East Meets West Logic...

[Lloyd Gillespie]

The Inductive (Scientific) Method



Historical Development:

Not everyone from 300 B.C. to 1600 A.D. was willing to bow to the authority of Aristotle. Many of Aristotle's arguments were faulty, but where did he go wrong, and what was the right way to proceed?

Galileo GalileiSir Francis Bacon (1561 - 1626)Tycho Brahe (1546 - 1601)About 1600 A.D., it became apparent to several people - Galileo Galilei in Italy, Francis Bacon in England, Tycho Brahe in Denmark, and others - that there were no subtle logical errors in Aristotle's use of the deductive method. The problem was that the deductive method, while wildly successful in mathematics, did not fit well with scientific investigations of nature.
In order to use the deductive method, you need to start with axioms - simple true statements about the way the world works. Then you use these axioms to build your logical system of nature. If your axioms are true, everything that follows will be true, but Galileo and his contemporaries realized that the problem was that it was enormously difficult to determine "simple true statements about the way the world works". In fact, they realized that it should be the goal of science - not the starting place - to determine what the "simple true statements about the way the world works" really are!
Since 1600, the inductive method has been incredibly successful in investigating nature - surely far more successful than its originators could have imagined. The inductive method of investigation has become so entrenched in science that it is often referred to as the scientific method.
Inductive vs. Deductive Method

The inductive method (usually called the scientific method) is the deductive method "turned upside down". The deductive method starts with a few true statements (axioms) with the goal of proving many true statements (theorems) that logically follow from them. The inductive method starts with many observations of nature, with the goal of finding a few, powerful statements about how nature works (laws and theories).
In the deductive method, logic is the authority. If a statement follows logically from the axioms of the system, it must be true. In the scientific method, observation of nature is the authority. If an idea conflicts with what happens in nature, the idea must be changed or abandoned.
Here is a diagram that attempts to depict the scientific (inductive) method. It is oversimplified and incomplete, but...
Is Science Entirely Inductive?

On the previous page, you learned that although mathematics is deductive in nature - that is, logical proof is the only acceptable evidence of truth - the process of mathematics is not entirely deductive. It is also true that although science is inductive by nature - observations are the only acceptable evidence of truth - the process of science can be deductive!
In particular, physicists make extensive use of mathematics as a powerful theoretical tool. Theoretical physicists often construct theories as "mathematical models" deductively, starting with assumptions about the inner workings of stars or atoms, for instance, and then working out the mathematical consequences of their assumptions. An essential difference between a mathematician and a theoretical physicist is that the physicist uses mathematics as a reasoning tool. The success of the mathematical model depends on how well its results agree with observations of nature - if they do not agree the physicist knows that this means that her assumptions - not the observations - need to be adjusted.

LINK

THE PHILOSOPHY OF FRANCIS BACON

[austintorn@aol.com]

Living Freely

http://gallery.me.com/austintorney#101681

‘Slideshow’, then pause and left arrow to go one by one.

[Lloyd Gillespie]

THE PHILOSOPHY OF FRANCIS BACON

History of Scientific Method...
Timelines of the History of Scientific Method...
Scientific Method...
Link...

Bacon's method presupposes a double empirical and rational starting-point. True knowledge is acquired if we proceed from lower certainty to higher liberty and from lower liberty to higher certainty. The rule of certainty and liberty in Bacon converges with his repudiation of Aristotle's old logic, which determined true propositions by the criteria of generality, essentiality, and universality. For Bacon, making is knowing and knowing is making (cf. Bacon IV [1901], 109–10). Following the maxim “command nature … by obeying her” (Sessions, 1999, 136; cf. Gaukroger, 2001, 139 ff.), the exclusion of superstition, imposture, error, and confusion are obligatory. Bacon introduces variations into “the maker's knowledge tradition” when the discovery of the forms of a given nature provide him with the task of developing his method for acquiring factual and proven knowledge.

