In this post we'll look at that philosophical feature which mankind had been unaware of for most of human history (that we know of), which is that 3,000 year old manmade technology that quickly became the power-tool of the Western mind: Logic (see Aristotle's Organon). For the fact is that while reasoning comes naturally to all men, doing so methodically, and logically, does not, and until men began paying conscious attention to the process of what they did when reasoning, the key tool for doing that more effectively, and for verifying reason's results, remained undiscovered.
|Guarding against Fallacies is important, but not enough!|
It would be especially hard for anyone interested in Epistemology to treat Logic as a separate and distinct system, as Logic cannot be 'done' without paying due attention to the metaphysics it is derived from, as identifying what is, what is true, what you know, and what follows from that, are the fundamental requirements that must be known before Logic can be used to test an argument's validity. Any exercise in 'logic' which ignores whether the terms or propositions it is built from reflect reality, is a waste of time and intellectual effort, as logically it cannot be interested in Logic. Yes, the rules of Logic's most visible feature, the Syllogism, are used to validate your argument, but that's just a means to an end, the actual point of logic is to detect inconsistencies, errors, and contradictions in your thinking and in what it is you think you are thinking about, and that requires clearly identifying the nature of your terms, noting how one term actually relates to another, and whether or not your premises are in fact true, and support - or invalidate - your argument.
That's why this primary prerequisite for Logic isn't just a formality, it's the whole point of the process:
, and there's no point applying any of the other rules of logic, if you haven't first ensured that your terms and premises are true, as what results cannot be logical.
- Ensure that your terms are clear and unequivocal, and that your premises are true
Disclaimer - I'm no expert on Logic, and I'm not intending to teach it here, but only to point out the too often neglected fundamentals, without which you can have no real ability to be logical. If you are interested in learning Logic properly and fully, I can suggest a comparatively brief, and very readable introduction to logical reasoning, in Peter Kreeft's 'Socratic logic: A Logic Text Using Socratic Method, Platonic Questions, and Aristotelian Principles (the first few pages are excerpted here). In that, Prof. Kreeft points out that the rules of logic are, perhaps surprisingly, rather simple, for instance, concerning the archetypal syllogism:
'Socrates is a man,, he points out the immediate understanding which we should take from that argument:
all men are mortal,
therefore Socrates is a mortal man'
What may not be immediately obvious in that, is that the form of the syllogism enables us to either relate and order that knowledge into a hierarchy of what we know and how it relates to reality, or it exposes the gaps and breaks and errors in our understanding, both of which enhances and reflects our grasp of Identity, Knowledge, and Causality. How it does so is through the terms, propositions, premises, and the conclusion which they argue towards. What's implicit in the working parts of the syllogism, is that its structure reveals three different aspects of the reality being taken into consideration:
- "What are we talking about? "Man"
- "What are we saying about it?","That man is mortal"
- "Why is it mortal?", "Because man is an animal, and all animals are mortal, therefore man is mortal."
Those terms, propositions, premises and arguments, are concerned with the metaphysics of what is, and what causally follows from that, is what Logic exposes, as well as expressing what should and should not follow from that, through Ethics. If you have eyes with which you permit yourself to see, you should be able to see that when Sophists' attack causality, they are indirectly attacking logic, identity, truth, and your ability to understand and respond accordingly to them, as we saw with the relativist's 'my truth' being an attack upon truth and reality as such. It is through the logical process, that we see how our knowledge is consciously validated from the grassroots of reality on up, and extended through to the highest of abstractions formed from them, into solid units of understanding.
- Terms reveal essences (What a thing is)
- Propositions reveal existence (whether it is)
- Arguments reveal causes (why it is)
Not surprisingly, in the modernist's treatment of logic, as with the supposedly 'mathematically rigorous' symbolic logic (Prof. Kreeft gives an excellent explanation of why that is of little value in reasoning), that fundamental rule is rarely even mentioned, and is more likely ignored or evaded, because modernism fundamentally ignores and evades identity, causality, and existence itself. Play your word games all you want, but don't pretend that dressing such games up in the operational rules of logic could make them any more logical, than dressing a man up in women's clothing would make him a woman.
