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A Refutation of the Diagonal Argument  [PDF]
Kazuhiko Kotani
Open Journal of Philosophy (OJPP) , 2016, DOI: 10.4236/ojpp.2016.63027
Abstract: The diagonal argument is a very famous proof, which has influenced many areas of mathematics. However, this paper shows that the diagonal argument cannot be applied to the sequence of potentially infinite number of potentially infinite binary fractions. First, the original form of Cantor’s diagonal argument is introduced. Second, it is demonstrated that any natural number is finite, by a simple mathematical induction. Third, the concept of potential infinity, created by Aristotle, is presented. Typically, the natural numbers are considered potentially infinite. However, although any natural number is finite, there is also no limit to how large a natural number can be. Fourth, the concept of the potentially infinite decimal is introduced. Fifth, it is easily proven that the diagonal argument cannot be applied to the sequence of all n-bit binary fractions in the interval [0,1). Finally, the diagonal argument is shown to be inapplicable to the sequence of the potentially infinite number of potentially infinite binary fractions, which contains all n-bit binary fractions in the interval [0,1) for any n.
Differential Calculus Based on the Double Contradiction  [PDF]
Kazuhiko Kotani
Open Journal of Philosophy (OJPP) , 2016, DOI: 10.4236/ojpp.2016.64039
Abstract: The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction.
What Is Number?  [PDF]
Kazuhiko Kotani
Open Journal of Philosophy (OJPP) , 2017, DOI: 10.4236/ojpp.2017.72008
Abstract: What is number? This question is difficult to answer. Because the number is one of the most basic concepts, it is difficult to define the natural number with other concepts. Still, this problem is worth trying to answer. Now, everything is digitized and processed on computer. The importance of the number is increasing day by day. Now is time to consider what number is. Throughout the history of humankind, the ancient Greeks considered this question most profoundly. In particular, Plato defined the natural number one. The natural number one is equal, invariable and indivisible. These properties are intuitively acceptable. However, we have never seen or touched the natural number one itself. How can we know it? Socrates said that we know it before birth. This claim is called anamnesis. In this paper, we use a method, in which Socrates’ anamnesis is studied by the contemporary science. From a modern viewpoint, we could take Socrates’ anamnesis to mean that the natural number one is written in our genes. This article considers whether there is a biological entity corresponding to the natural number one. As a result, we find that a life itself is the prototype of the natural number one, and then properties of life make a critical base of DNA similar to the natural number one through natural selection. A life is an integrated and indivisible system, which resists the law of entropy. Furthermore, the basic properties of life enable natural selection, which conserves genetic information despite the law of entropy. The source of the power, which enables life to resist the law of entropy, is the genetic information. In conclusion, a life is a prototype of the natural number one. Furthermore, a life recognizes nature using natural numbers and resists the law of entropy using natural numbers.
Life from the Viewpoint of Information  [PDF]
Kazuhiko Kotani
Open Journal of Philosophy (OJPP) , 2019, DOI: 10.4236/ojpp.2019.94031
Abstract: We shall consider the relationship between life and entropy from the viewpoint of information. Firstly, as long as life is alive, it tries to keep the order of its body. In contrast, inanimate materials quickly become in equilibrium. Life seems to have a special nature. However, since life is an open system, the maintenance of the order of the living body does not conflict with the second law of thermodynamics. Living life maintains its order using information and energy from the outer world. Secondly, due to the second law of thermodynamics, it is impossible to preserve information permanently. How can living organisms preserve such information? The key feature of living organisms is that there are two phases: life and death. Natural selection uses both life and death. When life is alive, life proliferates and retains genetic information. When life dies, its body is rapidly degraded and genetic information is lost. Both of them increase the number of advantageous genes for survival and eliminate disadvantageous genes for survival. In conclusion, it was confirmed that neither the maintenance of order in living body using information and energy nor the preservation of information by natural selection is inconsistent with the second law of thermodynamics.
