The
first two definitions are introductory, and everything that follows is
from my Philosophical
Dictionary:
Nature:
The totality of all living things (on earth), or the totality of all real things.
The term "nature"
is ambiguous, and redundant if one means the same by it as by "reality". But it
makes sense to use the term "nature" to refer to all living things on
earth, on the assumptions that, first, living things are distinct and
in some way more complex than dead things, and second, that it is at
least possible that life of some kind evolved elsewhere in the universe,
and possibly third, that such life probably is not quite of the same
kind as earthly living things.
Naturalism: In philosophy:
The thesis that there is nothing real that is not part of natural reality, or 
also or alternatively  that all phenomena can be explained in natural terms.
There are various other
definitions of philosophical
naturalism, but the common core is the rejection of the need or
cogency of supernatural explanations for natural things and events.
Some naturalists have been
deists, e.g. by
prefering the second of the given definitions, and by holding there is
or may be a god,
but his
existence is not necessary to explain anything in natural reality.
This Philosophical
Dictionary has been written from a point of view that is
naturalistic, indeed in both senses of 'naturalism' given.
One important reason for
this position is
that so extraordinarily much that has been explained and achieved by science,
including the enormous amount of scientific technology that is
currently involved in the lives and possibilities of everybody who is
alife, is completely lacking from all holy religious
books, religious texts, communications by religious prophets, etc.
If there is a benevolent,
allpowerful,
omniscient deity (or deities), then why did he in his goodness and
wisdom not supply a cure for cancer, spina biffida, polio, leprosy, or
any of the other awful medical ills that have afflicted mankind for so
many centuries and have produced so much human pain and misery? And if
there is a god,
why is there no decent physics, chemistry, biochemistry or
mathematics to be found in any of the statements attributed to
him?
Another important reason
for this
position, that is related to the previous point, comes in two moves.
First, all the religious
believers agree
on one thing: That all religions except their own are mistaken,
and therefore believe in something that is, properly speaking, fiction or fantasy. Why not
extend that position to all religions
instead of all but one: All religion  until proved otherwise, by a
logically valid
argument
with true premises  is (at
best) fantasy,
inspired by fear, wishful
thinking or would be false authorities?
Second, why assume more
than is necessary
to explain nature?
Nearly all men have agreed that there is a natural reality, made up of
living and dead things, and that they are part of this natural reality. And the
last several centuries have shown, and proved this in so far this is
possibly by a working technology based on scientific understanding,
that the only truly succesful schemes of explanation,
that work experimentally regardless of one's faith, if any, are
scientific, and in terms of hypotheses of
natural things only.
A third important reason
for naturalism is
that it neither denies what most men agree on (natural reality) nor
affirms what most men disagree about (religion): It seems one needs to
assume natural reality and some principles of natural and logical
explanation to explain anything at all; it seems that natural science,
based on logic, guessing and
experiments is by far the most succesful method of trying to know and
understand; and it seems nothing else is really needed or useful to explain
things and to invent working technologies.
A fourth important reason
for naturalism
is that so much of so many religions is
evidently false and outdated, when compared with modern science, and
when allowing for the ignorance of the original religious founders, who
usually lived many hundreds and sometimes several thousands years ago,
and that so much of what so many religious people have done to other
people in the name of their religion was immoral, totalitarian
or cruel.
Natural
Philosophy: General term I use for my
own philosophy, that may be seen as a kind of scientific
realism; until ca. 1800 "natural philosophy" was a near synonym
for "science" as opposed to "metaphysics" and "theology".
The reasons for and general outline of Natural
Philosophy are given in this entry and in the entries Natural Logic,
Natural
Realism and Rules
of Reasoning:
Philosophy, so
the Shorter Oxford English Dictionary on Historical Principles tells us
is
1. (In the original and
widest sense.) The love, study, or pursuit of wisdom, or of knowledge
of things and their causes, whether theoretical or practical.
2. That more advanced study, to which, in the medieaval universities,
the seven liberal arts were introductory; it included the three
branches of natural, moral, and metaphysical philosophy, commonly
called the three philosophies.
3. (= natural p.) The knowledge or study of natural objects and
phenomena; now usu. called 'science'.
