It would be nice to know something for certain, wouldn't it?
We should be able to easily find examples of things that we know without a doubt.
Let's start with something we can all agree on: that there is a world outside of our individual selves,
the world we all share together, full of objects.
Simple, right? Let's call this outside world reality.
Now, let's come up with a fact we can assert about our claim: that the world and the things we see in it is reality.
To clarify a bit more on what we'd like to assert,
let's use the term sense-data to refer to all the impressions of reality that we receive through our senses.
That is, sense-data is the name we give for all sensations like color, sound, texture, smell, and the like.
Now our claim is that the sense-data we receive and feel is identical to true, objective reality.
Can we really say such a thing?
That reality and all the things in it are their sense-data?
With closer inspection, we find that any claim as to what an object intrinsically is breaks down quite easily.
Scientific experiment tells us nothing is a color on its own;
what appears to us as the color of an object is really an interaction of many factors.
For example: the presence of enough light, the presence and quality of reflective surfaces,
the chemical composition of the object, the condition of our eyes, and so on.
The color of an object is not independent of all these factors outside of the object itself.
Unfortunately for us, this same logic applies to all phenomena of the senses.
The texture of an object wholly depends of how big the subject is in relation to the object being touched,
the sound produced by an object depends on the receivers location relative to the sound waves and their perceptivity of different frequencies,
and on it goes.
To further illuminate the problem we now have,
we say the sense-data we receive is the object's appearance,
and the "physical" or "objective" object represented by the appearance is reality.
So what then can be said about reality and all the things that it contains?
At this point in our investigation,
all we can say is that to say what something is is a lot less straight-forward than we first thought.
Turns out our claim was not so simple after all!
Let's try to work with another claim in our search for certainty.
We can be certain that, as we observe the world outside of ourselves,
we are perceiving sense-data.
This seems to be one of the few things that can be posited without argument
(try arguing against it, and see how far you get!).
But, can we assume the sense-data are signs of a "physical",
independent-of-ourselves existence?
Put another way, is solipsism,
the belief that only your mind truly exists, valid?
There actually is no logical process we can use to prove this is the case!
But, it seems likely that it is. Why?
We can safely believe so because other beings behave as if they have their own internal processes,
much like the ones we observe in ourselves.
Thus, by the principal of coherence* (the idea that our beliefs should not contradict each other),
and the lack of evidence to believe otherwise,
it seems likely that beings and objects outside of ourselves have their own "physical" reality,
and the "physical" reality corresponds to the resulting sense-data.
It is possible this is wrong! '
We are only talking about probability here.
However, there aren't any strong reasons to believe that it is wrong,
and reality achieves higher coherence when this is assumed.
Thus, we can safely believe that matter exists.
*: Though the given reason for belief (the principal of coherence) may not be as strong as desired,
it is the best we can do.
The principal of coherence is based on the belief that reality forms a connected, harmonious system.
When we apply this principal, we try our best to connect our beliefs together.
We reject those beliefs that clash, and accept those with the highest likelihood of possibility.
The principal states that the likelihood of error in accepting an idea is decreased the more harmonious our worldview becomes with its inclusion.
This is the most that philosophy can provide.
If this does not satisfy, the reader may be interested in reading about
the laws of thought.
A very interesting subject! We touch on it again in Chapter 7, but it's not fully covered in the scope of this book.
Ultimately, there isn't anything we can definitively, with 100% certainty, prove about the nature of matter or reality,
since all we can experience is the sense-data.
At most we can say it is likely that the "real" object is similar to the appearance of the object.
This is also true of space and time (eg. there is a "physical" space in which the "real" object inhabits,
but what we as individuals experience is our own private space, our own private sense of time,
which affects how we perceive these "real" objects).
The curious (and mathematically adept!) reader can explore the idea in physics called
general relativity if they want to know about this particular topic.
Unfortunately, this is as far as philosophy can take us on the subject.
However, something we should consider here is that,
while we don't have any real certainty about the nature of reality at it's deepest level
(what things truly are),
we can say with greater certainty what the spatial arrangements of objects,
or the temporal order of events, with more confidence than other attributes of objects.
For example, statements like "this building is larger than that building," or "this car arrived before that car," etc.
This isn't to say that the order of the sense-data of an event is the same as the order of the events themselves,
as when we see lightning before we hear thunder, even though both are started simultaneously.
Our individual position may change how much later we experience an event,
but the order of events is preserved
(at least locally! In relativistically relevant conditions, the order of events are not fixed,
but Albert Einstein didn't complete his theory of general relativity until after this present book was published!).
So what we find here is that, although it is difficult to say what objects are,
it is much easier to say with confidence how objects and events relate to each other.
Thus, the most we can say about the nature of matter itself is that, though we cannot truly know it,
it likely correlates with our sense-data.
So much for certainty!
So if we can't say anything definitive about reality outside relations, maybe we're not approaching the problem correctly?
Maybe reality isn't what we thought it was after all? Maybe it doesn't even exist!
The concept of idealism,
or the idea that reality is not actually made of matter at all but is only an idea in some mind,
perhaps has some solution for us.
Idealism has a long history, with many different philosophers sharing ideas and arguing about it.
In general it rests upon the idea that,
"We can never truly judge that something with which we are not acquainted exists",
where acquainted here means to have experienced with our own senses (we're going to use this term a lot!).
