ME + me: Philosophy, Wittgenstein, Hertz and Leibniz
The Shorter Oxford English Dictionary on Historical Principles tells us is
This is as clear a definition as any, and we shall presume it for our subject. It also immediately poses a problem we have to give some sort of initial answer to.
fundamental problem of presuppositions
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.
For the purpose of doing philosophy, in the sense 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 philosophies that conclude 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 they 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.
Examples of such logical terms are: "and", "or", "not", "true", "false", "if", "therefore", "every", "some", "necessary, "possible" and many 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 so-and-so is such-and-such, and this is a so-and-so, then one may write down that this is a such-and-such" (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:
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 or philosophical reasons: In most places, at most times, people have not been allowed to speak publicly about all assumptions they can make.
Three other assumptions about argumentation that should be mentioned here are
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.
Next, it seems that most users of most natural languages presuppose a metaphysics I shall call Natural Realism. This may be stated in many ways, for example in terms of the following assumptions:
What this might mean precisely, especially what may be meant by the bold terms, will concern us later.
However, the present point is that 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.
We shall assume it 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 assumptions like those of Natural Realism are involved in much human reasoning about themselves and others, and about language, meaning and reality.
I shall presuppose Natural Language, Natural Realism and Natural Logic in what follows, and shall repeatedly turn to the issues what these assumptions all might mean in more precise (but at least equally intuitive and clear) terms and whether they are true, and if so, in what sense.
Philosophy and the making of mental models
The bias I admit to concerns especially two points, one ethical or moral and one scitientific or cognitive.
To start with the moral or ethical point.
It seems to me of fundamental importance to try to solve disagreements by rational argumentation that freely admit both human desires and human beliefs, that also involves the admission that most of the disagreements that exist between people seem to be based on the fact that there is only one world, in which all people live, about which different people may have different, often contradictory, desires and beliefs.
My assumptions have been chosen, among other reasons, to support this claim about how disagreements between people should be solved.
Someone who believes - for whatever reasons - that 'might is right' or that all human points of view, beliefs and desires are quite relative and only have validity, if any, in a personal and private way for the persons holding the beliefs and desires will probably have to disagree here or at some earlier point in the present argument.
To end with the scientific or cognitive point.
It seems to me that the most striking differences between human animals and other animals is that human beings have and develop language, culture and science, and that one of the things any philosophy should explain is how - scientific and any other kind of - knowledge is possible, found, extended, qualifed, repaired, given up etc.
My assumptions have been chosen, among other reasons, to explain scientific knowledge, the making and finding of which may be indicated thus, by a quote from Heinrich Hertz, that explains the fundaments of scientific reasoning. I will insert some numbers to make a few comments after the quotation
In endeavoring thus to draw inferences as to the future from the past, we always adopt the following process. 
We form to ourselves images or symbols of external objects; and the form which we give them is such that the necessary consequents of the images in thought are always the images of the necessary consequents in nature of the things pictured. 
In order that this requirement may be satisfied, there must be a certain conformity between nature and our thought. Experience teaches us that the requirement can be satisfied, and hence that such conformity does in fact exist. When from our accumulated previous experience we have once succeeded in deducting images of the desired nature, we can then in a short time develop by means of them, as by means of models, the consequences which in the external world only arise in a comparatively long time, or as the result of our own interposition. 
We are thus enabled to be in advance of the facts, and to decide as to present affairs in accordance with the insight so obtained. 
The images we speak of are our conceptions of things. With the things thenselves they are in concormity in one important respect, namely, in satisfying the above-mentioned requirement. For our purpose it is not necessary that they should be in conformity with the things in any other respects whatever. 
As a matter of fact, we do not know, nor have any means of knowing, whether our conception of things are in conformity with them in any other that this one fundamental respect.  (H. Hertz, "The Principles of Mechanics", quoted from p. 349-350 of "Philosophy of Science" Ed. Danto and Morgenbesser).
This is an exemplary clear quotation (first published in 1899), that does require some remarks, mostly elucidatory.
