given (necessarily
conditional) conclusion, where we defer until later just what this
process is and how it works.

Since we are making the whole thing up in our heads, we can therefore
perfectly reasonably ask whether or not we can *equally* well think
up *other* definitions and rules for a a symbolic reasoning process
constituting Laws of Thought in which the imagined objects of the
reasoning process *are not* required to strictly either ``be''
exclusively or ``not be'', with no middle ground possible. Maybe we
can, maybe we can't, but there is no harm in trying.

Although we won't discuss the details until later, we already have what
we need to develop the primary ideas of this book, neatly captured in
the observation that the process is *imaginary* and truths are at
best *conditional*. This means that there is a fundamental rational
disconnect between abstract rational systems and the real world that can
only be bridged by means of a system of axioms that permits us to relate
our symbolic conclusions to our instantaneous experience.

Subject to this whole raft of assumptions, if you are reading this at
all you are old enough and wise enough to know that the *real*
reason we adopt the Laws of Thought is that they seem to *work* to
describe our experiences trapped as memories of that which we call the
``real world''. It seems worthwhile then, to look at some of the *details* of that real world as revealed by our experience in the form of
experiments, as well different sorts of experiments with alternative
forms of reasoning systems. Our goal will be to see whether the Laws
above are really *assumptions* or whether they are instead *necessary truth* - not assumptions at all, but rather things that
cannot be *conceived* of as being any different.

Let us begin, then, by looking at a wee bit of physics.