Elementary my dear Watson
The practice of attempting to 'do logic' by the technical rules while ignoring its overall purpose, often leads to one of the common excuses or *criticisms* of syllogisms, such as: "That just deals with deductive logic!', meaning that it's too simple, and also that deductive logic is somehow more obviously and perceptually *true*, and then that inductive or inferential logic deals with conjectures that we cannot ever be ultimately 'certain' of. Before we open ourselves up to the Inigo Montoya treatment, let's get clear on what the meaning of the words we're using, are:
Ok... so how different is Deductive logic, from Inductive logic? Well, seemingly very different, and yet not so different after all. You see, making inferences isn't as mysterious as modernists would like you to infer, and those who do so would like you to forget (or better yet, never realize) that all deductions, are themselves derived from inferences!
- Deductive reasoning progresses from general ideas to specific conclusions.
- Inductive reasoning starts with specific observations and forms general conclusions about them.
Look again at the classic example of deductive logic:
'Socrates is a man,The three Propositions that the syllogism is made up of, each of which has two terms, and form a premise about reality, with each building upon the previous one, are leading to the argument's conclusion that is and must be true - if it agrees with experience, and that is the key.
all men are mortal,
therefore Socrates is a mortal man'
To be logical, your basic logical units, the Terms used, and the propositions formed from them, must be clear, and unambiguous, meaning that there can be no doubt about what is being referred to (Identity). The 1st particular concrete term, is identified as belonging to the 2nd general abstract term, and all within the 2nd general term are related to the particular attribute of the 3rd term, forming the conclusion which clearly follows by demonstrating that there is a relationship between the 1st, 2nd, and 3rd terms. That integrated meaning causes the conclusions, and not the happenstance of a premise's position in an argument, or the surface rules it abided by, and modernity is fundamentally opposed to that understanding (more on that in coming posts).
One too common example that's given of inductive reasoning today, is this exceedingly poor example which was the very first result I received from a Bing search (from liveScience.com),
"The coin I pulled from the bag is a penny. That coin is a penny. A third coin from the bag is a penny. Therefore, all the coins in the bag are pennies."What this deliberately gives the impression of, is that induction is just a matter of happenstance and seemingly sensible conjecture of one thing that happens to follow another (Oh, Hello there Hume!), which is unreliable and easily invalidated by any unexpected 'black swan' event, such as the fourth coin coming out of the bag as a nickel - Oops! However the fact is that this is not a valid example of Inductive Reasoning, and is in fact only a hasty generalization (which is itself a logical fallacy - see #3 in '10 Commandments of Logic' pic above).
We can easily come up with a better and more appropriate example of inductive logic practically off the cuff, by looking at how the experience of different particulars, leads to a conclusion that relates to every particular instance, by way of a generalized abstraction of 'mortality':
"It's been observed that man requires food and drink in order to live and that he will die without them. In most climates, men require clothing and shelter to survive, and in too harsh conditions without them, even briefly, whether hot, cold, or excessively wet, will likely cause his death. Like other animals, man is subject to diseases which can cause his death, and man, as with other animals, becomes more frail and subject to disease by aging itself, which also eventually leads to his death. Man is also made vulnerable to death by any number of injuries and wounds that, whether sustained by accident or incident to his person, will cause his death. Seeing that there are numerous means for causing a man's death, and that death will eventually come to him even without obvious external cause, and that not only is there no evidence of any men ever having been impervious to fatality, all of the evidence gathered from every relevant direction, indicates that man cannot escape death, and so we infer that it is part of the identity of man that all men are mortal."Unlike the exceedingly weak example of the three pennies 'proving' that all coins in the bag are pennies by sequential happenstance, this example looks at what becomes an integrated whole through a variety of ways in which man experiences mortality, and inescapably leads to the conclusion that because of the nature of what we know man to be, we are able to infer that part of his identity is that all men are mortal.