Form is for Bacon a structural constituent of a natural entity or a key to truth and operation, so that it comes near to natural law without being reducible to causality. This appears all the more important, since Bacon – who aims exclusively at causes necessary and sufficient for their effects – rejects Aristotle's four causes (his four kinds of explanations for a complete understanding of a phenomenon) on the grounds that they are not well distributed into material, formal, efficient, and final, and that they fail to advance the sciences (especially final, efficient, and material causes): “There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms at last. This is the true way, but as yet untried” (Novum Organum, I, Aph. XIX, Bacon, IV [1901], 50).

Historians of science, with their predilection for mathematical physics, used to criticize Bacon's approach, stating that “the Baconian concept of science, as an inductive science, has nothing to do with and even contradicts today's form of science” (Malherbe, 1996, 75). In reaching this verdict, however, they overlooked the fact that a natural philosophy based on a theory of matter cannot be assessed on the grounds of a natural philosophy or science based on mechanics as the fundamental discipline. One can account for this chronic mode of misunderstanding as a specimen of the paradigmatic fallacy (cf. Gaukroger, 2001, 134 ff.; see Rees, 1986).

Thus, for Bacon, the acquisition of knowledge does not simply coincide with the possibility of exerting power. His scientific knowledge is a condition for the expansion and differentiation of civilization as a process. Therefore, knowledge and charity cannot be kept separate:

“I humbly pray … that knowledge being now discharged of that venom which the serpent infused into it, and which makes the mind of man to swell, we may not be wise above measure and sobriety, but cultivate truth in charity… Lastly, I would address one general admonition to all; that they consider what are the true ends of knowledge, and that they seek it not either for pleasure of the mind, or for contention, or for superiority to others, or for profit, or fame, or power, or any of these inferior things; but for the benefit and use of life; and that they perfect and govern it in charity. For it was from the lust of power that the angels fell, from lust of knowledge that man fell; but of charity there can be no excess, neither did angel or man ever come in danger by it.” (Preface, Inst. Magna: Bacon, IV [1901], 20 f.).

Finally, the view that Bacon's Nova Atlantis “concerns a utopian society that is carefully organized for the purposes of scientific research and virtuous living” (Urbach, 1988, 10) holds true for his entire life's work.

[labelwench]

… Lastly, I would address one general admonition to all; that they consider what are the true ends of knowledge, and that they seek it not either for pleasure of the mind, or for contention, or for superiority to others, or for profit, or fame, or power, or any of these inferior things; but for the benefit and use of life; and that they perfect and govern it in charity.
Originally posted by Lloyd Gillespie

The pursuit of knowledge is a privilege, which bears with it, a responsibility.

It has ever been said that 'Knowledge is Power', and to leave such power unused, when there is need, is as much a failing as to use same for personal fame or gain, while neglecting the greater application.

That being said, there is ever the case where knowledge must await the best time for the greater benefit of such application, IMO.

Were I the keeper of some powerful secret, I would feel obligated to discharge it at the appropriate time, and it would be my concern that I did so to the best of my ability, and with the greatest possible result.

[RascalPuff]

