Q: Is Logic simply a matter of axioms at play in an abstract logical world unconnected to external reality? A: Nope

As we continue to look at the issue of first principles of right reason, one of the key steps being taken by critics of the Law of Non-Contradiction [LNC] is to assert that we are here dealing with axioms unconnected to the real world, at least in relevant cases.

First, let us clip a recent comment to refresh our recollection of the why behind the classical laws of thought, which can here be seen as self-evident and thus “natural,” rather than arbitrary projections unto reality conditioned by genes and memes:

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KF, 125: >>Reasoned thought itself is under attack in this ultra-/post- modern era.

So bad is this, that there are ever so many who think that something is wrong if one sticks up for longstanding, self-evidently true and indisputably certain first principles of right reason. (Did you notice how Aristotle described the concept of self-evident first principles of right reason in the clip from last night? [Read above.])

{Let me clip from 119:

[Ari, Metaphysics, defining self evidence and arguing that LNC is such:] >>. . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . >>

(NB: Aristotle, then, sees self evident truths as real, as certain beyond doubt, as natural, and as first principles that are foundational to thought on particular topics. We can define such as truths we understand, based on our existence and experience of the world as intelligent, conscious communicating, en-conscienced creatures, which we see as true, and as necessarily true on pain of patent absurdity if rejected, without further proof. Such, rather, are start-points for proof.)}

Lest we forget (I know, I know, this cuts across what we have been ever so confidently taught by the professed wise and brilliant, complete with convincing — but misleading — talking points and claimed proof cases), let me again clip the basic summary developed above:

Consider the world:

|| . . . ||

Identify some definite A in it:

|| . . . (A) . . . NOT-A (the rest of the world) . . . ||

{Or, let us use a full diagram:}

 

Now, let us analyse:

[1] A thing, A, is what it is (the law of identity);

[2] A thing, A, cannot at once be and not-be (the law of non-contradiction). It is worth clipping Wiki’s cites against known interest from Aristotle in Metaphysics, as SB has done above:

1. ontological*: “It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect.” (1005b19-20)

[*NB: Ontology, per Am HD etc, is “The branch of metaphysics that deals with the nature of being,” and the ontological form of the claim is talking about that which really exists or may really exist. Truth is the bridge between the world of thoughts and perceptions and that of external reality: truth says that what is is, and what is not is not.]

2. psychological: “No one can believe that the same thing can (at the same time) be and not be.” (1005b23-24)

3. logical: “The most certain of all basic principles is that contradictory propositions are not true simultaneously.” (1011b13-14)

[3] A thing, A, is or it is not, but not both or neither (the law of the excluded middle).

[4] “to say that what is is, and what is not is not, is true.” (Aristotle, on what truth is)

[5] “Of everything that is, it can be found why it is.” (Principle of sufficient Reason, per Schopenhauer.)

[6] If something has a beginning or may cease from being — i.e. it is contingent — it has a cause.* (Principle of causality, a direct derivative of 5)
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*F/N: Principles 5 & 6 point to the possibility of necessary, non contingent beings, e.g. the truth in 2 + 3 = 5 did not have a beginning, cannot come to an end, and is not the product of a cause, it is an eternal reality. The most significant candidate necessary being is an eternal Mind. Indeed, down this road lies a path to inferring and arguably warranting the existence of God as architect, designer and maker — thus, creator — of the cosmos. (Cf Plato’s early argument along such lines, here.)

These six claims, once we reasonably understand them in light of our experience of the world, will patently be seen as true, and necessarily so on pain of absurdity. So soon as we can identify something, A as a definite object, A is itself, not something else at the same time and in the same sense. Similarly, the understanding of what truth is, is the ordinary and reasonable meaning: telling it like it is. And if something is, there is a reasonable question: why, which can be answered. That answer, for something that begins or may cease, is that it has a cause, and this raises the root question of beings that are necessary, and have no cause. (Cf the previous discussion in the ID Foundations series, here.)

This then points to the question, what best explains the contingent cosmos we observe, which turns out to be fine-tuned for C-chemistry, cell based life. Cosmological design thought and theory therefore point to a designer and builder of our observed cosmos . . .  >>

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Of course those onward connexions are big issues, but the core question is the bridge between principles of logic and reality.

A good place to look at that is the response in the same thread, to a recent post by Dr Liddle at her blog. It is revealing that she has entitled that post, “The RULES of Right Reason” [Emphasis added], rather than “The FIRST PRINCIPLES of Right Reason,”  which says something very different.

For, we make up rules for games, we start reasoning from first principles that present themselves to us as a good place to begin. And if the first principles in question show themselves to be warranted as self-evidently true, they are natural principles, not artificial rules for a game we may or may not elect to play.