The last words there, of "... all men are mortal", of course are what form the 2nd premise of the classic 'Socrates is...' example of deductive logic, and what you should infer from that, is that all such abstract terms are arrived at through the same inductive manner (soundly or unsoundly), which begin in experience, and rising up by abstraction to become accepted concepts - and inescapably lead to the conclusion that the premises used in Deductive logic, are derived from Inductive reasoning. The terms of a deductive syllogism are the answers at the end result of a process of inductive reasoning that created them, and while it can and does save time, it shouldn't be forgotten that it can and should be used as a means of making more plain any oversights or errors that might've been missed in the more detailed process of inductive reasoning.
To fully appreciate Logic and the benefits it reveals to us, we need to understand the nature of the reciprocal 'fact checking' role that is implicit in the complementary roles of deductive and inductive reasoning, which they'll perform for each other, if attended to diligently, in that - so long as you expect that to the best of your knowledge your premises & terms are true - if your deductions and inferences are technically valid, and yet the inescapable conclusion differs in some way from what experience actually shows, that's an indication that there are gaps or even errors in your assumptions and knowledge of the terms you're reasoning with.
For instance, the following example which abides by only the surface rules of the syllogism:
'Socrates is a Greek,, leads to a conclusion which does not agree with our experience which indicates that at least one of the premises are not fully sound and true, which should cause you to acknowledge that this argument inescapably 'proves' that something in 'what you know' is false.
All Greeks eat olives,
Therefore, Socrates eats olives.'
Discovering errors in your logical reasoning, by means of logical reasoning, is not a bug, that's a feature, and it means that there's more to learn in what you're thinking about, and it clearly shows you that your premises and possibly even your terms, need to be explored further, qualified, and possibly even entirely revised.
To ensure that our 'logically inescapable' conclusions don't become traps for us, we need to do our best to ensure that every step in our logic, and our understanding of its premises, and that its terms are clear and unambiguous, all fully comport with what is real and true. The rules for arranging terms and premises in a syllogism are an important part of the process of logical reasoning, but they do not substitute for the entire process which they too depend upon. That requires that you incline towards a wider view of your knowledge, and ensure that it is more than an arrangement of 'facts', and that there are good reasons to believe that the soundness of your knowledge, and the terms and premises derived from it, lead to, rather than are constricted by, the technical rules of the syllogism itself. By adhering to the primary rule, before, during, and after, we are able to learn from what we know.
Deductive Logic, and Inductive Logic, are two complementary and interdependent approaches to validating your reasoning, and you can bet that when people criticize logic as being 'too pat', or rationalistic, it's because they've allowed those terms to become divided from each other in their minds. It should come as no surprise that modernity was practically established upon pitting deductive and inductive reasoning against each other, they've a number of methods for confusing you into allowing them to do just that.
This issue came to the forefront with Hume, and then exploded in maximum density with Kant's reaction to him, but it is enough for now to know (we'll get into further details in later posts) that when you see the terms 'analytic vs synthetic', or in their more technically detailed form of 'a priori' vs 'a posterori', in either case you'd be wise to treat them as flashing red warning signs being used to divert you into taking the offramp of their '4th branch of philosophy', which is designed to lead you astray from what is, and what can be understood to be, real and true.
You should know that those lights are flashing red, whenever you see examples such as this:
'A Bachelor is an unmarried man' and 'Grass is green', and they're attempting to force you to exit onto modernity's epistemological offramp, through those 'analytic'/'synthetic', or 'a priori'/'a posterori' terms just mentioned, which they assert are only 'true' (scare quoted as this is the means of reducing Truth to small 't' truths') either by definition alone, or through empirical evidence.
Before looking closer, how they typically define these terms are, that Analytic or:
"A priori claims are those you can know independent of experience", or is 'contained by it' (as 'unmarried' is 'contained' by 'bachelor') while on the other apparent hand, a Synthetic or:
"a posteriori claims are justified based on experience"If something about those statements seems unsettling, congratulations, your internal B.S. detector is working well, and you can see the issue by asking 'What is this, How do I know it, What if anything should I do about that', yourself.
We can and should say that, and without advancing a materialist position, it is true that there is nothing that we can know of this world, independent of experience. The word 'Bachelor' was not magicked into our minds from somewhere beyond time or space, we know that a bachelor refers to an unmarried man, and because through experience we know what a man is, and we know what marriage is, and that 'Bachelor' is the word we use to identify a man that is not married - it is self-evident that the word, its terms, and its premise, are all derived from experience.