This is likely false,
as we often take as "true information" things we ourselves have not and can not experience,
such as any study of current or historical events.
The roots of idealism started in theories of knowledge
(a study known as epistemology),
and what it means to "know" something.
Earlier thinkers (such as Bishop George Berkeley)
posited that it's only sense-data that we can claim to know,
and asserted from this that since an individual can only truly say they know sense-data they experience
(since we have seen that we can not know the object which causes the sense-data),
that it is only things that exist in minds that can be known.
Some early idealists say that the "mind of God" is the mind which knows the universe,
in order to allow for objects to exist without anyone actively looking at them.
Much of the idealist argument hinges on what it means to be "in" a mind.
They make an equivocation between the act of apprehending something,
and the object of the apprehension itself, by labeling both as "ideas."
But, can't we easily believe that just because something is apprehended in the mind,
it doesn't mean the object of apprehension is a mental object as well?
There isn't a strong reason that this has to be the case.
This leaves idealism as perhaps not the most tenable philosophy out there,
but it's arguments still deserve to be understood in order for us to look for stronger ones.
OK, so we found that there isn't much we can say about the nature of reality,
and we've now been introduced to epistemology, the study of how we know things,
via a short diversion into idealism.
Perhaps there's something to this epistemology business, something we can find some certainty about?
Thankfully, here there is some steady ground!
To start, let's say there are only two types of knowledge: knowledge of things, and knowledge of truths.
START ADDING DIAGRAM OF ALL TYPES OF KNOWLEDGE: things and truths, acquaintance and description,
induction and deduction, a priori and a posteriori, synthetic and analytic, etc.
Knowledge of truths involves judgements, things which we can believe are true,
but of which we can be wrong about
(we'll talk more about knowledge of truths later).
Knowledge of things, on the other hand, can be further broken down
into either knowledge by acquaintance or knowledge by description.
To know an object by acquaintance is to experience the sense-data with our own senses, first-hand.
(To be super clear, what we know is the sense-data, never the object itself, since, as we noted above, this isn't possible.)
Let's imagine a table real quick.
What we can say with this new concept of knowledge is that what we know of the "real" table is only knowledge by description,
as the sense-data describes the table, but isn't the table itself.
The sense-data of the table we know by acquaintance, since we directly apprehended it.
It turns out that all knowledge has knowledge by acquaintance as it's lowest foundation.
Knowledge by acquaintance not only refers to what is known from sense-data,
but also includes things like memory, introspection, and self-consciousness,
experiences that are only accessible to ourselves.
Strangely enough, it is hard to say definitively that we are acquainted with ourselves.
It is likely we are, but without a strong definition of "Self" (which you're welcome to try and formulate!),
it seems probable that we can only say we are "self-acquainted."
Outside of these aforementioned acquaintances with particular things,
there's another category of acquaintance: acquaintance with universals,
also known as abstract ideas or concepts.
This will also be discussed later.
Now, all things not known through knowledge by acquaintance are known by description.
Common words and names are descriptions, and the things they describe, once we become familiar with the word,
we would then say we know by description (the descriptions themselves we would know via acquaintance!).
The descriptions used for a single thing can vary,
and necessarily do vary between people who are thinking of the same object,
since they may have different descriptors.
The words we personally use for things will be the descriptions we know by acquaintance,
the things that were at some point shown to us either through direct sensory experience, reading or being taught about it.
Fundamentally,
every proposition which we can hope to understand must be composed wholly of constituents with which we at some point became acquainted
(again, these acquaintances can just be descriptors).
When we are using words to communicate, we are using them as we personally know how these words work,
which at some point we learned through knowledge by acquaintance, either through reading, or by being taught.
But what we are most often acquainted with are just what the words describe, not what they are direcly describing.
To summarize what we have so far:
knowledge by description is how we can know things beyond ourselves and what we directly experience,
and knowledge by acquaintance is how we know sense-data and our inner experiences exist.
This may come off as very obvious and pedantic, but the ideas will be built up in upcoming chapters.
From the things we know to exist (via acquaintance),
can we make inferences about the existence of other things?
We must be able to,
since we so often rely on knowledge by description, not acquaintance, to know anything, right?
Conside the following: why do we all believe the sun will rise tomorrow?
Well, we believe this because it has always been true,
and outside of that we even can point to physical laws of celestial bodies as proof.
But we can also question why we believe the physical laws to be eternal.
The principal we use to justify this is called the principle of
induction, which can be stated as the following:
1. When thing "A" has been found associated with thing "B",
and "A" has never been found without "B",
then with the greater the number of cases we find "A" and "B" together,
the greater the chance a new case of "A" will also have "B".
2. Eventually the number of cases of association between "A" and "B" will reach such a high number,
that new cases of "A" will approach a certainty that "B" will also be present.
We should note here that the inductive principle here cannot be proved or disproved by experience.
If, for example, we believe that all swans are in general white,
due to our experience of only ever seeing white swans,
then seeing a black swan doesn't change our belief that most swans are white.
And also, notice that induction doesn't actually give us full certainty of anything.
What it does give us is the ability to argue certain events will occur in the future due to experience.
It is also the principle of induction which tells us that someone we met today is likely to be the same person when we meet them again,
and that scientific principles, when found, continue to operate as we've seen them to.