Ironically, it seems Dr Liddle has made an unwarranted design inference here:

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KF, 126: >>I skimmed the thread and OP that Aleta has now repeatedly linked. I can see that from the outset they are making the little error at the beginning that Adler has highlighted, and which is discussed in more details here: failing to recognise the reality of self-evident truths of right reason, and in particular the first principles of right reason.

For instance, in the OP, Dr Liddle remarks:

They are indeed axiomatic – in other words, they are axioms on which a certain form of logic is based. Now I’m no logician, but I am capable of seeing that if we assume those axioms are true, we can construct a logical language in which useful conclusions can be drawn, and useful computations performed.

But there are some propositions that simply are not possible in that language, because those axioms themselves are based on more fundamental assumption: that we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .

Let me clip Wikipedia, speaking against its known ideological interest:

In epistemology (theory of knowledge), a self-evident proposition is one that is known to be true by understanding its meaning without proof.

Some epistemologists deny that any proposition can be self-evident. For most others, the belief that oneself is conscious is offered as an example of self-evidence. However, one’s belief that someone else is conscious is not epistemically self-evident . . . .

A self-evident proposition cannot be denied without knowing that one contradicts oneself (provided one actually understands the proposition). An analytic proposition cannot be denied without a contradiction, but one may fail to know that there is a contradiction because it may be a contradiction that can be found only by a long and abstruse line of logical or mathematical reasoning. Most analytic propositions are very far from self-evident. Similarly, a self-evident proposition need not be analytic: my knowledge that I am conscious is self-evident but not analytic . . . .

For those who admit the existence [i.e. reality] of abstract concepts, the class of non-analytic self-evident truths can be regarded as truths of the understanding–truths revealing connections between the meanings of ideas.

That is, a self-evident truth is one that — providing we understand what is being said in light of our undeniable (and self-referential) experience of the world as intelligent, language-using, knowing and communicating creatures — we see is so, and that it MUST be so, on pain of obvious absurdity if we try to deny it. That is, these are foundational truths that we know or should know are so and must be so. So, to willfully reject such a truth is to implant an absurdity in the heart of our reasoning, and to open ourselves up to that en-darkenment of heart and mind that leads us to reject truth because we have swallowed an error.

The reality of such truths is too often disputed, so let us give a key case, Warranted Credible Truth no 1, per Josiah Royce via Elton Trueblood: error exists.

This is of course an all too familiar and universally accepted truth. That’s why we have arguments over what is correct!

But there is a subtler and highly instructive side to it: it is UNDENIABLY true, on pain of self-referential absurdity. That is, if we try to deny that error exists, as a test, we immediately have a choice of which of two claims is in error: (a) that error exists, or (b) that error does not exist. One of these must be in error, on the common sense understanding that even philosophers must respect.

And obviously, the correct one is (a), as it affirms what we have seen is undeniably so: error exists.

Now, that looks trivial, doesn’t it?

NOT.

WCT 1 implies that truth exists, and undeniably true truth exists. Warranted credible truth — knowledge — exists. So, those who would dismiss the reality of truth, or the know-ability of truth beyond seeming true to me or you, etc, are in error.

This actually cuts a wide swath across many popular worldview level opinions: radical relativism and its many friends and kissing cousins.

In addition, “error” is not a tangible reality: we cannot touch error as such, though we may see cases of error. Just like we cannot touch two as such though we may touch glyphs that represent it and illustrate with concrete cases. Reality is not to be conflated with [material] physicality; and indeed it is precisely because mathematics often captures logical, abstract facets of reality, that we so often see its awesome power in science, engineering and even day to day life.

Going further, we have in hand a case where we can see for ourselves that axioms are not always arbitrary and merely evaluated on being useful. Some axioms are warranted and credible as self-evident truths. So, the notion that we are free to select whatever axioms we want and then just look to see if it works well enough to be useful, crashes to the ground in flames.

For, there are what Aristotle identified as the most certain of all truths, truths that are certain and know-able to all on pain of patent self-referential absurdity.

It so happens that the first principles of right reason belong to exactly that category of truths.

Now of course, one of the points that are being disputed is that: “we know what an “object” is; that we know what “time” is – in other words, that we know what “is” is . . .”

This actually inadvertently shows what is at stake here: if we reject the first principles of right reason, our ability to communicate itself disintegrates into a chaos. (So, apply Kant’s Categorical Imperative here . . . ) But in fact, we premise our whole structure of knowledge on the undeniable self-referential and in-common common sense facts of human existence, which includes that we can and do communicate using language and keystone concepts such as our ability to answer to who or what [objects], to when [time] and to existence or non existence [is]. Or else, who is speaking, what does s/he say, and about what, when, where, and how accurately, how well warranted, evaporate in a chaos of confusion and contention.

In short, we are patently seeing absurdity piled upon absurdity here.