Wiki

The Fall of Constantinople was the capture of the capital of the Byzantine Empire which occurred after a siege laid by the Ottoman Empire, under the command of Sultan Mehmed II. The siege lasted from Thursday, 5 April 1453 until Tuesday, 29 May 1453 (according to the Julian Calendar), when the city was conquered by the Ottomans. Constantinople was defended by the army of Emperor Constantine XI. The event marked the end of the political independence of the millennium-old Byzantine Empire, which was by then already fragmented into several Greek monarchies.
Following his accession to the Ottoman throne, Mehmed had been applying pressure on Constantinople and the Byzantines by building forts along the Dardanelles. On 5 April, he laid siege to Constantinople with an army numbering 80,000 to 200,000 men. The city was defended by an army of 7,000 of whom 2,000 were foreigners. The siege began with heavy Ottoman artillery firing at the city's walls while a smaller Ottoman force captured the rest of the Byzantine strongholds in the area. Ottoman attempts to blockade the city completely failed at first owing to the boom blocking the entrance to the Golden Horn thus allowing four Christian ships to enter the city. At the entrance to the Golden Horn, there was a large chain pulled across from Constantinople to the Tower of Galata on the northern side, preventing unwanted ships from entering. Mehmed was not able to enter his ships into the city, which is why he had his ships rolled into the Golden Horn on greased logs. Byzantine effort to destroy the ships with fire ships failed, allowing the Ottomans to seal the city off.
The Turkish frontal assaults on the walls were all repulsed with heavy casualties and the Turkish attempts to undermine the walls were all countered and abandoned. Mehmed's offer to lift the siege, if he was given the city, was rejected. On 22 May, the moon rose in eclipse prophesying the fall of the city and a few days later Constantine received news that no Venetian relief fleet was coming. After midnight of the 29, the Ottoman army attacked the walls. The first wave of irregulars was thrown back. The second Turkish wave of Anatolians managed to breach the Blachernae section of walls. The defenders pushed back the Anatolians and managed to hold out against the Sultan's elite Janissaries. During the fighting, the Genoese commander, Giovanni Giustiniani was fatally wounded and retreated to his ships with his men. The Emperor and his men continued to hold off the Turks until the Turks discovered an unlocked gate upon which they flooded into the city. Constantine reportedly fell leading a charge against the invaders, though his body was never found. The last defenders were murdered and the Turks proceeded to loot the city.
This battle marked the end of the Byzantine Empire, an empire which had lasted for over 1,100 years. The city's fall was a massive blow for Christendom. Pope Nicholas V ordered an immediate counter-attack, but his death soon after marked the end of the plan. Mehmed made Constantinople his capital and proceeded to conquer the last two Byzantine states, the Despotate of Morea and the Empire of Trebizond. Many Greeks fled the city and migrated to other parts of Europe, in particular Italy. This move is thought to have helped fuel the Renaissance. The Fall of Constantinople is seen by some scholars as being a key event in leading to the end of the Middle Ages, and some mark the end of the Middle Ages by this event.[9]
------------------------------------------------------------------------------------------------

Please consider the effected (compound) irony in the sequence of events of what was formerly called Istanbul - as an inherently Eastern establishment - being 'acquired' and claimed (by the Roman Empire) as what spontaneously became the easternmost outpost of (what H. G. Wells <Outline of History> aptly observes as the geographic axis of the dominant presence and <reciprocal> cultural influence of) Western Civilization (on the Eurasian continent), in the sobriquet name of Constantine and spiritual cause of Christianity (for no less than eleven hundred years), finally to be reclaimed by Eastern elements (implementing Western originated pyrotechnic artillery); marking the advent of Western Civilization's 'Middle Ages'. Please take further notice (in deference to Labelwench's above observation regarding the import of 'the appropriate time') of Sultan Mehmed II's place as 'the person and the moment' confluencing to a successful outcome, in what may at any other - especially previous - time, have been an unsuccessful endeavor. - RP

[austintorn@aol.com]

An earlier seige of Constantnople, a thousand years before it fell, from Austin’s ‘Last Knight’s Almanac’…

(I unearthed these Chronicles from an iron box that was buried 1400 years ago under the Abbey of Glastonbury.)

Constantinople

The scene: The Moslems and Turks are laying on the longest siege that the holy city of Constantinople has ever known. Great siege engines have been constructed and rolled hundreds of miles over roads carved ahead of them to reach the wall of the fabled city. Hordes of crazed madmen encircle the city on every side.

Constantine IV supervises the action at the latest trouble spot on the wall and watches yet another mighty siege tower go to blazes from the effect of his newly discovered Greek Fire. There, on another wall, comes a human wave assault with ladders. Archers on the ingenious triple tiered walls let loose arrow after arrow into the mob. The slaughter is endless, for when one Turk falls, another takes his place to meet death and glory. To die in war was the ambition of every Turk, or so the Great Khan would have them believe.

Finally, the blessed darkness falls as the attackers retreat to their camps for the night, and the city’s defenders sneak outside the walls to make repairs. The attacks begin anew the next morning at some other gate or portion of the wall, but Constantinople was built to last! Well stocked with food, water, warriors. and weapons, the Christians’ finest city has easily survived the first one hundred days of siege.

Indeed, as Constantine IV turns from the wall and looks inward, his city and its churches look quite eternal in the bright summer sunlight, especially Holy Sancta Sophia, the most magnificent church in all of Christendom, its gold glittering dome a symbol to all of that which is forever good and eternal.