It's hard to imagine a world in which induction is not a base assumption,
as perptual doubt over the continuity between sense-data would never allow for an accumulation of facts
Nothing could be learned!
Imagine never understanding that a person you've met over and over is the same person,
or that the route back home isn't constantly changing!
Every moment would be completely unique from the previous one, which could only lead to total confusion.
All knowledge which, because of our experience, tells us something about what we haven't experienced,
is based upon our belief in induction, a most necessary basic assumption.
Let's continue with our study on how it is we know things,
since it appears we actually have made some progress in gaining a bit of certainty.
So, when we believe general principles
(such as "all birds have feathers", "worms only come out when it rains", or, more abstractly, 2+2=4),
what we are actually doing is using induction.
We realize that what's particular about the principle is irrelevant,
and can use just the general part in any specific instance.
Arithmetic is a great example of this idea.
We first see that two apples and another two apples come together to makes four apples,
and then remove the particulars of the principle (the apples), and arrive at 2+2=4.
This new general principle can then be applied to two sets of two bananas,
two sets of two playing die, etc.
Basic logic of the form "if this, then that," follows this very same pattern.
If we then want to argue that these general principles are true,
we must use certain logical principles.
These are almost self-evident principles that people must believe if any argument or proof of any kind is even possible.
These special principles are sometimes called the Laws of Thought,
and are often stated as the following:
1. The Law of Identity: Whatever is, is.
This law is how we assert that we don't need to doubt the experience of sense-data, sort of re-formulation of the inductive principle.
2. The Law of Contradiction: Nothing can both be and not be.
Put another way, an object can either display an attribute, or that attributes negative, but not both.
3. The Law of the Excluded Middle: Everything must either be or not be.
This is the same as saying there is no "middle" state between existing and not existing.
The Laws of Thought are important because when we think while applying them,
we think truly.
They help us determine what is true, and are implicitly believed by pretty much everyone.
We cannot even conceptualize about truth or what is true without a priori believing in these principles.
When we say a belief is a priori, we mean that the belief is known to be true without having experienced it in reality.
We can compare this against a posteriori beliefs, which do require experience before we can validate the belief.
a posteriori knowledge is what is given from the inductive sciences,
a priori will be discussed in later sections.
The argument over how it is we can know things led to one of the great historic conflicts in philosophy,
the debate between two different schools of epistemology:
the empiricists and the rationalists.
The empiricists believed knowledge comes from experience, and expirence alone (ie. we are at birth a tabula rasa, a blank slate).
The rationalists believed that in addition to experience there are also ideas we know independent from experience.
Today, most evidence sides with the rationalists,
as we have shown above that there are some ideas (like the Laws of Thought) we must maintain but cannot prove empirically,
as the whole concept of proving something "true" entirely relies on them.
We call those general ideas which cannot be proved in any empirical sense,
but are needed all the same as foundational assumptions, a priori principles.
These a priori ideas can be caused by some experience but not proved,
as in our demonstration of arithmetic with the apples.
The empirical experience caused us to be aware of the general principle,
and allowed us to develop an a priori, general mathematical concept.
Despite the necessity of a priori knowledge, the empiricists were right about one thing:
nothing can be known to exist except with experience,
there are no a priori principles that can help there.
If we wish to prove something exists, and we don't have direct experience with it,
we must include at least one thing in our proof which we do have direct experience with.
Put another way, all knowledge which asserts the existence of something has to be empirical.
But just as we learned before, this object of experience can be known via description,
as in history book or spoken testimony,
it doesn't need to be a first-hand observation.
Outside of the Laws of Thought, there are many forms of a priori ideas.
Ethical judgments are included in this category, which we can intuitively understand,
since it seems obvious that the existence of something isn't enough to tell us if it is "good" or "bad".
Pure mathematics too is a priori knowledge, though the empiricists have argued otherwise.
The empiricists argue that mathematics is given its power by repeated exposure to it's operations,
while it can be seen that repeatedly seeing 1+1=2 is not how our confidence in math is created
(Math is a deductive, not an inductive, science!).
Deduction, which uses a general principle (sometimes called an axiom) to prove a specific instance,
(and can almost be seen as the reverse version of induction,
which goes from specific instances to a general principle),
is what it is called when we apply our general a priori ideas to real specific instances.
When we want to argue for the existence of an a priori idea, deduction is most useful.
In arguing for empirical generalizations, induction gives a greater probability of truth.
So what we've learned here is that general principles are created either as a priori concepts via deduction,
or are known thru empirical observation, and then proved inductively.
You may be wondering after the last section how it is that a priori concepts
(outside of math) can even be useful, since in many ways they appear "made up".
To help in their study of these ideas, epistemologists created two categories of a priori knowledge:
analytic and synthetic knowledge.
Analytic knowledge is of the type where the predicate, or the assertion,
of the claim includes part of the identity of the subject.
For example, the statement "A bad poet is a poet" is a claim where the subject,
or what the assertion is about, is a bad poet,
and the predicate is that this subject "is a poet".
The predicate only affirms part of the identity of the subject.
Put another way, the predicate is in some way redundant information, given the subject.
a priori judgements were considered by the rationalists to all be of this form.