But of course, the underlying question on the issue being touted is that such words defy precising definitions that state necessary and sufficient conditions that infallibly tell us what they mean and/or operations that we can use to observe or measure them, etc. And, a selectively hyperskeptical voice can have great fun making such efforts at definition seem ridiculous.

The only problem is that the process of making or challenging such definitions alike would depend on the common sense recognition of what these things mean. That is the one pushing such skeptical talking points is being self-referentially incoherent.

So, are we locked into a circle of confusion and begged questions, with knowledge and reason themselves evaporating?

Not at all.

We start from the reality that we exist as intelligent and communicating creatures in a real world, and that we recognise many concepts on the basis of knowing cases, intuiting connexions and using that abstracted pattern to identify further cases on family resemblance. This process obviously can err, but the very fact of error is a case of existence and of truth existing and of knowable truth existing. So, we know well enough what things are, both concrete things and abstract ones of the order of the truth in the statement 2 + 3 = 5.

We know full well that we can recognise cases of such things, and mark them off with labels, like A.

Once that is done, we know full well that A is distinct from NOT-A, just as Dr Liddle is distinct from the rest of the world: her husband, her cat, her car, her workplace, her blog etc etc.

In short, we see the basic laws of thought swinging into action, as has been repeatedly described and explained. And, in a case where to deny such is to end immediately in self-referential absurdity.

What is more, if I were to take what Dr Liddle wrote and say that it means the opposite, she would rightly object that I am distorting what she said.

In short, she full well knows that in relevant cases we know the difference between an assertion and its denial.

She knows or should know that if one stands at the four-state point or the like, one can be “in” four states at once, but only if we take “in” in an inclusive sense. If we take “in” in the exclusive sense, that is not possible, and so the problem being posed turns out to be a case of needing to be clear what we are asking about.

And of course there are things that shade off into one another, indeed Aristotle discussed white and black and grey in the very passage in Metaphysics we have been talking about. Does that mean there is no difference between white and black, or that something can be white and not white in the same sense and time etc?

Patently not.

That stricture on being in the same sense and time etc, is an invitation to be precise enough to mark whether we are equivocating when we say A and NOT-A. As Ari himself observed:

. . . the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every one must have who understands anything that is, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, to guard against dialectical objections, any further qualifications which might be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and if it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premiss too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms . . . .

We did not suddenly see things that Aristotle was blind to, in the past 100 or so years! . . . >>

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In short, the first principles of right reason are not merely arbitrary axioms, but in crucial aspects are self-evident truths of right reason. That allows us to bridge the gulf that has been made in modern thought through an error of Kant.

An error of Kant?

Yes:

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KF, 67: >> . . . All of these [cases were given] real world interactions of the intelligent mind rely on the bridge between the world of thought and the world of experienced reality.

But, if you are thinking in light of Kant’s cut, you will still think nope the gap is not bridged. It is un- bridgeable.

Therein lieth the rub: self-referential incoherence. Kant and others are here committing one of those little errors in the beginning that spring up into ugly chasms of error cutting wide swaths across our life of thought and experience alike.

Here is the overlooked problem of self-referentiality: to assert that we know and can know naught of the external world as it is, is to already and inescapably claim to know something about the external world, its alleged un-know-ability. So, which is it, we can know something about the external world (and indeed we can make errors in so claiming to know), or we truly cannot know in which case we could not even know that much.

Or, as William Lane Craig pointed out in his debates with Gerd Ludemann:

insofar as these . . . assumptions include Kant’s strictures on the scope of scientific knowledge, they are deeply, fatally flawed. For Kant must at least be claiming to have knowledge of the way some things (e.g., the mind and its structures and operations) exist in themselves and not merely as they appear; he confidently affirms that the idea of God, for instance, has the property of unknowability. [10] So the theory relies on knowledge that the theory, if it was true, would not — could not — allow. [ Jesus’ Resurrection: Fact or Figment, ed. Paul Copan (Downer’s Grove, IL: IVP, 2000), p. 13. NB: Ref. [10] is to Plantinga’s Warranted Christian Belief, pp. 3 – 30, and is shortly followed by a reference to F. H. Bradley’s gentle but stinging opening salvo in his Appearance and Reality, 2nd Edn.: that “The man who is ready to prove that metaphysical knowledge is impossible has . . . himself . . . perhaps unknowingly, entered the arena [of metaphysics] . . . . To say that reality is such that our knowledge cannot reach it, is to claim to know reality.” (Clarendon Press, 1930), p.1]

Given the self referential absurdity, and the patent confusion, the answer should be plain.

We can and even do in many cases know about the external world.

Indeed, utterly abstract principles like 2 + 3 = 5, routinely and reliably strictly constrain what can be at all in that world. There is no possible world in which we can have heap A, two tokens, and heap B, three tokens, then push together and not get five tokens in the new heap we have so formed. It is only sheer familiarity that blinds us to how astonishing such a finding truly is.

