In the Nihilism thread, Aleta has asked whether A = A is of real-world importance.
Given the depth of the breakdown in reason that we are seeing, I think this is important to take up.
I took a moment to suggest an answer, which I think I should headline:
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KF, 111: >>Aleta,
100: >>can anyone give an example of a logical argument that uses A = A to help advance the argument?
Examples from math are easy. In solving 2x – 5 = 17, students write 5 = 5 in order to “add 5 to both sides of the equation”, invoking a principle [–> an axiom held to be self-evident, in fact] from Euclid that “if equals are added to equals, then the wholes are equal.”
But is there any example of a use of A = A in a logical chain of reasoning about the real world that adds anything to the argument? A = A is true, but outside of pure logic, is it ever useful?>>
103: >>we use such things as the transitive property, logical conditionals, the law of the excluded middle, etc., all the time. However, A = A, it seems to me, doesn’t advance any argument, so I’m thinking it’s not used in real-world chains of reasoning as opposed to its uses in math such as I mentioned.>>
First, in thinking, arguing and speaking we must recognise and respect distinct identities if we are to be sound. Echoing Aristotle, truth says of what is [A], that it is [A = A], and of what is not [~A] that it is not [~A != A].
That immediately brings to bear all three laws: identity is recognised, antithesis between a thing and not the thing is respected, dichotomy is understood.
And, the three are inseparable.
We recognise distinct identity A, and the world partition:
W, the world
A in W, a distinct thing
~A in W, what is not that thing
W = {A|~A}, partition that exhausts W
LOI: (A=>A) = 1, where in this case single implication entails equivalence.
LNC: (A AND ~A) = 0
LEM: x in W => x is in A or else in ~A due to the partition
In very practical terms, many issues hinge on recognising that a distinct identity pivots on core characteristics so that relabelling not-a-thing as though it were the thing fails. Likewise, relabelling a thing as though it were not the thing, fails too.
Lincoln’s folksy example of relabelling the tail of a sheep a “leg” and insisting that a sheep must now be reckoned as having five legs is aptly illustrative of the problem.
And, it speaks quite directly to the situation of policy making, liberty and justice and war. Notice his second inaugural:
AT this second appearing to take the oath of the Presidential office there is less occasion for an extended address than there was at the first. Then a statement somewhat in detail of a course to be pursued seemed fitting and proper. Now, at the expiration of four years, during which public declarations have been constantly called forth on every point and phase of the great contest which still absorbs the attention and engrosses the energies of the nation, little that is new could be presented. The progress of our arms, upon which all else chiefly depends, is as well known to the public as to myself, and it is, I trust, reasonably satisfactory and encouraging to all. With high hope for the future, no prediction in regard to it is ventured.
On the occasion corresponding to this four years ago all thoughts were anxiously directed to an impending civil war. All dreaded it, all sought to avert it. While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without war—seeking to dissolve the Union and divide effects by negotiation. Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish, and the war came.
One-eighth of the whole population were colored slaves, not distributed generally over the Union, but localized in the southern part of it. These slaves constituted a peculiar and powerful interest. All knew that this interest was somehow the cause of the war. To strengthen, perpetuate, and extend this interest was the object for which the insurgents would rend the Union even by war, while the Government claimed no right to do more than to restrict the territorial enlargement of it. Neither party expected for the war the magnitude or the duration which it has already attained. Neither anticipated that the cause of the conflict might cease with or even before the conflict itself should cease. Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible and pray to the same God, and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God’s assistance in wringing their bread from the sweat of other men’s faces, but let us judge not, that we be not judged. The prayers of both could not be answered. That of neither has been answered fully. The Almighty has His own purposes. “Woe unto the world because of offenses; for it must needs be that offenses come, but woe to that man by whom the offense cometh.” If we shall suppose that American slavery is one of those offenses which, in the providence of God, must needs come, but which, having continued through His appointed time, He now wills to remove, and that He gives to both North and South this terrible war as the woe due to those by whom the offense came, shall we discern therein any departure from those divine attributes which the believers in a living God always ascribe to Him? Fondly do we hope, fervently do we pray, that this mighty scourge of war may speedily pass away. Yet, if God wills that it continue until all the wealth piled by the bondsman’s two hundred and fifty years of unrequited toil shall be sunk, and until every drop of blood drawn with the lash shall be paid by another drawn with the sword, as was said three thousand years ago, so still it must be said “the judgments of the Lord are true and righteous altogether.”
With malice toward none, with charity for all, with firmness in the right as God gives us to see the right, let us strive on to finish the work we are in, to bind up the nation’s wounds, to care for him who shall have borne the battle and for his widow and his orphan, to do all which may achieve and cherish a just and lasting peace among ourselves and with all nations.
A big part of the run-up to the US civil war of the 1860’s pivoted on refusing to recognise that a black man is just as much a man as any other and so if by endowment of the Creator there is an unalienable right to life, liberty and pursuit untrammelled of happiness/ purpose one is here for, then surely a black descriptive modifier does not alter the fact that a man is a man. And if more was needed, many a white man fathered children upon a black slave woman; often under conditions where because of her enslaved status she had no recourse of refusal and no respect of being wife or even concubine.