They believed that this meant we could determine all valid predicates,
all possible assertions, of an a priori judgement just by analyzing the subject of the judgement closely.
Now, synthetic knowledge is of the type which the predicate cannot be derived from the subject.
This type of knowledge includes arithmetic and geometry,
and is best explained by demonstration.
Take the example the philosopher Immanuel Kant
used in his original argument on this topic, the basic equation 7 + 5 = 12.
If this statement was analytic, that would mean that the sum of 12 (the predicate) is contained in the individual values of 7 and 5 (the subjects).
This, however, is not the case, as 7 and 5 need to be put together before 12 is the result,
12 is not a part of the individual subjects at all.
An operation needs to be performed on the subjects before the predicate is known,
and we cannot say that the operation is a part of the individual subjects themselves.
Since the predicate (the result) cannot be gleaned from the individual subjects,
we call such statements of math synthetic, not analytic.
The truth of such statments must be synthesized with other outside claims.
To put it succinctly, an analytic statements truth value is contained in the statement itself,
while a synthetic statements truth value requires outside knowledge.
The discovery of synthetic a priori knowledge was a new development in epistemology,
and for Kant it created a big problem.
How is it that we think of math as certain, and not merely probable, if it is synthetic?
If, by being synthetic knowledge, it requires investigation outside of it's subjects for us to determine it's truthiness,
how can it also be true without experience?
If it requires some sort of empirical study to know the statement is true,
how is it also non-empirical, how is it a priori?
Synthetic and a priori? Sounds contradictory!
This problem was a major curiosity for Kant.
In an effort to explain how this was possible he maintained that in our empirical experience,
there are always two elements at play:
the physical object and the sense-data of the object, in the same way as we discussed above.
One of these elements is a physical reality, and the other is transformed by our own psychology.
He believes that the base sensory aspects (texture, color, etc.) of the sense-data are given by the "real" object,
but what we as observers supply is the objects relations within space and time,
since he felt all people have an intuitive, a priori understanding of these concepts
(general relativity has shown this is not quite the case,
but as stated above, general relativity is a much later development).
Kant's reason for this belief is that since our knowledge of space, time
causality, and comparison is a priori,
and since there can be no experience without these concepts,
that they must be an innate, human preconception,
and inseparable from our nature.
He considers the "thing-in-itself" as the unknowable reality of the object,
and the "phenomenon" of the object to be the sense-data mixed with our a priori assumptions.
In this way, he shows that the "thing-in-itself", a subject that is impossible to truly experience,
cannot supply the "predicate" of our beliefs about them, and thus any judgement about them is synthetic.
To reiterate, he believed that all judgments about reality must then be necessarily synthetic.
However, Kant finds that math and logic are included within that class of assumptions we supply to any observation,
and as such are known a priori, thus they must be synthetic a priori judgements.
But by claiming that math and logic finds it source within human nature,
we can find a refutation against Kant's views.
If we believe that human nature is a changing entity like the rest of the natural world,
and if mathematics is an innate concept to us (not to mention time and space),
that it would make it also a changeable entity.
But can it be the case that 1 + 1 ever equals anything other than 2?
There's an enduring, eternal quality to math that Kant's idea that mathematics is tied to human nature does not account for.
It seems then that Kant's view of mathematical concepts unduly limits the scope of what they can claim.
It must be believed that when we make and apply mathematical concepts,
we are describing true reality, not just through the filter of human nature.
There is something universal about our synthetic a priori concepts,
not just math but concepts like the law of contradiction as well.
The reason for the general applicability of synthetic a priori judgements must be due to other, non-changing reasons.
Now that we have seen that there are some general ideas that are seen because of experience,
but are not derived from experience, perhaps we need to study these ideas a little more closely.
The study of these ideas leads to what are known as universals.
The study of universals can be traced back to ancient Greek philosopher Plato,
whose theorizing about them is still relevant today.
His strategy in discovering what are universals was to select some set of objects that have a commonality,
and by thinking about what each object shares with the other in the set,
he would arrive at the pure universal, or idea, as he liked to call them.
In Plato's sense, an idea is not purely an object of the mind, nor is it an object of sense,
but exists in some new, previously unforeseen way.
Universals do not and cannot exist in the empirical world,
however, real objects partake of and use universals.
Because they do not exist in our world empirically,
universals have a kind of eternal quality,
which for Plato felt made them even more real than our world of sense-data.
He maintained that when we talk about things in our world of sense,
we only truly talk about the universal quality of these things.
This line of thinking quickly becomes mystical in nature, but Plato's thought does start in logic,
and as such can be still be useful to us without resorting to mysticism.
For those allergic to any mysticism, it may also help to just view universals
as a particular element of language.
Before moving further ahead, let's define some of Platos terms so we understand what he's talking about.
Particulars are whatever is given in direct sensation
(what we can see about an object in the empirical world),
while universals are any qualities which can be shared by many particulars,
and are not directly visible as objects of sense.
So in language, particulars are referenced using proper names and pronouns
("Leonard Cohen", "the girl in the red dress", "Trinity College", etc.),
while universals are referenced using general nouns ("islands"),
adjectives ("smooth"), prepositions ("below"), and verbs ("weeping").
We find that no sentence or proposition can be made without using at least one universal.
Maybe this is just some quirk of our human-created language,
but if we think about it there really aren't many things that can be communicated
without the use of any universal!