Paraoxonase 1 in Chronic Kidney Failure
Alejandro Gugliucci,Kazuhiko Kotani,Satoshi Kimura
Journal of Lipids , 2012, DOI: 10.1155/2012/726048
Abstract: In this review we summarize the findings from the literature and our own laboratory on the decreased PON1 activity in renal failure, the mechanisms proposed and the effect of interventions. In addition to profound alterations in lipoproteins, reduced serum PON1 activity has been clearly established in the past decade and could contribute to accelerated development of atherosclerosis in ESRD and in HD. PON1 lactonase activity is lower in ESRD patients. Hemodialysis partially restores PON1 lactonase and the other activities. PON1 activity recovery after dialysis suggests that uremic toxins may play a mechanistic role in PON1 inactivation. Lower PON1 activity in CRF patients is associated with low thiol concentration, high CRP, and is beneficially enhanced with vitamin C and flavonoids. Changes in HDL subclasses, namely lower HDL3 in these patients may also play a role in PON1 lower activity. Future research should focus on: (1) mechanistic studies on causes for low PON1 activity and mass; (2) prospective studies focusing on whether there is an added predictive value in measuring PON1 activity (and PON1 activity in HDL3) in this patient population; (3) intervention studies attempting to increase PON1 activity. 1. Introduction The major cause of mortality in patients with end-stage renal disease (ESRD) receiving renal replacement therapy is cardiovascular disease. More than one million of these patients throughout the world are surviving with the assistance of renal replacement therapy [1–8]. More than 800,000 patients receive hemodialysis (HD), the most frequent modality. Survival on HD has improved, although vascular accidents, such as ischemic heart disease and hemorrhagic stroke, remain major problems [2, 7, 8]. All patients with chronic renal failure (CRF) have increased risk for death from cardiovascular disease, especially those undergoing HD [1, 2, 9]. They have numerous metabolic disorders that may hasten the development of plaques, such as insulin resistance, hypertension, and dyslipoproteinemia, along with other ESRD-related risk factors such as the classical calcium and phosphate metabolism disorders and secondary hyperparathyroidism [1–9]. CRF patients frequently have lipoprotein abnormalities such as low high-density lipoprotein (HDL)-cholesterol concentrations, increased remnant particles and hypertriglyceridemia. HDL-cholesterol concentrations are inversely correlated with atherogenic risk [3, 4, 6, 7]. HDL is not only a key player in reverse cholesterol transport but has the ability to protect low-density lipoprotein (LDL) against
The association between adiponectin, HDL-cholesterol and α1-antitrypsin-LDL in female subjects without metabolic syndrome
Kazuhiko Kotani, Toshiyuki Yamada, Nobuyuki Taniguchi
Lipids in Health and Disease , 2010, DOI: 10.1186/1476-511x-9-147
Abstract: In asymptomatic females (n = 194; mean age, 54 years) who were divided into non-MetS (n = 108) and MetS groups (n = 86), the fasting levels of serum AT-LDL, adiponectin and glucose/lipid panels were measured, in addition to body mass index (BMI) and blood pressure.The MetS group showed significantly higher BMI, blood pressure, glucose and triglyceride levels as well as significantly lower levels of HDL-cholesterol and adiponectin than the non-MetS group. A multivariate-adjusted analysis revealed that in the non-MetS group, AT-LDL was significantly, independently and positively correlated with adiponectin (β = 0.297, P < 0.05), along with HDL-cholesterol (β = 0.217, P < 0.05). In the MetS group, AT-LDL was significantly, independently and positively correlated with LDL-cholesterol only (β = 0.342, P < 0.05).These data suggest that AT-LDL may exert anti-atherosclerotic effects in female subjects without MetS. More studies are required to clarify the clinical roles of AT-LDL in relation to the pathophysiology of MetS.Atherosclerosis is an important health concern, because it leads to cardiovascular disease [1]. Oxidation of low-density lipoprotein (LDL) is involved in the atherosclerotic processes, and oxidized LDL (oxLDL) can exhibit atherogenic properties [2,3]. Recent research has shown that various types of oxLDL exist both in atherosclerotic lesions and in the circulation, and the circulating oxLDL is presently thought to be a useful marker reflecting one's atherosclerotic state [4-6]. On the other hand, it is becoming increasingly clear that oxLDL exerts dual effects on atherosclerosis [7-15]. Namely, low levels (small amounts) of oxLDL can exert an atheroprotective (anti-atherosclerotic) effect. However, the clinical data about this phenomenon are limited, and more clinical investigations are needed.While α1-antitrypsin (AT), a serine-proteinase inhibitor, protects tissues from damage caused by excess activities of proteinases [16], when AT is oxidized, it loses
