Nov 25, 2012


By Marsigit, Yogyakarta State University, Indonesia


Ross, K.L., 2001, exposed that Kant proposes that space and time do not really exist outside of us but are "forms of intuition," i.e. conditions of perception, imposed by our own minds. While Gottfried, P., 1987, noted from Kant that although the forms of time and space are "subjective conditions of sensation" and depend for their appearance on perceptual activity, they are nonetheless characterized as being a priori: antecedent to the specific sensations for which they provide a conceptual frame.  Kant stated that time existed is not for itself or as an objective quality in things; to conceive of time as something objective would require its presence in things which were not objects of perception; however, since time and space were only knowable as the a priori forms of intuition, any other assumption about them, apart from this context, could not be substantiated. According to Kant, time was also the form of our inner sense, of our intuition of ourselves and of our own inner situation; belonging neither to any pattern nor place, it determined the relationship of perceptions within our inner situation; because this inner intuition as such assumed no shaper, it had to be imagined by positing succession through a line extending ad infinitum in which sensory impressions form a uni-dimensional sequence and by generalizing from the attributes of this line to those of time itself.
Kant summed up that time was to be seen as the formal a priori condition for all appearance; whereas space remained the pure form of al outward intuition, time supplied the subject with an inward orientation essential for perceptual relations (Gottfried, P., 1987). Kant argued that the structure for the a posteriori representations we receive from sensation must itself be a priori; this leads him to the science of a priori sensibility, which suggests that our capacity to receive representations of objects includes a capacity to receive representations of the a priori form of objects. Accordingly, since space is one of two such a priori forms, a priori sensibility includes a capacity to receive pure representations of space (Shabel, L., 2003). Kant denied that time and space as an absolute reality, and maintained that outside of its cognitive function time is nothing; the objective validity of time and space was limited to the regularity of their relationship to sensation, yet within this limited framework their activity was constant and predictable. (Gottfried, P., (1987)

Pure Intuition and Empirical Reality

It was elaborated in “IMMANUEL KANT (1724-1804): Kant's Criticism against the Continental Rationalism and the British Empiricism”, http://www.Google Search that space and time do not exist by themselves that is they are not real things existing outside of our mind. Kant perceived that Space and Time are not qualities, nor relations belonging to the things in themselves; they are the forms of our empirical intuition and are rooted in the subjective structure of our mind. Further, he claimed that we sense space and time with two forms of empirical intuition and they-themselves intuition at the same time. These intuitions are pure, since they are capable of becoming objects of our inquiry quite apart and independent from our empirical intuition. Kant also claimed that space and time are also a priori, because these intuitions as the forms of empirical intuitions precedes from all empirical intuitions, as long as they are the subjective conditions in which something can be an object of our empirical intuition. Space and time, therefore, are not containers in which all the real things are encompassed, nor the dimension or order which belongs to the things in themselves; they are the forms of our intuition. Kant claimed that our ideas are in regards to their origin either pure or empirical; they are intuitions or concepts.

Kant then strived to demonstrate that space and time are neither experience nor concepts, but they are pure intuition. He called it as Metaphysical Demonstrations of space and time; and concluded that: firstly, space is not an empirical concept obtained by abstraction due to any empirical concept obtained from the external senses such as even "next to each other" presupposes the notion of space; and this means that two things are located at two different spaces. Time is not obtained by abstraction or association from our empirical experience, but is prior to the notion of simultaneous or successive. Space and time are anticipations of perception and are not the products of our abstraction. Secondly, the idea of space is necessary due to the fact that we are not able to think of space without everything in it, however we are not able to disregard space itself. We can think of time without any phenomenon, but it is not possible to think of any phenomenon without time; space and time are a priori as the conditions for the possibility of phenomena. Thirdly, the idea of space is not a universal concept; it is an individual idea or an intuition. There is only one time and various special times are parts of the whole time and the whole is prior to its parts. Fourthly, space is infinite and contains in itself infinitely many partial spaces. (“IMMANUEL KANT (1724-1804): Kant's Criticism against the Continental Rationalism and the British Empiricism”, http://www.Google)