The closest we can get is a sentence like "I like this", but the word "like" is a universal,
since "I" may like other things, and other people also like things as well
(Remember, universals are any commonalities between many particulars).
This also means that all truths (being expressed in language) involve universals,
and so it follows that knowledge of truths require an acquaintance with universals.
Historically, the types of universals studied are the ones that can be exhibited by a single object ("green"),
not the types in the form of prepositions and verbs ("above").
This is likely because prepositions and verbs require relations between objects,
and as such always felt too contextual or incomplete to exist on their own.
Metaphysical philosophers put their attention instead toward those universals named by adjectives and substantives,
like objects and their sensory qualities.
This one-sided focus would ultimately result in beliefs like
Spinoza's monism,
the idea that there's truly only one object in the universe and relations aren't real.
Monism, and
Leibniz's related philosophy monadism,
arise from too much focus on these singular universals in the form of adjectives and substantives.
Even though these and other philosophers argue against the existence of relational universals,
it can actually be shown that it is easier to prove the existence of universal relations
than it is to prove universal adjectives like qualities.
Those that argue against relational universals believe that when we think of a universal (say "green", for example),
we are reasoning against a particular example we've seen in reality,
say a green leaf.
However, this example already relies on the abstract idea of a universal,
since how do we know that this particular object is "green"?
We have to admit that it's because it has the same quality as other green things we've seen,
which would then show that there is a universal relating these objects together!
Now that it seems we can say universals exist, let's now prove they're not only mental constructions.
By this we mean to prove that universals exist independent of the thinking being.
It feels easy to prove that "Chicago's Loop is West of Lake Michigan" is a true statement no matter if someone
is currently thinking it.
What's tricky is to say that the relation "is West of" exists in the same way a singular object exists.
One argument for the independent existence of universals is that if they weren't independent of observers,
no two people could think about the same exact universal, but we clearly do (consider the "is West of" example).
Additionally, no single person could think of the same universal twice,
as a person's thinking at one moment is a different act from the same thought at a different moment.
It is of course true that these acts are possible; two people can think of the same universal,
and a person can think of the same universal many times over without it's meaning changing.
It is the commonality between all these thoughts which is what is meant when we call something a universal.
The fact that they don't exist in time like most things is not to say universals don't exist,
we instead say they subsist, timelessly.
We can call this mode of existence as subsisting in the world of being, versus just existing.
This particular world is where metaphysics lives, like math, logic, relations,
and the rest of the synthetic a priori propositions we saw last chapter.
We can now safely say that universals are real, despite their immateriality.
(Editor's note: can we not argue that universals are just a function of language?
If we are OK with saying that "being" isn't real due to the constant change in nature,
how is it we can say the relation between "natural", empirical objects is static?
Isn't the relation "The lake is west of the forest" in constant change?
Position is in constant subtle change, just as being is.
Universals are just a name for abstractions.)
Universals can become known through three different methods: knowledge by acquaintance, knowledge
by description, and through a new method, neither by aquaintance nor description,
that we'll see at the end.
Knowing universals by acquaintance is easy to comprehend;
take the color green for example.
If we see something green (a leaf, perhaps), and then we see some green grass,
the commonality between them reinforces our idea of what the universal green is.
These universals describe sense-data, and are the easiest universals to understand.
Another type of universal is the relation,
and is understood in a similiar way to the sense-data universals:
namely, that we see a commonality between two examples of the universal (take above, for example),
and the more examples of this relation we see, the more we become acquainted with it.
This same method applies to relations in time,
and the universal of resemblance, as well.
With our new concepts,
we can now describe a priori knowledge much better than before.
We can now say:
All a priori knowledge deals exclusively with the relations of universals.
Put another way, all knowledge of things that are known without experience,
always fits the category of knowledge on how abstractions relate to each other.
This is true even if we "sub in" particulars in the place of universals,
as in when we say "Two things and any other two things is four things".
This statement can be understood even if we aren't aware of any particular examples,
even though particular examples can be implied from the statement.
To know the statements empirical truth though,
we need to actually experience the particulars.
We know a priori that two things and two things make four things,
but we do not know a priori that if Brown and Jones are two,
and Robinson and Smith are two, then Brown and Jones and Robinson and Smith are four.
More simply, our general principal is a priori,
but its application requires an empirical element.
Let now contrast a general a priori judgement with an empirical generalization,
since these are different claims.
We can understand a statement of either sort as soon as we understand it's constituent parts.
For example,
the phrase "All people are mortal" is understandable as soon as we know the words "people" and "mortal."
As far as understanding the statement,
it is not necessary to meet all people in order to know what the statement is saying.
With empirical statements, the evidence for the truth of the statement requires particular instances.
In our example, that would be in the fact that there are numerous examples of people dying,
and no instances of people living past a particular age.
The truth content of the assertion has nothing to do with some universal,
abstract connection between the words in the statement themselves,
like we do with mathematical statements.
With empirical generalizations,
it's possible that the empirical evidence that supplies the truth changes over time.
For the statement "All people are mortal",
science may find that people are necessarily mortal without requiring the evidence of people dying
(genetic necessity, for example).
This would only mean our original empirical assumption is now subsumed by a wider assumption,
which is a common occurence in the progress of science.