Constantinople! Unconquerable for centuries, heart and soul of the Eastern Roman Empire, New Rome, sister city of Camelot, built on seven hills and ever protected by the mountains, the sea, and three solid walls. Constantinople now stands alone in the East as the world crumbles around it.

When founded and laid out by Constantine I (declared Caesar in wild and old Roman Britain), his followers were aghast when he walked out the boundaries of the city he was to have them build—for the walls were to be several miles on each side! But no site was so fortified by nature: The hills gave it height and view, the harbor of the Golden Horn and the Sea of Marmora gave it access and control of the sea and protection from attack, and cold winters helped, also, as did the strong winds on the Bosporus. Many a Caliph had attacked it, over long periods of time, and each went home in despair, never to return to power.

Blockaded for two hundred days now, the city yet stands solid; where outer walls weaken, new inner walls are built overnight. There is no longer any grain left from the steppes of Russia, but the city is large and every spare patch of dirt is put to the task of growing food which is to be carefully rationed, two portions a day to warriors, one to all others.


…and elsewhere, the Huns cross the Danube, the Vandals enter Rome, casting an eye on North Africa, and, somewhere, in the uncharted waters of the foggy Aegean Sea near the Misty Isles, a nation of born sailors goes to war while another great navy enters at the other end of the Great Inland Sea and passes the Rock of Gibraltar. A crippled sailor looks out from the first ship—it is the man with a peg leg and a hook hand, the one who built the ships that he thought he would never sail, Sir Gundar Harl, now commander of Britain’s war fleet.

A fast ship now bears into Camelot’s harbor, carrying another dreaded messenger, dreaded because they always bring bad news of late. The news: The Hun has crossed the Rhine to take unfair advantage of Europe’s plight; the Vandal marches to sack Rome and mark its final fall; the Turk retakes Jerusalem; and the Visigoth pushes the Franks to the sea in Gaul; and the Franks ask for your evacuation aid.

{Out of that Ocean’s wrecks had Guilt and Woe Framed a dark dwelling for their homeless thought.}

Clovis II, King of Gaul, facing certain defeat, does what he must do and calls a retreat to allow the finest of the Frankish troops to seek refuge across the channel so they might live to fight another day when the odds are better.

Percivale immediately dispatches every available ship to the shores of Gaul in one of the largest successful evacuations of an army that the world has known—and it succeeds because Clovis II will not leave his beloved land, and entices the Goth with the bait of his ready capture as he draws inland with a few brave men, and so diverts his pursuers away from the fast retreating Frankish army.

The French soil that he loved so much now surrounds Clovis II in eternal and everlasting comfort in an unmarked grave where a few dedicated followers buried him while the twelve Goths that he took with him rot in the fields abandoned in death. But where, oh where, is young Clovis III?

A defeated, but mostly intact army, arrives safely in Britain, and it is then declared that if and when Europe is invaded, that Frankish shock troops shall lead the way home to retake all of French soil or join Clovis II beneath it.


Our continuing story: The time for invasion is not yet at hand. However, equipment arrives daily in Britain from free foreign shores; blacksmiths work day and night, early and second plantings continue in the fields; spring freshens the air; regiments are formed and trained; Frankish troops grow healthy once again. King Percevale can only hope that all will be in readiness by the time that the geese fly south and the leaves begin to fall.

Victory at Sea

Our Story: Deserted for decades now, Rome falls easily to the Vandals, but the words “Rome has fallen” still hang heavy in the air as the messenger speaks them before the King’s court. …

[labelwench]

I'm reasonably certain that the owner of this thread, and those following it, will see the humor in this cartoon, given some of the more recent posting on other threads.

A bit of an out-take on the 'Einstein Gap'.

(Blame Burnett. He started it, lol.....)

http://www.treelobsters.com/2010/04/...-analysis.html

[Lloyd Gillespie]

Hyperfine Structure Measurements, (for those interested in fine structured time...) Wiki Link...
Hyperfine interactions can be measured, among other ways, in atomic and molecular spectra and in electron paramagnetic resonance spectra of free radicals and transition-metal ions.