{I add, a portrait of the Evans family likely just before the American Civil War, and — please read the painful story here — this was an actual marriage between a white man and a free black woman:}
The leg of a sheep is a leg, the tail of a sheep hath not the characteristics of and cannot be a leg.
So, if a black enslaved woman can have fertile children when her white massa’s son or massa himself takes a fancy to her, even under circumstances tantamount to rape, that already shows that we are “of one blood” . . . one common kind of life as “the life of the flesh is in the blood.” (That ties to Ac 17, in the same scriptures read by all.)
Refusal to recognise and respect distinct identity (here, held in common by whites and blacks) was the pivot of what led to war. In a context where a key argument for union in the Federalist Papers was that union was the best means of securing the peace, the common good and a prosperous future. As the history of regional divisions, alienation and wars in Europe so clearly showed.
In our day, it is highly arguable that refusal to recognise that the unborn child is as we all once were and at minimum should have the benefit of doubts is an engine driving the worst holocaust in human history, which in turn enmeshes the public, parliaments, courts, police and more across our whole civilisation in the terrible blinding and benumbing power of bloodguilt.
As one direct consequence, in the leading country of our civilisation, leadership from the party of mass abortion is implicated in many other things and the other party on average is half-hearted.
Some kinds go not out save by scripture so let me put it this way: they say peace, peace, when there is no peace.
In such a context where there is a habit of refusal to acknowledge that the right hand side restates what is on the left hand side . . . what equals means . . . we now face a policy of enabling the leading terrorism sponsoring nation in the world in its determination to acquire nuclear weapons as the effective means of intended genocide.
Linked to that there is a refusal to acknowledge that per foundational history, texts and policy sustained for 1400 years, there has been a major militarily backed or implemented IslamIST expansionism. Indeed, I find it interesting in a saddening, sobering way, how — while the media are ever so eager to pounce on all sorts of convenient stories — there has been persistent refusal to have a sustained focus on things like the Muslim Brotherhood’s 100 year global conquest plan (which I first found online on Sept 11 2001, along with recipes for building nukes when I sought to understand what was going on), or the papers documenting the settlement-jihad strategy (mass immigration of the violently hostile is invasion), and more.
{I add, here is that eye-opening image first seen by me on Sept 11, 2001, note the insert bottom-right:}
So, I find that being willing to recognise distinct identity and acknowledge that a certain implement with a long handle and a wide thin blade at one end shaped for digging into and lifting the soil is a spade is pivotal.
In short, are we willing to acknowledge that a spade is indeed a spade?
Scripture, again, from 2700 years ago:
Isa 5:18 Woe to those who draw iniquity with cords of falsehood,
who draw sin as with cart ropes,
19
who say: “Let him be quick,
let him speed his work
that we may see it;
let the counsel of the Holy One of Israel draw near,
and let it come, that we may know it!”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 shrewd in their own sight!22
Woe to those who are heroes at drinking wine,
and valiant men in mixing strong drink,
23
who acquit the guilty for a bribe,
and deprive the innocent of his right!24
Therefore, as the tongue of fire devours the stubble,
and as dry grass sinks down in the flame,
so their root will be as rottenness,
and their blossom go up like dust;
for they have rejected the law of the Lord of hosts,
and have despised the word of the Holy One of Israel.25
Therefore the anger of the Lord was kindled against his people,
and he stretched out his hand against them and struck them,
and the mountains quaked;
and their corpses were as refuse
in the midst of the streets.
For all this his anger has not turned away,
and his hand is stretched out still.26
He will raise a signal for nations far away,
and whistle for them from the ends of the earth;
and behold, quickly, speedily they come!
27
None is weary, none stumbles,
none slumbers or sleeps,
not a waistband is loose,
not a sandal strap broken;
28
their arrows are sharp,
all their bows bent,
their horses’ hoofs seem like flint,
and their wheels like the whirlwind.
29
Their roaring is like a lion,
like young lions they roar;
they growl and seize their prey;
they carry it off, and none can rescue.30
They will growl over it on that day,
like the growling of the sea.
And if one looks to the land,
behold, darkness and distress;
and the light is darkened by its clouds.
The price for apostasy and twisting truth into falsity, calling darkness light and light darkness is destructive defeat by way of fatally weakening oneself through marches of folly that “draw iniquity with cords of falsehood.”
A is A, A = A.
Calling A by its right name and acknowledging its right definition is a first step to wisdom.
A sound, thorough and accurate vocabulary or dictionary or encyclopedia — Wiki[d . . . ]pedia this speaks to you — is a revolutionary act of courage in an evil day.
A is A.
The tail of a sheep is not, cannot be a leg.
A leg is a leg.
It all starts with truthfully acknowledging (or with ill-advised refusal to acknowledge . . .) distinct identity.
A = A.>>
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A = A is indeed important and highly relevant in a world where it can be an act of sometimes almost suicidal courage to acknowledge, state and act on the simple truth. END