Effects of Lifestyle Intervention Performed by Community Pharmacists on Glycemic Control in Patients with Type 2 Diabetes: The Community Pharmacists Assist (Compass) Project, a Pragmatic Cluster Randomized Trial  [PDF]
Hiroshi Okada, Mitsuko Onda, Masaki Shoji, Kazuhiko Kotani, Takeo Nakayama, Yasushi Nakagawa, Naoki Sakane
Pharmacology & Pharmacy (PP) , 2016, DOI: 10.4236/pp.2016.73016
Abstract: Background: Community pharmacists should be involved in diabetes care, while there has been less evidence about whether a brief lifestyle intervention is effective for diabetes care in community pharmacies. Objectives: To examine the effects of brief lifestyle intervention on glycemic control in patients with type 2 diabetes mellitus (T2D) by using a coaching style, provided by community pharmacists. Methods: A prospective, cluster-randomized, controlled trial was conducted in 50 groups of community pharmacies in Japan. In all, 132 patients with T2D (age, 20 - 75 years, ≥8.0% of hemoglobin A1c (HbA1c)) were assigned to the intervention group (n = 90) or the usual care group (n = 42). The intervention group (IG) underwent brief lifestyle coaching for self-care of T2D for 6 months. The standard care group (CG) received usual care by pharmacists and was given a general newsletter. The primary outcome was changes in HbA1c levels. Results: After 6 months, the IG had significantly improved HbA1c (IG: -0.6 ± 0.9 vs. CG: -0.2% ± 0.9%; p = 0.021 using the last observation carried forward analysis). Although the number of drugs reduced from 2.3 ± 0.8 to 2.0 ± 1.2 in the IG, the number increased from 2.3 ± 1.1 to 2.5 ± 1.1 in the CG (-0.2 ± 0.9 in IG vs. 0.2 ± 0.6 in CG; p = 0.023). Conclusions: The brief lifestyle intervention by community pharmacists improved glycemic control in patients with T2D. Community pharmacists may more positively participate as lifestyle coaches for diabetes care.
The Effect of Antihypertensive Drugs on Endothelial Function as Assessed by Flow-Mediated Vasodilation in Hypertensive Patients
Michiaki Miyamoto,Kazuhiko Kotani,Shun Ishibashi,Nobuyuki Taniguchi
International Journal of Vascular Medicine , 2012, DOI: 10.1155/2012/453264
Abstract: Endothelial dysfunction is found in hypertensive patients and may serve as a prognostic marker of future cardiovascular events. Endothelial function can be assessed noninvasively by flow-mediated vasodilation (FMD). The goal of this paper is to summarize comprehensively the clinical trials that investigated the effects of antihypertensive drugs on endothelial function assessed by FMD in hypertensive patients. A PubMed-based search found 38 clinical trial papers published from January 1999 to June 2011. Significant improvement of FMD after antihypertensive treatment was shown in 43 of 71 interventions (among 38 clinical trial papers). Angiotensin II receptor blockers and angiotensin converting enzyme inhibitors appeared to improve FMD more than other drug types. Antihypertensive treatment can improve endothelial dysfunction when assessed by FMD, although there are conflicting data that require further research. 1. Introduction Atherosclerotic risk factors such as hypertension (HTN), diabetes mellitus, dyslipidemia, obesity, and smoking cause endothelial dysfunction [1–5]. Endothelial dysfunction occurs in the early stages of atherosclerosis and is involved in disease progression as well as the morbid cardiovascular events that often occur in advanced stages of the diseases [1–5]. The endothelium is involved in the control of the coagulation/fibrinolytic system, platelet aggregation, adhesion of leukocytes, and smooth muscle cell proliferation and is important in the maintenance of vascular tone [1, 3]. The response-to-injury hypothesis, proposed by Russell Ross [6], states that atherosclerosis is due to an inflammatory reaction in response to endothelial injury or dysfunction and is supported by numerous basic and clinical investigations [1, 3]. The evaluation of endothelial function is available as a predictor of cardiovascular events and as a surrogate marker for early atherosclerosis [1–3, 7, 8]. There are several methods to evaluate endothelial function that include an invasive method using endothelium-dependent vasodilators injected into a coronary or peripheral artery [7], and flow-mediated vasodilation (FMD), a noninvasive method based on endothelium-dependent arterial vasodilation [9, 10]. FMD was first reported in 1992 by Celermajer et al., as an innovative method of detecting endothelial dysfunction [10]. The sudden release of an artery after transient occlusion causes an increase in shear stress on the vessel wall due to hyperemia and this stimulates endothelial cells to release various physiologically active substances. Nitric oxide (NO) is