Applications
Astrophysics
As the hyperfine splitting is very small, the transition frequencies usually are not optical, but in the range of radio- or microwave frequencies.
Hyperfine structure gives the 21 cm line observed in HI region in interstellar medium.

Carl Sagan and Frank Drake considered the hyperfine transition of hydrogen to be a sufficiently universal phenomenon so as to be used as a base unit of time and length on the Pioneer plaque and later Voyager Golden Record.

In radio astronomy, heterodyne receivers are widely used in detection of the electromagnetic signals from celestial objects. The separations among various components of a hyperfine structure are usually small enough to fit into the receiver's IF band. Because optical depth varies with frequency, strength ratios among the hyperfine components differ from that of their intrinsic intensities. From this we can derive the object's physical parameters.[9]

Nuclear technology
The AVLIS process uses the hyperfine splitting of between optical transitions in uranium-235 and uranium-238 to selectively photoionize only the uranium-235 atoms and then separate the ionized particles from the non-ionized ones. Precisely tuned dye lasers are used as the sources of the necessary exact wavelength radiation.

Use in defining the SI second and meter
The hyperfine structure transition can be used to make a microwave notch filter with very high stability, repeatability and Q factor, which can thus be used as a basis for very precise atomic clocks. Typically, the hyperfine structure transition frequency of a particular isotope of caesium or rubidium atoms is used as a basis for these clocks.

Due to the accuracy of hyperfine structure transition-based atomic clocks, they are now used as the basis for the definition of the second. One second is now defined to be exactly 9,192,631,770 cycles of the hyperfine structure transition frequency of caesium-133 atoms.

Since 1983, the meter is defined by declaring the speed of light in a vacuum to be exactly 299,792,458 metres per second. Thus:
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

Precision tests of quantum electrodynamics
The hyperfine splitting in hydrogen and in muonium have been used to measure the value of the fine structure constant α. Comparison with measurements of α in other physical systems provides a stringent test of QED.

Qubit in ion-trap quantum computing
The hyperfine states of a trapped ion are commonly used for storing qubits in ion-trap quantum computing. They have the advantage of having very long lifetimes, experimentally exceeding ~10 min (compared to ~1 s for metastable electronic levels).

The frequency associated with the states' energy separation is in the microwave region, making it possible to drive hyperfine transitions using microwave radiation. However, at present no emitter is available that can be focused to address a particular ion from a sequence. Instead, a pair of laser pulses can be used to drive the transition, by having their frequency difference (detuning) equal to the required transition's frequency. This is essentially a stimulated Raman transition.

[Lloyd Gillespie]

From Giambattista Vico's New Science

But in the night of thick darkness enveloping the earliest antiquity, so remote from ourselves, there shines the eternal and never failing light of a truth beyond all question: that the world of civil society has certainly been made by men, and that its principles are therefore to be found within the modifications of our own human mind. Whoever reflects on this cannot but marvel that the philosophers should have bent all their energies to the study of the world of nature, which, since God made it, He alone knows; and that they should have neglected the study of the world of nations, or civil world, which, since men made it, men could come to know. This aberration was a consequence of that infirmity of the human mind by which, immersed and buried in the body, it naturally inclines to take notice of bodily things, and finds the effort to attend to itself too laborious; just as the bodily eye sees all objects outside itself but needs a mirror to see itself.

Now since this world of nations has been made by men, let us see in what institutions all men agree and always have agreed. For these institutions will be able to give us the universal and eternal principles (such as every science must have) on which all nations were founded and still preserve themselves.

From Vico's Autobiography

Signor Giambattista Vico, he was born in Naples in the year 1670 of upright parents, who left behind them a very good reputation. The father was of cheerful humor, the mother of a quite melancholy temper; and both came together in the fair disposition of this little son of theirs. As a boy he was very lively and restless; but at the age of seven he fell headfirst from high on a ladder to the floor, and remained a good five hours motionless and senseless, fracturing the right side of the cranium without breaking the skin, hence from the fracture arose a shapeless tumor, and from the many deep lancings of it the child lost a great deal of blood; such that the surgeon, having observed the broken cranium and considering the long state of unconsciousness, made the prediction that he would either die of it or he would survive stolid. However, neither of the two parts of this judgment, by the grace of God, came true; but as a result of this illness and recovery he grew up, from then on, with a melancholy and acrid nature which necessarily belongs to ingenious and profound men, who through ingenuity flash like lightning in acuity, through reflection take no pleasure in witticism and falsity.