Next, Kant developed Transcendental Demonstrations to indicate that the possibility of synthetic a priori knowledge are proven only on the basis of Space and Time, as follows: first, If space is a mere concept and not an intuition, a proposition which expands our knowledge about the characters of space beyond the concept cannot be analyzed from that concept. Therefore, the possibility of synthesis and expansion of Geometric knowledge is thus based on space's being intuited or on the fact that such a proposition may be known true only in tuition. And thus the truth of a Geometric proposition can be demonstrated only in intuition. Second, the apodeicticity of Geometric knowledge is explained from the apriority of intuition of space and the apodeicticity of Arithmetics knowledge is explained from the apriority of intuition of time. If space and time be empirical, they do not have necessity; however, both Geometric and Arithmetic propositions are universally valid and necessary true. Third, mathematical knowledge has the objective reality that is, based on space and time by means of which our experiences are possible. Forth, in regard to time, change and motion are only possible on the basis of time. (“IMMANUEL KANT (1724-1804): Kant's Criticism against the Continental Rationalism and the British Empiricism”, http://www.Google)

On the other hand, Kant claimed that the relations which are a priori recognizable in space and time are valid to all the possible objects of experience. However, they are valid only to the phenomena and not to the things in themselves; therefore, space and time have the Empirical Reality and the Transcendental Ideality at the same time. Kant insisted that any thing as long as it is an external phenomenon necessarily appears in spatial relationship; while any phenomenon necessarily is in temporal relationship. It called that space and time are objective to everything which is given in experience, therefore, space and time are empirically real; however, they do not have the absolute reality, because they do not apply to things in themselves, whether as substances or as attributes. Due to space and time have no reality, but are ideal, this then is called the Transcendental Ideality of Space and Time. Kant insisted that we are never able to recognize things in themselves; any quality which is to belong to the thing in itself can never be known to us through senses. At the same time, anything which is given in time is not the thing in itself; therefore, what we intuitively recognize ourselves by reflection, is how we appear as a phenomenon, and not how we really are. (“IMMANUEL KANT (1724-1804): Kant's Criticism against the Continental Rationalism and the British Empiricism”, http://www.Google)

The Concepts of Understanding and the Method to Discover

The faculty of understanding is a faculty for synthesis, unification of representations; the functioning of this faculty can be analyzed at two different levels, corresponding to two different levels at which we may understand representations:  a general logical level, and a transcendental level.  In terms of the former, synthesis results in analytic unity; in terms of the latter, synthetic unity.  The latter takes into account the difference between pure and empirical concepts.  Analytic Unity is an  analysis of a judgment at the level of general logic indicates the formal relationship of concepts independently of their content. Synthetic Unity refers to objectivity.  At the transcendental level, judgments have transcendental content; that is, they are related to some object; they are given to the understanding as being about something.  This is more than a matter of having a certain logical form; inasmuch as the Categories are at play in a judgment, that judgment is a representation of an object. 

Wallis, S.F, 2004, noted that Kant's next concern is with the faculty of judgment, as Kant said "If understanding as such is explicated as our power of rules, then the power of judgment is the ability to subsume under rules, i.e., to distinguish whether something does or does not fall under a given rule.". He summed up that the following stage in Kant's project will be to analyze the formal or transcendental features of experience that enable judgment, if there are any such features besides what the previous stages have identified; the cognitive power of judgment does have a transcendental structure. He also identified that Kant argues that there are a number of principles that must necessarily be true of experience in order for judgment to be possible; Kant's analysis of judgment and the arguments for these principles are contained in his Analytic of Principles.

Kemerling, G.,2001, considered that, according to Kant, the sorts of judgments consists of: each of them has some quantity;  some quality; some relation; and some modality. He noted that, according to Kant, any intelligible thought can be expressed in judgments of these sorts; but then it follows that any thinkable experience must be understood in these ways, and we are justified in projecting this entire way of thinking outside ourselves, as the inevitable structure of any possible experience. The intuitions and the categories can be applied to make judgments about experiences and perceptions, but cannot, according to Kant, be applied to abstract ideas such as freedom and existence without leading to inconsistencies in the form of pairs of contradictory propositions, or “antinomies,” in which both members of each pair can be proved true.( Kant, http:// www.encarta.msn. com/).