4. (= moral p.) The knowledge or study of the principles of human
action or conduct; ethics.
5. (= metaphysical p.) That department of knowledge or study that deals
with ultimate reality, or with the most general causes and principles
of things. (Now the most usual sense.)
6. Occas. used esp. of knowledge obtained by natural reason, in
contrast with revealed knowledge.
7. With of: The stude of the general principles of some particular
branch of knowledge, experience or activity; also, less properly, of
any subject or phenomenon.
8. A philosophical system or theory.
9. a. The system which a person forms for the conduct of life. b. The
mental attitude or habit of a philosopher; serenity, resignation;
calmness of temper.
This is as clear a definition as any, and I
shall presume it for philosophy. It also immediately poses a problem we
have to give some sort of initial answer to.
The
fundamental problem of presuppositions
If we want to know or
study "ultimate reality" (whatever that
will turn out to be), what may we or may we not presuppose?
This is a relevant question, if only because it seems that whatever we
do presuppose will have some influence on whatever we come to conclude
while also it seems we cannot conclude anything without presupposing
something: To reach any conclusion one needs some assumption(s).
It is clear that any
human philosophy is the product of people who already know and suppose
something, in particular some Natural Language to reason and
communicate with. So any human being concerned with philosophy uses and
presumes in some sense some Natural Language.
Natural Language
Hence we start with
presuming some Natural Language

consisting of words and statements
(both sequences of letters) that
enable its speakers to represent things
to themselves and to other speakers by pronouncing or writing down the
words or statements that represent those things

in which, at least initially, we can
frame philosophical questions and provide philosophical answers, where
we take "philosophy" in the sense just given, or in brief as: The
search for rationally tenable explanations for all manner of things;

and it is also clear that each and every
human being that speaks a natural language therewith has a means to
claim about any of its statements that it is true or not, credible
or not, necessary or not, and much more ("probable",
"plausible", "politically correct", "sexist", "morally
desirable" a.s.o.)
For the purpose of doing
philosophy, in the sense of seriously attempting to ask and answer
general questions, some natural language must be considered given,
for without it there simply are no questions to pose or answer. And
indeed, all philosophy, including any philosophy that concludes there
is no human knowledge, in fact presumes some natural language.
This is itself a fact of
some philosophical importance that is often disregarded. One of its
important applications is to show that people who propound skeptical
arguments to the effect that human beings cannot know anything, or
cannot know anything with certainty, or cannot know anything with more
or less probability than its denial (these are three somewhat different
versions of skepticism,
that also has other variants that are less easy to refute) must be
mistaken, since thy all presuppose some natural language known well
enough to state claims that nothing can be known.
It should als be noted
with some care that a natural language is not given to human beings in
a completely clear, perfect and obvious way (since, for example, it is
very difficult to clearly articulate the rules of grammar one does use
automatically and correctly when speaking it), but it is given to start
with as a tool for communication and expression that may be improved
and questioned, and that enables one to pose and answer questions of
any kind.
Natural language is, in
other and somewhat technical words, a heuristic, i.e. something
that helps one find out things. What other heuristics do come with
being human? Every Natural Language includes many terms and many 
usually not very explicit and articulated  rules that enable its users
to represent their experiences, and to reason or argue with
themselves or others. We shall call this body of terms and rules Natural Logic.
Natural Realism: A minimal metaphysics
that most human beings share may be called Natural Realism and
stated in terms of the following fundamental assumptions:

There is one reality that exists apart from what human beings think and
feel about it.

This reality is made up of kinds of things which have properties and stand in relations.

Some of these things, properties and relations are invariant, at
least for some time, and therefore predictable.

Human beings form part of
that reality and have experiences and fantasies
about it that originate in it.

All
living human beings have beliefs and desires about many real
and unreal entities, that are about what they think is
the case in reality and should be
the case in reality.

All living human beings have very similar
or identical feelings, sensations
and beliefs and
desires in many ordinary similar or identical circumstances.
Some assumption like
natural realism is at the basis of human social interaction, at the
basis of the law, and at the basis of promises,
contracts and agreements, while the last of the assumptions I used to
characterize Natural Realism amounts to an assumption of a
shared human nature.