--First paragraph of the Life of Giambattista Vico Written by Himself, 1725-1728.

Giambattista Vico (1668-1744)
Vico was professor of Latin Eloquence at the University of Naples. In the last decade of his life he was appointed Royal Historiographer by Charles of Bourbon. Vico's major work is the New Science (Scienza nuova), which was translated into English by the Italianist Thomas Goddard Bergin and the philosopher Max Harold Fisch in 1948. In this work, Vico presents the principles of humanity and gives an account of the stages common to the development of all societies in their historical life. He also shows how all human thought and action is connected to imagination and memory as well as to reason.

Vico is generally regarded as the founder of the modern philosophy of history. He may also be regarded as the founder of the philosophy of culture and the philosophy of mythology. Ernst Cassirer, the great twentieth-century philosopher of culture and symbolism, called Vico "the real discoverer of the myth." Vico's work has attracted attention for the modern study of rhetoric, language, poetry, architecture, aesthetics, law, moral philosophy, politics, education, metaphysics, society, culture and history. Vico's thought has importance for the full range of problems within the sphere of humane letters and the study of the self and of social institutions.

The New Science was written in Italian and published in a first edition in 1725. Vico rewrote it completely and published a second edition in 1730, which he was revising for a third printing at the time of his death in 1744. Vico wrote his autobiography, which was published in 1728. He also wrote a continuation of it in 1731.

Prior to the New Science Vico wrote a number of Latin works, principal among which are his conception of human education developed in his six Inaugural Orations from 1699-1707 (collected under the English title, On Humanistic Education) and in On the Study Methods of Our Time (De nostri temporis studiorum ratione) (1709). He presents a conception of knowledge and metaphysics based on a criticism of Descartes in On the Most Ancient Wisdom of the Italians (De antiquissima Italorum sapientia) (1710). These works and the autobiography have been translated into English. He wrote a collected work on jurisprudence. In the 1720s, he published the three parts of this work, which he referred to by the general title, Il diritto universale (Universal law). This work is equal in size to all Vico's other major works taken together. In it he develops a conception of law through its connections to human culture, and in one chapter, "Nova scientia tentatur" (A new science is essayed), Vico projects his conception of the New Science. Il diritto universale has been translated into English with the title, Universal Right.

In addition to these Vico wrote a number of smaller works and orations as well as commissioned histories, poems, and panegyrics. A few of these are available in English translation, as are some of his letters.

Vico's work had great influence on Jules Michelet, who translated the New Science and Autobiography into French and incorporated Vico into his own philosophy of history; Benedetto Croce, who founded his own idealist philosophy through a combination of Vico and Hegel and who, with Nicolini, created the standard edition of Vico's works in Italian; and James Joyce, who based the general structure of Finnegans Wake on the New Science, referring to Vico by name in various places and beginning the work with a play on Vico's name in Latin, "a commodius vicus of recirtculation."
Goethe acquired a copy of the New Science which he lent to Jacobi. Hamann read Vico, as did his disciple, Herder. Coleridge was the first English disseminator of Vichian ideas. Marx cites and discusses Vico in Capital. Yeats was interested in Vico and was influenced by Gentile's interpretation. Sorokin read Vico. Trotsky quotes Vico on the first page of his History of the Russian Revolution. Collingwood translated Croce's book on Vico and was influenced by Vico's conception of history, and Edmund Wilson began his influential To the Finland Station with a discussion of Vico.


"If Italy had listened to Giambattista Vico, and if, as at the time of the Renaissance, she had served to guide Europe, would not our intellectual destiny have been different? Our eighteenth-century ancestors would not have believed that all that was clear was true; but on the contrary that "clarity is the vice of human reason rather than its virtue," because a clear idea is a finished idea. They would not have believed that reason was our first faculty, but on the contrary that imagination was. . . . There was not an object that Vico touched without transforming it into gold."

--- Paul Hazard, La pensee europe enneau XVIII siecle de Montesquieu a Lessing

Link...
Link...