This does supply a greater degree of certainty in our generalization,
but not a different kind of certainty.
As in, our certainty is still inductive in nature,
it is still derived from individual instances.
There is an interesting point to be made about general a priori statements,
which is that it is entirely possible to make true statements about certain instances,
without being able to know of any instance that fits the claim.
As an example, due to infinite nature of integers,
we can say "All products of two unknown integers are over 100".
Any two numbers we do think of will by necessity not fit the statement,
yet we know the statement to be true.
This type of logical,
a priori generalization is what's at play when we assert the existence of other people's minds,
or the existence of actual physical object and not just sense-data.
We know the statements to be necessarily true,
without being able to directly point to empirical examples.
With all this in mind, and keeping in mind the previous chapters,
we can say that all our knowledge of truths depends upon intuitive knowledge.
(Editors note: Can we not think of general a priori statements,
especially those of math, as just rules of the game?
We created some abstractions, and some rules of relations,
and we have consensus about how they work,
and sometime these rules take us far beyond the empirical world?)
So, just what is intuitive knowledge?
We find that if we look at all our beliefs, even the most mundane,
and interrogate the reasons for these beliefs,
and just continue this interrogation for all subsequent beliefs in a chain,
we will eventually come to a belief that appears self-evident,
an intuitive belief,
and at that point we discover that it isn't possible to find more essential, underlying beliefs.
In all these intuitive beliefs, we will find that the inductive principle is at play,
that belief in how repeat exposures to something increases the chance we will seeing it again,
up to a near certainty.
The inductive principle, like other similar logical principles (remember the Laws of Thought mentioned earlier?),
is not capable of being more fully explained,
or found to be inferred from some prior belief,
it is only self-evident, it is only intuitive.
Intuitive self-evidence isn't just a property reserved for logical principles, however.
Ethical values are also commonly of this type of intuitive knowledge.
Another very important type of intuitive knowledge are the "truths of perception",
or the self-evidence of truths immediately derived from perception.
However, when discussing these truths,
it must be noted that we are not discussing the actual existence of the sense-data.
but of beliefs arising from the existence of the sense-data.
Sense-data on its own is never true or false,
its just is.
The judgments derived from the sense-data is where truth and falsity can arise
(truth and falsehood will be discussed in a later chapter).
The intuitive truths we obtain from sense-data are different from the sense-data themselves.
The kinds of intuitive judgments we can make about the sense-data we perceive come in two kinds.
The first is simply asserting the existence of the sense-data,
that the perception of the data is occurring, "I see a cloud", etc.
The second is any claim about the relations of sense-data, ie.
"the spot on the stone is brown".
Both of these claims cannot be broken down any farther;
there's no deeper reason for belief than the occurrence of the sense-data itself.
However, they may contain levels of doubt though,
just as in the next class of intuitive judgments, memory.
Memory seems to have a continual gradation of self-evidence,
in that more recent memories appear the most self-evident,
while the memory of things and events farther in the past have less self-evidence,
and more doubt.
These degrees of self-evidence in memory is a quality all intuitive knowledge share.
We now see that intuitivity is not a quality that judgements simply have or don't have.
The more self-evidence some knowledge has, the more "true" it is,
and the less doubt there is about it, but this occurs in gradations.
Truths of perception and immediate experiences have almost no doubt at all,
while memories further and further in the past have increasing levels of doubt,
as in any perceptions that are harder to pin down.
Is that blue-green color more blue, or more green?
Another complication with intuitive knowledge:
it is possible to believe in the existence of false memories.
In these cases, what is believed is not the subject of the memory,
but something associated with it, such as the repeated assertion of it's truth.
To reiterate, intuitive knowledge has as its basis no possible deeper reason for their belief,
and that the truth or falsehood of our intuitive knowledge can come in degrees.
Unlike with knowledge of things, knowledge of truths have an opposite: error.
With knowledge by acquaintance, things can either be known or not known.
There is no such thing as erroneous knowledge of things by acquaintance;
we can't be acquainted with not sense-data!
With knowledge of truth however, there is a dualism with knowing.
As in, we can believe false things as well as true things.
Is there a way we can distinguish erroneous beliefs from true beliefs?
No completely satisfactory answer is possible unfortunately,
but progress can be made in the right direction.
We can at least start by distinguishing what we mean by truth and falsehood.
There are three requisite points that a theory of truth must fulfill:
1. A theory of truth must be able to admit its opposite, falsehood.
2. It must be able to show that truth and falsehood are properties of beliefs and statements,
and not of matter.
Without the existence of beliefs, there would be no such concepts of truth and falsehood.
3. It must be able to show that the truth or falsehood of a belief depends upon something outside the belief itself.
They are properties dependent upon the relations of the beliefs to other things,
not upon any internal qualities of the belief itself.
For example, for the belief that Bertrand Russell was born in 1872,
the truth of the statement is found in historical fact,
the truth is not dependent on the belief itself.
To account for these points,
previous attempts at a definition of truth revolved around the idea of coherence,
an idea we've worked with earlier.
In this framework, a falsity would then fail to cohere to our beliefs,
and truth would be able to fully cohere to the greater system of truth.
This view has two great difficulties.
One, why should we believe there is only be one coherent body of beliefs?