We shall assume Natural
Realism is also at the basis of philosophy, at
least initially, firstly, because we must assume something to
conclude anything; secondly, because even if we  now or eventually 
disagree with Natural Realism it helps to try to state clearly what it
amounts to; and thirdly, because it does seem an assumption like that
of Natural Realism is involved in much human reasoning about
themselves and others, and about language, meaning and reality.
Finally, since this
implies not only a logical and rational approach to knowledge but
also an empirical and scientific approach, we assume, to start with,
and until we have found better rules, next to logic, Newton's "Rules
of Reasoning" in his "Mathematical Principles of Natural
Philosophy".
Natural Logic: A collection of terms and rules that
come with Natural Language that allows us to reason and argue
in it.
1. Introduction
2. Rules
of Natural Logic
3. Brief
assessment of the Rules of Natural Logic
4. A
realist context for Natural Logic
1.
Introduction
In any Natural Language
there are the elements of what may be called its Natural Logic:
Examples of such logical
terms are: "and", "or", "not", "true", "false", "if", "therefore",
"every", "some", "necessary", "possible", "therefore", "is the same
as", "any (arbitrary)" and "one (specific)", and quite a few more.
Examples of such logical rules, that are here formulated in
terms of what one may write down on the strength of what one already
has written down (pretending for the moment that natural language is
written rather than spoken) are: "If one has written down that if one
statement is true then another statement is true, and if one has
written down that the one statement is true, then one may write down
(in conclusion) that the other statement is true" (thus: "if it rains
then it gets wet and it rains, therefore it gets wet") and "If one has
written down that every soandso is suchandsuch, and this is a
soandso, then one may write down that this is a suchandsuch" (thus:
"if every Greek is human and Socrates is a Greek, therefore Socrates is
human").
We presuppose Natural
Logic in much the same way as we presuppose Natural Language:
as something we have to start with and precisify later, and that
may well come to be revised or extended quite seriously, but also
as something that at least seems to be in part given in more or
less the same way to any able speaker of a Natural Language: In it
there are a considerable number of terms and  usually
implicit  rules
which enable every speaker of the language to argue and reason, that
every speaker knows and has extensive experience with.
Again, it does not follow
that these rules and terms are clear or sacrosanct. All that I assume
is that they come with Natural Language and are to some extent
articulated in Natural Language and understood and presupposed by
everyone who uses Natural Language.
Three very fundamental
assumptions about the making of assumptions that come with Natural
Logic are as follows  where it should be noted I am not stating these
assumptions with more precision than may be supposed here and now:
1. Nothing can
be argued without the making of assumptions.
2. An assumption is a statement that is supposed to be true.
3. Human beings are free to
assume whatever they please.
These I suppose to be
true statements about arguments and
people arguing, where it should be noted that especially the third
assumption, factually correct though it seems to be, has been widely
denied in human history for political, religious, philosophical or ideological
reasons: In most places, at most times, people have not been
allowed to speak publicly about all assumptions they can make.
Four other assumptions
about argumentation that should be mentioned here are:
1. Conclusions are statements that
are inferred in arguments from earlier assumptions and conclusions by
means of assumptions called rules
of inference, that state which kinds of statements may be
concluded from the assumption of which kinds of statements
2. Definitions of terms are assumptions to the effect that a
certain term may be substituted by a certain other term in a certain
kind of arguments
3. Rational argumentation about a topic starts with
explicating rules of inference, assumptions and definitions of terms,
and proceeds with the adding of conclusions only if these do follow by
some assumed rule of inference.
4. A statement is true
precisely if what it says is in fact the case.
The first two assumptions
need more clarification than will be given here and now, but, on the
other hand, again every speaker of a Natural Language will have some
understanding of setting up arguments in terms of assumptions,
definitions and rules
of inference, and drawing conclusions from these assumptions
and definitions by means of these rules of inference.
The third assumption,
when compared with the normal practice of people arguing, entails that
mostly people do not argue very rationally, at least in the
sense that all too often they rely in their arguments on rules of
inference, assumptions or definitions they have not explicitly assumed
yet have used in the course of the argument. (Often such assumptions
are made because of wishful
thinking.)