Serum aspirin esterase is strongly associated with glucose and lipids in healthy subjects: different association patterns in subjects with type 2 diabetes mellitus
Kazuhiko Kotani, Satoshi Kimura, Tetsu Ebara, Russell Caccavello, Alejandro Gugliucci
Diabetology & Metabolic Syndrome , 2010, DOI: 10.1186/1758-5996-2-50
Abstract: The study was aimed at investigating the correlations of serum AE activity with cholinesterase (ChE) and metabolic variables in healthy subjects in comparison to subjects with type 2 diabetes mellitus (T2DM).In cardiovascular disease-free T2DM subjects and healthy controls, the AE activity levels and/or the correlation patterns between AE and the other variables were analyzed.Neither AE nor ChE activities were higher in the subjects with T2DM. Serum AE activity strongly correlated with ChE as well as glucose/lipids variables such as total cholesterol and triglyceride in healthy subjects, while the correlations between AE and glucose/lipids variables were not present in T2DM subjects.These data may reflect the pathophysiological changes between healthy and T2DM subjects. Our data may thus provide the basis for future studies to unravel the mechanisms.Aspirin (acetylsalicylic acid), by virtue of its antipyretic, analgesic, anti-inflammatory and anti-platelet actions, is one of the most widely employed drugs in the prevention of cardiovascular disease. While its prophylactic use against athero-thrombosis is well-documented, the optimal dose that confers maximal anti-platelet action without increased risk of bleeding remains to be determined [1,2]. Serum aspirin esterase (AE) activity may account for part of aspirin pharmacokinetics and has been proposed as one source of variation in aspirin effectiveness [3].Type 2 diabetes mellitus (T2DM) is a common health problem associated with cardiovascular disease, with an increasing incidence worldwide [4]. One study has recently reported an increased level of AE activity in patients with T2DM, and it has been suggested that this may be modified by lipoprotein-cholesterol metabolism in these patients [5]. In addition, serum cholinesterase (ChE) has shown a tight correlation with AE and an association with the dyslipoproteinemia of the metabolic syndrome [5,6]. However, these relationships remain yet to be fully established. We
The relationship between oxidized lipoprotein(a) and carotid atherosclerosis in asymptomatic subjects: A comparison with native lipoprotein(a)
Kazuhiko Kotani, Shingo Yamada, Toshiyuki Yamada, Nobuyuki Taniguchi, Ikunosuke Sakurabayashi
Lipids in Health and Disease , 2011, DOI: 10.1186/1476-511x-10-174
Abstract: The atheroscrerosis-related variables including Lp(a) and oxLp(a) were measured in 136 cardiovascular disease-free subjects (61 males and 75 females, mean age of 64 years). The serum oxLp(a) level was quantified using a sandwich ELISA system. The CIMT level was ultrasonographically measured on bilateral carotid arteries.The median level of Lp(a) was 120 μmol/L, oxLp(a) was 0.06 nmol/L, and CIMT was 0.7 mm, respectively. A simple correlation test showed that the CIMT was significantly and positively correlated with age, systolic blood pressure and oxLp(a) (r = 0.208, P < 0.05). A multiple linear regression analysis revealed that oxLp(a) continued to show a significant and positive correlation with the CIMT (β = 0.202, P = 0.01). Although the similar analyses were conducted for Lp(a), it showed only a weak correlation with the CIMT (r = 0.011, β = 0.041, both P < 0.05).These results suggest that oxLp(a) may be more closely associated with accelerated carotid atherosclerosis, in comparison to Lp(a), in this population. This finding can be important for obtaining a better understanding of the different atherogenic roles played by oxLp(a) in comparison to Lp(a).The oxidation of lipids and lipoproteins is involved in the pathogenesis of atherosclerosis [1]. Lipoprotein(a) (Lp(a)) contains low-density lipoprotein (LDL)-like moieties, in which the apoB-100 component is covalently linked to the unique glycoprotein, apolipoprotein(a) (apo(a)), and a high circulating level of Lp(a) is considered to be a risk factor for atherosclerotic diseases [2,3]. While the physiological role of Lp(a) in atherosclerotic diseases remains incompletely understood, the oxidization of Lp(a) may be one of the crucial clues that atherogenesis has occurred. Of note, the existence of oxidized phospholipids on Lp(a) in the circulation has been reported to be strongly associated with coronary artery disease [4]. The earlier studies used an assay system that determines the content of oxidized phospholi
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