We can believe in the possibility of a fantasy writer creating a whole fictional past for the world
which could still perfectly fit into our current understanding of the human history.
Thus, coherence as a definition of truth on its own fails,
because there is no proof that there can be only one coherent system.
The second difficulty is that the idea of coherence presupposes the truth of the laws of logic.
To determine truth, we would need to assume the laws of logic (like the law of contradiction) are already true;
the rules themselves cannot be established by coherence.
Thus, coherence cannot be used as the meaning of truth,
though we can still find it as a good test for truth,
at least after a certain amount of truth is already known and accepted.
A better definition for truth could be correspondence with fact.
The relationships required for a definition of truth given above must be made of the constituent objects
of the belief and the act of believing itself.
It would help at this point to break down the elements of a belief.
There is a subject of the belief (the one that holds the belief), and the objects of the belief.
We can call the subject and object(s) together the constituents of the belief or judgement.
Different orders or configurations of the constituents would create different judgements, so the order matters
(eg. "I love cats" is a different belief than "Cats love me", despite the same objects of belief).
Among the objects of the belief must be a relation between the other objects (ie. Harry loves Sally).
For a true belief, the relation between the objects actually exists.
In a false belief, the relation does not exist.
A true belief corresponds to this complex relation (a fact), a false belief has no such correspondence(there is no fact).
Thus, we can see beliefs rely on two requirements:
1. Beliefs depend on minds for existence.
2. Beliefs depend on facts for truth.
So does our new criteria helps us determine what is true and what is false?
We would think that to know something is to have a "true belief".
However, that definition would allow for the knowledge that became true but was just a guess,
which we would not consider real knowledge.
We don't want to accept as "knowledge" believing it's going to rain tomorrow,
and then being proven right, if it was just a random guess.
Is knowledge what is validly deduced from true premises?
We would have to add to our definition of knowledge that premises cannot only just be true, they must be known as well.
But this creates a circular definition, since how can "known" premises be part of the definition of knowledge?
We can use this formulation as definition of derivative knowledge, which we can compare against intuitive knowledge.
Derivative knowledge is knowledge which is validly deduced from premises known intuitively
(we'll return to intuitive knowledge shortly).
This definition would not allow knowledge gained from reading though.
Beliefs from reading could very well be true (as they often are),
but no logical inference occurred,
since the belief only came from the understanding of the words written down.
Thus derivative knowledge is probably best described more as probable opinion,
and is otherwise hard to precisely define.
So what about intuitive knowledge then?
This also proves tough to define,
as all of our knowledge of truths will necessarily have some degree of doubt.
How can we deal with this fact?
Intuitive knowledge is knowledge that is "self-evident",
which we have touched on earlier.
Let's also review our other versions of knowledge:
We have knowledge when we hold a true belief, and we also have knowledge from perception,
which we have been calling knowledge by acquaintance.
For any complex fact, there are two ways for it to be knowledge, for it to be known:
1. By means of judging the constituent parts of a fact as true.
2. By means of perceptive acquaintance with fact itself.
All sense-data facts of the second kind (mental facts) can only be known by one person,
the person experiencing the sense-data (unlike universals, which can be known by acquaintance by many).
Being acquainted with the fact in this way, we can say the truth of the fact is self-evident,
and the fact is guaranteed to be true.
This is intuitive knowledge.
Keep in mind though, a fact guaranteed to be true doesn't mean judgements about the fact are always true,
since you can read the fact wrong or misunderstand in some way.
Self-evidence of truth can also occur in degress,
such as in perception that occurs in gradations.
For example, when listening to a car drive away,
there are moments that you can self-evidently and undoubtedly hear the car,
but after a certain a point you can be sure you no longer do hear the car.
So in between, there are moments when you think you can still hear it,
but aren't entirely sure.
Probable opinion is what we call our beliefs in which there are less degrees of certainity in the beliefs truthiness.
Finally, we call knowledge that which we believe that is both true and is learned intuitively or derived in a logical process from intuitive knowledge.
Error is largely the same, except in one obvious detail: the belief is false.
This means even if the belief is intuitively learned, it can still be in error.
Probable opinion is that knowledge which we believe but isn't supported by the highest possible degree of self-evidence.
Most of what passes as knowledge is probable opinion.
We rejected coherence as a definition of truth earlier, but we can use coherence to judge a body of probable opinions.
The more coherent a collection of probable opinions are, the more likely they are to be knowledge.
This is how the scientific process works;
if a single idea fits coherently in a system of probable ideas,
the entire system becomes more probable.
This is about as much as we can say on knowledge!
Now that we have done our best to describe what philosophy can best do for us,
we should ask what philsosophy is not capable of doing for us.
Many of those interested in philosophy are interested in finding answers about big questions concerning the universe.
Unfortunately many of the questions cannot be answered philosophically.
Hegel was one such philosopher who attempted to answer some of these big metaphysical questions we may be concerned with.
His main belief was that any "piece" of reality is just a fragment of the "Whole" of reality,
and that necessarily these pieces can be fit together and used to help understand reality.
As an illustration, it's as if reality was a jigsaw puzzle, and each fragments edges can help us understand the greater
puzzle that is the Universe.
In a physical sense there's definitely a logic to this, but Hegel applied this same process to ideas as well.
In his view, if we forget the incompleteness of an idea, we become involved in contradictions.