The fourth assumption is in
fact a definition of the term "true" that expresses
an idea that is older than Aristotle, who seems to have been the first
to formulate it clearly and stress its central importance. It needs
also more explanation than will be given here and now, but it seems to
clearly express the meaning of "true" people use when they discuss
ideas about reality that are personally important to them.
2.
Rules of Natural Logic
There are the following Rules
of Natural Logic one may propose for the logical connectives I
mentioned above: : "and", "or", "not", "true", "false", "if",
"therefore", "every", "some", "necessary", "possible", "therefore", "is
the same as", "any (arbitrary)" and "one (specific)".
To formulate them, I in
fact extend English with variables: Terms that are not words of
the language, but which may be substituted by any arbitrary term of a
certain kind of the language, in certain conditions.
Also, the spirit in which I
propose and state these rules is both tentative and confident  tentative,
in the sense that I believe many speakers of English, when thinking
about it, will agree they often reason and argue according to such
rules for the logical connectives as follow, if possibly not quite the
same, while I know this is an empirical generalization; and confident
in the sense that all of the rules I propose have more precisely
formulated and conditioned counterparts in formal logic, where these
counterparts are provably valid in the
formal semantics
for these logical rules.
In what follows, capital
letters X, Y and Z are variables for English statements, and undercast
letters x, y and z are variables for English terms. A formula in what
follows is an English statement in which one or more terms have been
replaced by variables. For clarity's sake I surround the formulas that
are claimed to be true or not true by dots, which may be taken for
parentheses  which I avoid to make things look less hairy.
General rule of
evaluation
It is true that if .X. is
any English statement, then .X. is true or .X. is not true.
This is a somewhat precise
form of the notion that English statements are true or not true, that
shows how "true" is used. See: Bivalence.
Rules for not:
not1:
If .not X. is true, then .X. is not true.
not2:
If .not X. is not true, then .X. is true.
not3: If .X. is not true, the .not X. is true.
not4: If .X. is true, then .not X. is not true.
The formula .not X.
corresponds to English expressions like "It is not so that X" that may
have quite a few forms in English that also have some ambiguities that
are not further considered here. See: Negation.
Rules for and:
and1:
If .X and Y. is true, then .X. is true.
and2:
If .X and Y. is true, then .Y. is true.
and3:
If .X and Y. is not true, then .X. is not true or .Y. is not true.
and4: If .X. is not true or .Y. is not true, then .X and Y. is not
true.
It is not intended to state
a minimal number of rules, though it is intended that all rules that
are stated are both intuitively valid and
formally valid when made more precise in formal logic. See: Conjunction.
Rules for or:
or1: If .X. is true and
.Y. is any English statement, then .X or Y. is true.
or2: If .Y. is true and .X. is any English statement, then .X or Y. is
true.
or3:
If .X or Y. is not true, then .X. is not true and .Y. is not true.
or4: If .X. is not true and .Y. is not true, then .X or Y. is not
true.
Note that here and in the
rules for and the term "true" distributes nicely over its
components. Also, it is noteworthy that the following rule
orD:
If .X or Y. is true, then .X. is true or .Y. is true.
is not valid
probabilistically, though it is valid in standard binary logic. A
counterexample is e.g. if .Y. = .not X. and 0<pr(X)<1. See: Disjunction.
Rules for ifthen or
implies:
implies1: If .X implies
Y. is true, then .not X. is true or .Y. is true.
implies2: If .not X. is true or .Y. is true, then .X implies Y. is
true.
implies3: If .X implies Y. is not true, then .X. is true and .Y. is
not true.
implies4: If .X. is true and .Y. is not true, then .X implies Y. is
not true.
The reason to write "implies"
is to have a oneword counterpart for "if .. then ". Some
readers may have some intuitive difficulties with the proposed rules
for implies, and they are right in the sense that these exist. Even so,
under the assumption that all statements are true or not true, and one
states no further conditions, the rules stated for implies preserve
most intuitions and validate most arguments involving them one
considers intuitively valid. See: Paradoxes of implication, Implies.