 Here the two points to notice are that to find more (supposed) knowledge we must use present (supposed) knowledge (where the addition of "(supposed)" is meant to indicate that the knowledge may be not so much absolutely irrefutable knowledge as hitherto experimentally supported guesses, and that all claims to knowledge may be revised), and that one central point about knowledge is that, if reality is as we suppose we know it is, then our knowledge enables us to say how reality will behave in the future and has behaved in the past, where it may be assumed that normally we do not have any other means to arrive at judgements about the future or the past than by making guesses in the way indicated by Hertz.
 Hertz seems to be correct in this claim, and it should be noted that he himself discovered electro-magnetism by using the present way of reasoning.
 Here the best analogy is that of a map and the territory it is a map of. If the map is accurate, the territory will be as the map says it is, and if the map is not accurate, then not. The relation discussed here will concern us a lot in what follows (and is known in mathematics as a homomorphism, probably best translated as 'having similar structures').
One important point to notice about this relation is that it is quite often exemplified in one's experience, namely if one sees two things that are similar, such as two people. This is important because some - one of the first was Kant - have claimed that one cannot know anything about what is not given in experience (see point  below) and others that there is no such thing as a relation of correspondence between a statement or idea and the facts represented by it.
 Here again there are two points to notice. First, ordinary experience works in the same way: we guess from our supposed knowledge - say: "I must have left it somewhere around here, some time ago, so since it doesn't move by itself it must still be around here" - and act experimentally on those guesses to support of infirm our assumptions - say: "Let's see. Ah, here it is!". And this often works. Second, since we may imagine what we please, we may and do indeed make mental maps or models of aspects of reality we think about, and proceed to support or infirm the assumptions that make up the model by comparing the consequences that follow in the model if the assumptions are true with the facts in our experience.
 Here we use in fact two probabilistic principles (that reduce mathematically to one and the same principle in probability theory and that conform to everyone's intuitions): First, if Q does follow from P, then if Q is false, P is is normally less probable than it was before finding Q false - theories with false predictions are less probable; and second, if Q does follow from P, then if Q is true, P is normally more probable than it was before finding Q true - theories with true predictions are more probable. (As the 'normally' indicates a little more should be said here, but this requires more probability theory than has been presumed here. But the reader can rest assured there are precise and strictly valid theorems of probability theory that correspond to the present points.)
Sofar, I have been in full - and admiring - agreement with Hertz, but his final remarks need some corrections, that will be more fully developed later in the text, when dealing with similar issues.
 Actually, we need to assume more, and normally scientists do assume more. The more they must assume must involve some principle to the effect (1) there are invariant relations in nature and (2) the guesses the scientist makes concern invariant relations. The reason invariant relations must be somehow assumed (where the invariance may be local and temporary, as a matter of fact) is that we need an assumption to the effect that the presumed facts of the theory we are testing experimentally will not unaccountably change while we're testing it. (It's interesting Hertz missed this assumption. Newton did not, as manifested by his 'Rules of Reasoning', that were included in the second edition of the 'Principia Mathematica Naturalis'.)
Incidentally, these invariant relations may be probability-distributions. Thus we may not know and have no means of knowing whether the next throw with this coin will come out head or tails, but we do know that if the coin is fair and no tricks are involved, the probability is 1/2 for either side. The invariance presumed here is the probability that of any and every fair coin that's thrown without tricks will fall half the time tail and half the time heads in any long series of such throws.
 This Herzian - Kantian - remark also is not quite true. First, we do have lots of evidence, in the form of very succesful technology based on and derived from science, that our presumption that there are invariant relations in nature is supported. And second we do have other means of knowing (or at least: rationally guessing, supported or infirmed by experimental evidence) what the real facts are, since we may make any assumption we please, and proceed to try to verify its consequences. To the extent these consequences are verified we may say that we know what reality is like - though it should also be clear that these claims that reality is thus and so always involve fundamental claims that go beyond the given evidence, while being supported by such evidence as one has - and indeed, that is the reason that there is something to test by experiment. (In this sense reality is rather like the backside of the moon before the days of space-travel. In these days it was also not rational, even if logically tenable, to claim that about the part of the moon one could not see there were no rational guesses, such as that it was much like the visible part.)
In case you are interested, there is
a lot more...
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