These contradictions evenutally turn the idea we're considering into it's opposite, which Hegel calls the antithesis.
The only way to solve the contradiction is to find a new, more complete idea that synthesizes
the original idea with it's opposite.
For Hegel, the synthesized idea will also be incomplete, and the process of "thesis, antithesis and synthesis"
continues until we reach the "Absolute Idea", an idea that is complete, totally rational, and without opposite.
He claims the Absolute Idea is the only full description of Absolute Reality.
From this follows that Absolute Reality forms one single harmonious system that is wholly rational and spiritual.
Any appearance to the contrary is due to our fragementary view of the Universe.
Hegel's philosopy is difficult to parse fully,
but one fundamental tenet that we can see just from the above example is that what is incomplete,
must not be self-subsistent,
and that the incomplete requires support from other things to exist.
To elaborate, in Hegels philosophy whatever has relations to things outside of itself must contain some reference to these
outside things within it's own nature.
For example, a man's nature includes his memories, his knowledge, etc.,
and without the objects which constitute this part of his nature,
he could not be what he is, ie. he is a fragment.
This point view requires a definition of the "nature" of a thing to mean "all truths about the thing".
This claim falls apart, as a truth about a thing is not part of the thing itself.
To know the "nature" of an object in Hegel's sense, we would need to know all it's relations to all other things.
But we'd still need to know the thing itself, without knowing its nature.
There's a confusion between knowledge of things and knowledge of truths when "nature" is used the way Hegel does.
As we've seen in prior chapters, we can know an object by acquaintance without knowing any truths about this object.
For example, we can know a toothache by acquaintance (as in, we have one), without having to go to a dentist
and learn everything there is to know about toothaches and its "nature".
This is all to say, we cannot deduce right from an object what it's relations to the rest of the universe might be.
An object's "nature" in the Hegelian sense cannot be determined from the object itself.
An object may have relations to other objects in the the universe,
but we cannot know them from the object itself, we must see these relations with other methods.
Ergo, we cannot prove the Universe forms the perfect system of Hegel's philosophy.
Modern philosophy tends to show that apparent contradictions were illusory, and that there isn't
a priori methods to prove what must be true.
For example, space and time, appear to infinite in extent, and in divisibility.
Philosophers however, have provided arguments to show that there cannot be an infinite collections of things,
and that this apparent infinitude of reality must be a contradiction.
Kant is one such philosopher who made this argument.
However, Georg Cantor has show mathematically that infinite collections are indeed valid and not contradictory,
showing that what was once seen as a contradiction is not the case.
It is becoming the case that many apparent contradictions were in reality just prejudices of human experience
and so-called "common sense", as in, our prejudices due to what we can empirically experience.
Now, our knowledge of what exists is separated from what can only be experience, and instead also includes
what things we can learn and infer from empirical experience.
To clarify, we must combine empirical experience with a priori principle like induction in order to all we can know.
Thus, philosophy and science do not greatly differ.
The fundamental characteristic that differs philosophy from science is criticism.
Philosophy examines critically the principles employed by science, and the principles assumed in our daily lives.
This criticism, however, must be limited.
A philosopher must not employ complete skepticism of all knowledge, as in that position there can be no persuasion.
The doubt and criticism a philsopher employs must be methodical, as in Descartes case.
The philosopher shouldn't aim to reject a belief for no apparent reason, but to criticise from a position of some
apparent evidence, in order to reduce error.
Some risk of error is always possible, as humans are fallible, but to promise more than this is not what philosopy advocates.
Is it worth our time to study philosophy?
Philosopy does not provide material benefits in the way engineering or physical sciences can. It is not "practical" in this way.
The study of philosophy only provides mental nourishment.
We can say the aims of philosopy is to provide a stable framework for the sciences,
to provide strong foundations through doubt and criticism of our prejudices and convictions.
However, as this may be the case,
philosophy has been better at asking the questions rather than answering them conclusively.
Some of this is due to the fact that once we do answer philosophy's question,
it no longer becomes philosophy, but a separate field of study entirely (astronomy, psychology, etc.).
It can be said then that philosophy's function is to just ask the questions.
Through philosophy we can see a vast possibility of answers, which can be freeing.
Our assumptions about life (given via upbringing, nation of birth, religion, etc.) may be challenged,
and through this challenge we can increase our knowledge and sense of possibility.
Philosophy can remove dogma from our lives.
It can also free us from our immediate, private life and allow us consider the greater world around us.
All acquisition of knowledge enlarges the Self.
Philosophy shows us that growth is obtained when we adapt the Self to our objects of study,
and not the other way around.
Knowledge is union of the self and the universe around it,
which is impaired by the desire for dominion.
The tendency for some philosophers to take man as the measure of all things,
that truth, space, time, and universals are constructs of the mind,
robs philosophy of its value, it's ability to de-center the philosopher.
The philosopher finds joy in every thing that magnifies the objects of contemplation.
Everything that depends on habit or self-interest distorts the object, and impairs the acquisition of knowledge.
A philosopher who becomes accustomed to the freedom and impartiality of contemplation will preserve
this same freedom in the world of action and emotion.
The impartiality learned through philosophy is in the world of the intellect a desire for truth,
in the world of action desire for justice, and in the world of emotion a universal love.