Rules for if and only if
or iff:
iff1: If .X iff Y. is
true, then .X implies Y. is true and .Y implies X. is true.
iff2: If .X implies Y. is true and .Y implies X. is true, then .X iff
Y. is true.
iff3: If .X iff Y. is not true, then .X and not Y. is true or .not X
and Y. is true.
iff4: If .X and not Y. is true or .not X and Y. is true, then .X iff
Y. is not true.
The reason to write "iff"
is to have a oneword counterpart for "if and only if".
According to the rules proposes, statements involving "iff" can be
equivalently replaced by statements involving "and" and "implies". See:
Equivalence.
Rules for not and
predicates:
not F1: If .x is F. is
not true, then .x is not F. is true.
not F2: If .x is not F. is true, then .x is F. is not true.
not F3: If .x is not not F. is true, then .x is F. is true.
not F4: If .x is not not F. is not true, then .x is F. is not true.
This concerns new notation:
".x is F." is a formula for any English statement in which occurs "x"
while the rest of the statement  all of it except all occurences of
"x" in it  are referred to by "F", which is termed a predicate while
"x" is termed a subject.
The "is" locution is meant as a help for intuition and provides one
instance of the type of statements covered.
Rules for is the same as
or =:
Id1: It is true that .x
= x. is true.
Id2: If .x = y. is true, then .y = x. is true.
Id3: If .x = y. is true and .y = z. is true, then .x = z. is true.
Id4: If .x = y. is true and .x is a F. is true, .y is a F. is true.
The reason to write "="
is to have a oneword counterpart for "is the same as" or "is
identical to", which also has the merit of being widely known from
arithmetic and algebra.
Also, there is new
notation: ".x is a F." is a formula for any English statement in which
occurs "x" while the rest of the statement  all of it except all
occurences of "x" in it  are referred to by "F". The "is a" locution
is meant as a help for intuition and provides one instance of the type
of statements covered.
The rule Id4 in which it
is used formulates a form of the rule of substitution of identities,
which in general terms must have some restrictions, that are not
further considered in the present context. See: Identity.
Rules for some or there
is:
some1: If .some x is F.
is true, then .one x is F. is true.
some2: If .one x is F. is true, then .some x is F. is true. (*)
The expressions "some" and
"there is" are called existential quantifiers. In standard
logic, they are taken to be synonymous, and here they are given with
the help of the idea of "one" or "one (specific)", the force of which
is that if  say  some persons are English, then one specific person
must make the claim true.
(*) It should be mentioned that in formal logic there are some
conditions here to be added, usually to the effect that the term for
the one specific soandso one introduces is new to the
argument (for else one might make claims that combined with earlier
claims are false). See: Existential Generalization.
Rules for every or all:
every1: If .every x is a
F. is true, then .any x is a F. is true.
every2: If .any x is a F. is true, then every .x is a F. is true. (*)
The expressions "every" and
"all" are called universal quantifiers. In standard logic, they
are taken to be synonymous, and here they are given with the help of
the idea of "any" or "any (arbitrary)", the force of which is that if 
say  any person is English, then any arbitrary person must make the
claim true.
(*) For the rule named every2 a similar restriction applies as to the
rule some2.
See: Universal Generalization.
Rules for any
(arbitrary):
any1: If .any x is P. is
true, then if .y is a constant. is true, then .y is P. is true.
any2: If .any x is P. is not true, then .one x is not P. is true. (*)
These rules concern in fact
the usage of variables and constants, and seem to be a little more
general or basic, intuitively, than the quantifier rules, in that they
also apply to context in which occur variables without quantifiers. The
any1 rule makes this explicit, and the any2 rule has again a
condition that relates to earlier occurences of the term. See: Variables.
Rules for one (specific):
one1: If .one x is P. is
true, then .any x is not P. is not true.
one2: If .one x is P. is not true, then .one x is not P. is true.
These rules supplement
those for any, which involve them via the any2 rule. See: Variables.
Rules
of inference:
ergo1: If .X. is true
and .X implies Y. is true, then one may write .Y. is true.
ergo2: If one may write .Y. is true, then there is a .X. such that .X.
is true and .X implies Y. is true.