Propositions, according to Kant, can also be divided into two other types: empirical and a priori; empirical propositions depend entirely on sense perception, but a priori propositions have a fundamental validity and are not based on such perception. Kant's claimed that it is possible to make synthetic a priori judgments and regarded that the objects of the material world is fundamentally unknowable; therefore, from the point of view of reason, they serve merely as the raw material from which sensations are formed. Objects of themselves have no existence, and space and time exist only as part of the mind, as “intuitions” by which perceptions are measured and judged .( Kant, http:// www.encarta.msn. com/). Kant, then stated that a number of a priori concepts, which he called categories, exist; and this category falls into four groups: those concerning quantity, which are unity, plurality, and totality; those concerning quality, which are reality, negation, and limitation; those concerning relation, which are substance-and-accident, cause-and-effect, and reciprocity; and those concerning modality, which are possibility, existence, and necessity.
Kant claimed that there is only one way in which a mediating element can be discovered, that is, by examining the single element which is present in all appearances, but at the same time is capable of being conceptualized that is “time”. According to him, we must therefore discover various ways of thinking of time, and if we can discover the ways in which this must be done, we can say that they both conform to the conditions of thought and are present in all appearances. Kant calls these conceptualizations of time "schemata"; he then found four fundamental modes of thinking time, one corresponding to each of the basic divisions of categories that are time-series, time-content, time-order, and the scope of time. 

Kant claimed that as a one-dimensional object, time is essentially successive that is one moment follows another; and in order to think time as a succession,  we must generate the time-series that is we must think one moment as following another. Kant suggested that at each point of the series up to that point; therefore, we always think time as a magnitude. Accordingly, since the categories of quantity are those of unity, plurality and totality, we can say that they apply to appearances in that all appearances must be thought as existing within a specific time- span which can be thought as momentary that is as a series of time spans or as the completion of a series of time spans. On the other hand, Kant insisted that we can think of a given time as either empty or full; in order to represent objects in time we must resort to sensation, so that in thinking a time we must always ask whether that time is filled up. Thus the schema of quality is the filling of time; it would be natural to assume that the question whether-a time is full admits of a simple answer of yes or no.

However, Kant claimed that reality and negation must be conceived as two extremes or limits, between which exist infinitely many degrees; he called these degrees as "intensive magnitudes"
Kant also claimed that schemata for the categories of relation are treated separately because the relational categories treat them in respect to one another and that time considered of it-self is successive but not simultaneous, and space is simultaneous but not successive. Kant, therefore noted to think objects in a time-order: as enduring through a number of times that is that of the permanence of substance, as "abiding while all else changes"; as in one state of affairs which succeeds another that is we think the states of substances as occupying a succession of times, in accordance with a rule; and as co-existing that is the schema of reciprocity or mutual simultaneous interaction. 

Meanwhile, Kant insisted that time is supposed to relate objects, not to one another, but to the understanding that is, we can think an object in one of three ways: as occupying some time or other, without specifying what part of time that is the schema of possibility in which we can think an object as possible in so far as we can think it as occupying some time or other, whether or not it actually occupies it; as existing in some definite time that is the schema of actuality in which we think an object as actual when we claim that it exists in some specific part of time; and as existing at all times that is the schema of necessity in which an object is thought as being necessary if it is something which we must represent as occupying all times, in other words, that we could not think of a time which does not contain that object. 

1.    See Mattey, G.J., 2004, Kant Lexicon, G. J. Mattey's Kant Home Page,
2.    ibid
3.    ibid
4.    ibid


  1. Anggoro Yugo Pamungkas
    S2 Pend.Matematika B 2018

    Assalamualaikum Warahmatullahi Wabarakatuh.
    Berdasarkan artikel diatas, membahas 2 pokok yaitu intuisi murni dan konsep murni dari pemahaman. Nah yang pertama saya ingin mwngomentari yang intuisi murni dari pemahaman terlebih dahulu. intuisi murni yaitu intuisi ruang dan waktu, dimana konsep-konsep pengetahuan dapat dikonstruksi secara sintetis. Intuisi murni menjadi landasan dari semua penalaran dan keputusan dari pengetahuan yang didapat. Jika penalaran tidak berlandaskan intuisi murni maka hal itu tidak mungkin bisa terjadi.