Thence, with elaboration, the so-called “unreasonable” effectiveness of mathematics in science, engineering and day to day life.

There are using abstract, conceptual realities that do control what can be in this or any other possible world.

And, as one of these, it so happens that once we can identify an item A, and distinguish it by whatever means from the rest of the world, under the usual rules of consistency in meaning etc:

(a) the part labelled A will be A (symbolically, [A => A] = 1),
(b) A will not be the same as NOT-A ( [A AND NOT-A] = 0); and
(c) there is no third option to being A or NOT-A ( [A OR NOT-A] = 1).

Such holds whenever an A exists. It is a necessary constraint on what is possible, once A exists as a distinct thing, even if it may have fuzzy borders. try this one: where does your arm end and the trunk of your body begin? Your nose? Your leg? sure, you can identify ever so many border zone points that you could debate what they are till the cows come home, but that has not changed the realities that we have arms, noses and legs etc. A nose is a nose and not also a non-nose. Something is nose or not nose but not both or neither. Regardless of fuzziness of the border.

This point will hold even where we struggle to decide if this is indeed A.

If it IS A in truth, the three principles apply. Our limitations as finite and fallible do not stop those consequences from actually following, they are just our limitations.>>

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So, it is plain that the issues at stake are truly foundational.

If we cannot come to agreement here, agreement later on will be a matter of accident, and attempted discussions will face the fatal flaw of playing games based on arbitrary rules. And, if someone is losing based on the rules in play, the temptation will be to challenge the rules. Consequently, if one sees logic as little more than a mental game played by rules that are essentially arbitrary, one will be temped to try to switch rules in mid-game if one seems to be losing.

Moreover, one who thinks like that will see the “game” as a game, without serious import, so gaming the game will seem a reasonable thing to do.

Suddenly, a lot of the features of exchanges on design theory and related areas make a lot of twisted sense: one side has been operating based on a rules for games model, where the rules are open to being pushed to one’s advantage.

And, if logic is a matter of a game, so is morality, hence the slide to nihilism we have been so frequently forced to comment on. That is, the “logic is a game” view multiplied by evolutionary materialism’s want of a foundational IS that can ground OUGHT leads to the playing out of the consequences of the agenda that thinks that might and manipulation make ‘right.’

Some pretty serious things are at stake here, things that explain how frequently post-/ultra- modern evolutionary materialist advocates become disruptive and uncivil.

So, we can easily see why in the end authorities may well need to restrain the disruptive, or at length remove them. For, if there are some who reject the basis for reasoned discussion and responsible debate, they cannot be reasoned with, they can only be removed if they become too disruptive and distractive in the teeth of repeated warning. To use the classroom metaphor, why should we allow those who have no intention to learn, to stop the learning process for those who do want to learn?

But also, we see here the diagnosis that allows us to identify and possibly fix the problem.

So, we really do need to settle the question of the first principles of right reason and the linked bridge between the world of thought and the world of external reality.

The argument here is that this bridge from mind to external reality is made up from self-evident first principles of right reason; which are thus natural, not arbitrary rules that can be changed at will.

If you reject that claim, why? What would you put in its place, why?

As for me, I am ever more led back to seeing the wisdom in this bit of classical literature that is so often despised and derided today:

Prov. 16:22 Understanding is a fountain of life to those who have it,
but folly brings punishment to fools.

23 A wise man’s heart guides his mouth,
and his lips promote instruction.[b]

24 Pleasant words are a honeycomb,
sweet to the soul and healing to the bones.

25 There is a way that seems right to a man,
but in the end it leads to death.

Isa 5:18 Woe to those who draw sin along with cords of deceit,
and wickedness as with cart ropes . . .
20 Woe to those who call evil good
and good evil,
who put darkness for light
and light for darkness,
who put bitter for sweet
and sweet for bitter.

21 Woe to those who are wise in their own eyes
and clever in their own sight.

Eph 4:17 So I tell you this, and insist on it in the Lord, that you must no longer live as the Gentiles do, in the futility of their thinking. 18 They are darkened in their understanding and separated from the life of God because of the ignorance that is in them due to the hardening of their hearts. 19 Having lost all sensitivity, they have given themselves over to sensuality so as to indulge in every kind of impurity, with a continual lust for more. [cf Rom 1:18 – 32]

So, which way will it be, for us and our civilisation? END

PS: Those who want to raise objections on quantum theory issues are asked to first see here (and, do, watch the Dr Quantum video). For more, cf. the comments and video here, the online exchange here (to see how such things play out in debates), and the papers here and here to see how the issues can be addressed at the next level. The famous exchange of Ravi Zacharias with an un-named professor over either-or vs both-and, is also helpful.