The same goes for their other favorite examples, that the sum of degrees in a triangle is always 180* is 'true in every universe', because we understand from experience the nature and properties of a triangle. Likewise with Number and numbering, as far from numbers being mysteriously ethereal concepts, they are what we arrived at after having abstracted the particulars being counted - apples, oranges, spears - away from the quantities being handled, we were able to give the names of 'one, two, three' to them, as a means of greatly simplifying the counting of them.
Yes, numbers show up in the darndest of places, but that's because quantities of this and that is all there is... everywhere! No part of 27÷9=3 exists outside of or prior to experience, and in case you've forgotten, learning that the answer to what 27 divided by 9 is, is devilishly difficult to get to - ask any 1st grader to verify that for you. It's only after you've understood what a number is, and what particular numbers refer to, and after you've experienced working through and counting it out a few times, that it gets easier. Yes, numbers, math, can be applied anywhere in place and time, and would apply whether or not people existed... by whichever intelligent creature existed that was able to learn the concept from experience. Don't fall for the 'a priori/a posterori' con, it is purely philosophical sleight of hand, and it is intended to take something from you - one of your most important handles on reality. Whatever example is waved in your face, don't buy into their conceptual Three Card Monty game - concepts are applicable in nearly every scenario we can imagine, but that does not mean that we came to know any of them through any means other than from experience.
Note: In recent years there've been attempts to dodge this, by objecting that "What makes something a priori is not the means by which it came to be first known, but the means by which it can be shown to be true or false" (Baggini), meaning that once it's been learned, we no longer need to refer to experience, to know what a triangle is, to which I give all the respect which is due that argument in my reply: B.S.! Someone who has somehow never seen or heard of a triangle, will not 'know' it by saying the word 'triangle', and until you ask them to imagine the shape made from three straight lines, laid end to end with the last connecting back to the first, they will then understand it, from having had that experience of imagining it, or you can show them a triangle and after having experienced seeing it, they'll recognize it... from that experience.
There are many technical differences between what I've lumped together here as being roughly equivalent between 'analytic vs synthetic', 'a priori' vs 'a posterori', but they are differences of degree, not kind, and the ugly fact is that people are working very hard to discredit your ability to apprehend reality, and they will try to confuse the issue of what is, and is not real, but their efforts are no more worthy of trust than those of the Three Card Monty dealer - don't fall for it. After cutting through all of the dense verbiage, what they're doing is attacking both Identity and Causality, and they're doing so in order to capture your mind - decline to accept their 'hypotheticals' - they're trying to bounce you right on out of the real world. I'd advise against accepting their invitation.
As we've already seen with the premise that 'man is mortal', when we examine our experiences, we don't simply infer a conclusion from a sequence of observations, as the lame example of taking coins from a bag asserted, rather, as we saw with 'man is mortal', we observe that in examining our experiences, when we find that the totality of our observations show the same results, which are also affirmed through all other conceivable variations, we are able to infer with certainty that within those contexts that conclusion is able to be understood to be true. We are able to infer that there is a basis for being certain of our conclusion, within appropriate contexts, and one reason why we should not separate deductive from inferential reasoning, is that they are interdependent and self-correcting, when previously unconsidered evidence and contexts arise.
It's important to point out that the famous 'black swan' event, is not a valid case of inference or exception, relying as it does on nothing more than the feeble 'this coin was a nickel, and the next coin was a nickel, so all coins are nickels' mockery of inference, in that as we know that chemical processes which produce the coloring of a swans feathers, are fully capable of producing other colors, and there's no reason to suspect that a mutation would be unable to produce a single black swan or even a new breed of them. The fact that swans are most likely to be white, is valid as a general rule of thumb, but the existence of one or more black swans does nothing to invalidate inferential reasoning.