These rules concern the act
of inference, which is here taken to be the form of writing down
a statement. The general idea of ergo1 is that ergo conforms
to implies with the added permission that one may write down
what is implied by an implication if the antecedent of the implication
is true. The general idea of ergo2 is that anything one may write down
(in this fashion, according to logical rules) must be such as to be
provable from some true hypothesis. See abduction, and
note that this does not mean one needs to shift back to ever further
assumptions, since if .Y. is an initial assumption one may use the
provable formula .Y implies Y. to conform to ergo2. See: Inference.
Rules for necessary:
nec1: If .X is
necessary. is true, then .X. is true.
nec2: If .X is neccesary. is true, then .X is possible. is true.
nec3: If .X is necessary. is not true, then .not X is possible. is
true.
One often claims soandso
is necessary and suchandsuch is possible. These are much like
quantifiers, but with some extra twists that are not discussed here.
See: Modal Logic.
Rules for possible:
pos1: If .X. is true,
then .X is possible. is true.
pos2: If .X is possible. is true, then .not X is necessary. is not
true.
pos3: If .X is possible. is not true, then .not X is necessary. is
true.
These supplement the rules
for necessary, which involve them via nec2 and nec3. In standard
modal logic either is definable in terms of the other, in terms of
theses that may here be summarized as: "It is necessary that X" =def
"It is not possible that not X" and "It is possible that X" =def "It is
not necessary that not X". See: Modal Logic.
3.
Brief assessment of the Rules of Natural Logic
As remarked, the rules are
meant to schematize rules of reasoning with logical connectives that
for everyone who speaks English must seem familiar and sensible, if
perhaps not fully precise or adequate for one's personal use in some
arguments.
Furthermore, they are
informed by formal logic: In fact, such rules as I proposed cover the
fundaments of Propostional Logic, Quantified Predicate Logic,
the theory of identity, and Modal Logic. And if the
reader is interested, there is much more to find out about these
topics, in more precise forms and terms, in mathematical logic
and
philosophical logic.
Also, anyone is free to set
up one's own set of rules for logical connectives or indeed any term in
English. Two reasons to try to do so are that it may clarify one's
intuitions and help to explicate and abide by rules one in fact uses.
There are also a
number of things left out, in particular rules for set theory, and
rules for propositional
attitudes. The intuitive basis of the rules for set theory in
English are English arguments with nounlike expressions and with
common and proper names. The intuitive basis of the rules for
propositional attitudes in English are English arguments with
attitudinal terms like "believes", "desires", "knows" and many more.
4. A
realist context for natural logic
It seems that most
users of most natural languages presuppose a metaphysics I
shall call Natural
Realism. This also provides the context for the above Rules of
Natural Logic, or indeed for other or more such rules, though it is not
really necessary, since on may differ about metaphysics while agreeing
about the rules of logic and language that one uses to argue about
metaphysics.
However, one of the
things which makes it intuitively easier
to make sense of assignments of the term "is true" to formulas is the
assumption of some reality
in which are the things (and possible properties, qualities, relations,
structures, numbers, fields, situations ...) that make one's formulas true if they exist
and false if
they don't.
Logically speaking though, even this may be replaced by a mere hypothesis,
inroduced to clarify one's terms and statements in logic: One speaks as
if they concern some Universe
of Discourse, that if made an explicit assumption may contain or
lack anything one pleases, at one's own discretion, limited only by the
demands that the rules be precise enough to unambiguously assign true
or not true to formulas, that are either provably consistent,
also with respect to other rules, or at least not known to be
inconsistent.

Notes
[1]
I have now been saying since the end of 2015 that xs4all.nl is systematically
ruining my site by NOT updating it within a few seconds,
as it did between 1996 and 2015, but by updating it between
two to seven days later, that is, if I am lucky.
They have claimed that my site was wrongly named in html: A lie.
They have claimed that my operating system was out of date: A lie.
And they just don't care for my site, my interests, my values or my
ideas. They have behaved now for 1 1/2 years as if they are the
eagerly willing instruments of the US's secret services, which I will
from now on suppose they are (for truth is dead in Holland).
The only two reasons I remain with xs4all is that my site has been
there since 1996, and I have no reasons whatsoever to suppose that any
other Dutch provider is any better (!!).