  2. Anggoro Yugo Pamungkas
    S2 Pend.Matematika B 2018

    Assalamualaikum Warahmatullahi Wabarakatuh.
    Berdasarkan artikel diatas, saya ingin mengomentari bagian yang kedua yaitu pemahaman konsep. Pemahaman adalah kemampuan yang dimiliki seseorang untuk mengerti atau memahami sesuatu. Dengan kata lain, memahami adalah suatu perbuatan seseorang yang mengetahui tentang sesuatu dan dapat melihatnya dalam berbagai segi. Seseorang dikatakan memahami suatu hal, jika dia dapat memberikan penjelasan dan menirukan hal tersebut dengan menggunakan kata-katanya sendiri. Namun, dalam kenyataannya menirukan sesuatu tidak mungkin bisa sama dengan apa yang ditiru, karena ruang dan waktunya sudah berbeda.

  3. Fabri Hidayatullah
    S2 Pendidikan Matematika B 2018

    Intuisi murni ruang dan waktu menurut Immanuel Kant menyajikan spektrum pengetahuan. Intuisi merupakan pengetahuan yang tidak tertata. Jiwa manusia yang cenderung ke arah penyatuan pengetahuan tidak berhenti pada intuisi ini, jiwa manusia selalu ingin bergerak maju ke pengetahuan pada tingkat yang lebih tinggi yang berpusat di kecerdasan. Aktivitas ini yang disebut sebagai penginderaan pemahaman. Menurutnya, penginderaan pemahaman memiliki kategori-kategori untuk memudahkan dalam mempersepsi. Kategori tersebut terdiri dari 12 item yang menjadi syarat apriori, yaitu kuantitas (universal, particular, singular), kualitas (affirmative, negative, infinitive), relasi (categorical, hypothetical, disjunctive) dan modalitas (problematical, assertorical, apotidical).

  4. Diana Prastiwi
    S2 P. Mat A 2018

    Pandangan Kant tentang matematika memberi sumbangan yang berarti ditinjau dari peranan intuisi dan konstruksi konsep matematika. Pemahaman maupun konstruksi matematika diperoleh dengan cara terlebih dulu menemukan “intuisi murni” pada akal atau pikiran kita.Sumbangsih matematika yang diberikan adalah suatu ilmu matematika kita mengerti suatu bilangan pada awlanya hingga menjadikan matematika abstrak. namun matematika adalah ilmu yang mempengaruhi banyak ilmu pengetahuan muncul.

  5. Fany Isti Bigo
    PPs UNY PM A 2018

    Dalam tulisan tentang intuisi murni dan teori pemahaman ini, Ross, KL, 2001, mengungkap bahwa Kant mengusulkan bahwa ruang dan waktu tidak benar-benar ada di luar kita tetapi bentuk intuisi yaitu kondisi persepsi yang dipaksakan oleh pikiran kita sendiri. Kant menyimpulkan waktu itu harus dilihat sebagai kondisi apriori untuk semua penampilan, sedangkan ruang tetap bentuk murni intuisi luar, waktu yang disediakan subyek dengan orientasi ke dalam bentuk penting untuk hubungan persepsi. Kita hendaknya mampu untuk memberikan pemahaman mengenai konsep yang ada berdasarkan intuisi yang ada.

  6. Amalia Nur Rachman
    S2 Pendidikan Matematika B UNY 2018

    Kant mengartikan intuisi sebagai proses penerimaan data mentah pengetahuan dari pengalaman tanpa melalui konseptualisasi. Sedangkan pemahaman digambarkan sebagai kemampuan intelektual yang spontan, aktif, dan kreatif dalam membentuk konsep. Pemahaman berbanding terbalik dengan sensibilitas yang bersifat sensual, pasif, dan reseptif. Pemahaman membutuhkan dua hal yaitu kemampuan konseptualisasi dan kemampuan pemahaman yang menerapkan kosep pada objek. Tiga tahapan dalam memahami yaitu synopsis, imajinasi, dan pengenalan

  7. Rosi Anista
    S2 Pendidikan Matematika B

    Dalam memahami konsep matematika diperlukan kemampuan generalisasi serta abstraksi yang cukup tinggi. Sedangkan saat ini penguasaan peserta didik terhadap materi konsep – konsep matematika masih lemah bahkan dipahami dengan keliru. Padahal pemahaman konsep merupakan bagian yang paling penting dalam pembelajaran matematika. Artinya dalam mempelajari matematika peserta didik harus memahami konsep matematika terlebih dahulu agar dapat menyelesaikan soal-soal dan mampu mengaplikasikan pembelajaran tersebut di dunia nyata.