With that being said, we can move onto the other evasion of 'synthetic' or 'a posteriori' examples, which are typically positioned through common examples of:
"Grass is green" and "Man is mortal" and "There are no black swans", and one of the ways that students are intellectually assaulted with these terms, is by means of hypotheticals - NEVER allow someone to propose violating a fundamental principle such as identity or causality, in order to engage you in a hypothetical that begins with your agreeing to imagine something that conflicts with what you know to be real and true; their purpose is not to expand your thinking, but to puncture it, to sow doubts into your existing thoughts, and to disable your ability to think clearly from then on.
As we've seen, the premises that 'man is mortal' or 'bachelor is an unmarried man', are inferred from experience in just the same manner as 'grass is green' (in most varieties, not all), and the sum of degrees within a triangle is always 180*. It is only from experience that we are able to conceive of and conclude with certainty that all triangles in a flat plane (important point) sum up to 180*, because we can quickly see that there are no possible variations within a flat plane, that could result in more or less that 180* - it isn't possible. And while laying a triangular shape upon a convex or concave surface will produce more or less that 180*, that's no longer dealing with triangles in the context of a flat plane. And we don't validate our concepts through hypotheticals such as 'imagine grass that's red, or striped', because experience shows that hypotheticals that do not exist in reality, are not valid 'points of view' for considering reality from.
That man is mortal, is a result of inference. That all triangles contain 180* is the result of inference. That Red is a color, is a result of inference (and the fact that there are edge colors where its difficult to say are blue or green, does not invalidate either, and the fact that noticing there are fuzzy edges affirms, rather than calls into question, that solid ground can be identified). That a Bachelor is an unmarried man is no less an inference because it is defined to express the difference between men, and married men. Even 2+2=4 is an inference. The fact that some terms and premises take more or fewer instances to reliably infer a conclusion, has no effect on the validity of inference. BTW, the same applies in ethical conclusions, when an argument is made that:
'All people need food and shelter to survive,, they are counting upon your accepting their premises - and the ones they are ignoring - without question, and you can bet that they will fight against your checking their premises about 'people', 'need', 'good', and 'government'. Don't allow it. Ever.
some people lack food and shelter,
therefore government should ensure they are fed'
The supposed 'ideal' of inerrant and infallible certainty, which they hold up as an ideal, is a confession of their failure to understand and hostility to, mankind and man's means of understanding.
Are you Certain?
Stay on the road to reality, don't take the detours and offramps. The reason for the rules of logic that Aristotle formulated, and why we should follow them, checking and verifying that your thinking is either valid, or invalid, is to bring clarity to our understanding of what is real and true, and to bring order to our thinking. Logic is less about proving that something is true, than with clarifying whether your ideas of what is true, correspond to what actually is real and true, and reveals to you whether the fault is to be found within your argument, or with your premises, or even the terms, that you're using.
With all of that having been said, and reviewed here, there are a few other notable cautions and root fallacies noted in previous posts, to point out here, as an awareness of them helps in keeping your mind on track:
All of that and a great deal more (but always at least that), are basic to what was expanded upon in Aristotle's Metaphysics, and what's been known as The Organon, made up of his Categories, On Interpretation, the Prior Analytics, the Posterior Analytics, the Topics, and On Sophistical Refutations.
- An infinite regress does not lead to an explanation (in an evasion of both inductive and deductive logic), and engaging in such an effort is a giveaway that either an error, or a deception, is being concealed ("It's turtles all the way down!")
- The hypothetical assault - when a modernist asks you to consider an unreal or impossible hypothetical - "If we hypothetically, imagine ice that sinks, or grass that floats and burns, then it would it be logical to say...", but they aren't teaching you to think logically, they're actively steering you away from the fundamental rule for logically building upon what is real and true, to send you instead down modernity's epistemological offramp, performing computational rules of flowcharting, rather than engaging in logical reasoning.
What 'Epistemology' is defined as being, then - though rarely practiced as such - a system that 'distinguishes justified belief from opinion', is only able to see that it's justified, because it first identifies what is real and true, and so can be argued for logically, and be ethically justified.
That process is, and was, and should again be, understood to be one that utilizes metaphysics, logic, and ethics, in identifying what is, what follows, and what, if anything, should be done about that, by examining claims in a methodical, reasonable, and logical manner... and the Ethical portion of how we go about determining 'what, if anything, should be done about that', is what we'll look at next.