[Lloyd Gillespie]

The Subjectivity and Universal Validity of the Aesthetic Judgment…LINK


(These are the highlights from an article I recently came across, that actually prove the universal validity of a fundamental fully grounded a priori morality, through a new understanding of aesthetic and esthetic judgment. See if you can put the picture together. Philosophers have hunted for this information, since the dawn of philosophical time…)

In Kant’s view, universality and necessity are the two indications of a claim that has an a priori character. In the Critique of Pure Reason, he says:

Experience teaches us, to be sure, that something is constituted thus and so, but not that it could not be otherwise. First, then, if a proposition is thought along with its necessity, it is an a priori judgment; if it is, moreover, also not derived from any proposition except one that in turn is valid as a necessary proposition, then it is absolutely a priori. Second: Experience never gives its judgments true or strict but only assumed and comparative universality (through induction), so properly it must be said: as far as we have yet perceived, there is no exception to this or that rule. Thus if a judgment is thought in strict universality, i.e., in such a way that no exception at all is allowed to be possible, then it is not derived from experience, but is rather valid absolutely a priori. (R, B4)

“They must thus have a subjective principle, which determines what pleases or displeases only through feeling and not through concepts, but yet with universal
validity”

(The a priori universal subjective esthetic laws of thought… Pure play and the law of universal liberty…LG)

Kant thinks that the transcendental principle of general acceptability is this principle that provides the a priori character of taste. Such a principle, he claims,
can be only common sense—sensus communis. This is common sense that everyone has to have since everyone has the same cognitive capacities—this common
sense emerges from the free play of our cognitive faculties. It is a sense of an internal harmony. By viewing the sensus communis in these terms, he does not
consider this notion in its traditional meaning—he does not view it as an element of our social and moral being. The Aristotelian notion of sensus communis, the
primary unifying cognitive faculty, is merely about combining various perceptions in unity and does not contain the Kantian thought that sensus communis
emerges from the free play of our cognitive faculties. It follows that the Aristotelian notion does not include the disinterestedness and universality features of
the Kantian notion of it. Therefore, the meaning that Kant assigns to the term, the a priori character of taste, is different from the Aristotelian meaning of the
term, which includes both reason and practical reason. We know that, in his moral theory, Kant excludes the notion of sensus communis that is an element of
our social and moral being, and the moral feeling that is based on such a notion. Morality is not based on our feelings, but it is based on our reason—it is based on our practical reason.

[O]f whose judgment I here offer my judgment of taste as an example and on an account of which I ascribe exemplary validity to it, is a merely ideal
norm, under the presupposition of which one could rightfully make a judgment that agrees with it and the satisfaction in an object that is expressed in
it into a rule for everyone. ( J, 5:239)

Therefore, every judgment of taste is related to the ideal norm in the course of this transformation of the person that makes a judgment, and it is presented as
an exemplary of this ideal norm.

By “sensus communis,” however, must be understood the idea of a communal sense [. . . ] this happens by one holding his judgment up not so much
to the actual as to the merely possible judgments of others, and putting himself into the position of everyone else, merely by abstracting from the
limitations that contingently attach to our own judging; which is in turn accomplished by leaving out as far as is possible everything in one’s representational
state that is matter, i.e., sensation, and attending solely to the formal peculiarities of his representation or his representational state. ( J, 5:293

The point that he stresses is not the abstract commonality of mind, but a concrete commonality that represents the community. Sensus communis, with
such a condition that it possesses, is not fed from actuality but from possibility. Here, the issue in taste is not to approve something as beautiful, but to have a
certain kind of taste: the issue is to have an eye that faces toward a whole in which everything beautiful reaches to an agreement through that eye. Only such
an eye is capable of overcoming the illusion that is an outcome of our subjective conditions. Otherwise, in such an illusion, one may make a subjective judgment
as if it were objective. The person is supposed to avoid such illusions that would create prejudice in her judgment: the notion of common sense becomes actuality
as universal taste. By this taste, we can withdraw ourselves from our subjective choices. Therefore, taste, by its structure, is not merely subjective, but also it is a
phenomenon that is related to a community.
(continued...)