  8. Nur Afni
    S2 Pendidikan Matematika B 2018

    Assalamualaikum warahmatullahi wabarakatuh.
    Kant mengklaim bahwa hanya ada satu cara di mana elemen mediasi dapat ditemukan, yaitu dengan memeriksa elemen tunggal yang hadir dalam semua penampilan, tetapi pada saat yang sama mampu dikonseptualisasikan yaitu "waktu". Menurutnya, oleh karena itu kita harus menemukan berbagai cara berpikir waktu, dan jika kita dapat menemukan cara-cara di mana ini harus dilakukan, kita dapat mengatakan bahwa mereka berdua sesuai dengan kondisi pemikiran dan hadir dalam semua penampilan. Kant menyebutnya sebagai skemata. terimakasih

  9. Janu Arlinwibowo
    PEP 2018

    Sesuai dengan hakekat berpikir itu sendiri maka pemikiran manusia itu dimulai dari kategori, sedang kategori dimulai dari intuisi. Proses membentuk kategori dalam pikiran tanpa kita sadari dan tidak ada seorangpun yang tahu kapan kita memperoleh kategori dalam pikiran kita karena itu bersifat pribadi, bersifat personal, bersifat konteks, dikatakan demikian karena itu berlaku pada semua orang dan diperoleh dari interaksi atau kegiatan. Oleh karena itu belajar matematika di sekolah didefinisikan sebagai interaksi maka penting sekali intuisi. Bagi anak intuisi itu penting karena dia melakukan kegiatan tapi tidak mengerti hakekat yang dikerjakan. Sama hanya dengan kita sebagai seorang guru kita harus tahu hakekat mengajar, sebagai seorang guru atau calon pendidik kadang kita tidak tahu kenapa kita mengajar demikian, kita hanya melaksanakan pembelajaran tanpa memikirkannya, sehingga guru maupun pendidik hanya sebagai pelaksana saja belum sebagai pengembang. Padahal setiap guru adalah researcher. Dan dalam matematika peran intuisi itu sangat penting.
    Banyak pemikir besar seperti Immanuel Kant yang menekankan pentingnya intuisi dan dampaknya yang besar terhadap kehidupan pribadi dan profesional. Yang disefiniskan sebagai pengetahuan 'a priori', dan sebagai alat penting dan sangat kita perlukan sebagai manusia. Intuisi adalah salah satu fungsi utama dari pikiran manusia selain perasaan. Dengan menyeimbangkan semua fungsi dalam diri kita sendiri, kita memiliki kemampuan untuk memaksimalkan potensi kita. intuisi sebagai fungsi psikologis dasar yang menengahi persepsi dengan cara tidak sadar. Filosof Immanuel Kant membangun pengertian intuisi dengan membedakan antara pertimbangan analitik dan pertimbangan sintetik. Pertimbangan analitik membutuhkan konfirmasi logis serta bersifat a priori atau tidak membutuhkan konfirmasi empiris untuk menjelaskan mengapa sesuatu hal benar.

  10. Sintha Sih Dewanti
    PPs S3 PEP UNY

    Kant dalam karyanya Critique of Pure Reason menyatakan ruang dan waktu merupakan bentuk intuisi inderawi, yang sekaligus menunjukkan adanya aktivitas pikiran yang menstruktur. Manusia hanya mampu menangkap fenomena saja melalui intuisi inderawi dalam ruang waktu yang kemudian dikategori dalam akal. Noumena tidak akan pernah tersentuh. Manusia dapat mengalami sebuah dunia karena ia terletak di dalam ruang, serta dapat selalu berubah karena ruang dan waktu adalah bentuk-bentuk subjektif inderawi.