Memristor Spice Model For Designing Memristor Circuits Economics Essay

Memristor Spice Model For Designing Memristor Circuits Economics Essay Memristors are novel electronic devices, a device that can be used and give a great advantage in many applications such as memory, logic, neuromorphic systems and so on. A computer model of the memristor would be a useful tool to analysis circuit behavior to help in develops application of this memristor as passive circuit element via simulation. In this paper, we incorporate a memristor SPICE for designing memristor circuit which is more focusing on non-linear model and analog circuits. SPICE model would be appropriate way to describe real device operation. We incorporating the memristor with various window functions that have been proposed in non linear ion drift memristor devices. In investigating and characterizing the physical electronic and behavioral properties of memristor devices, the circuit analysis of the proposed memristor models are then been studied. The simulation output should have a current-voltage hysteresis curve, which looks like bow tie. The loops map the switch ing behavior of the device. Then, we come out with a simple analog circuit which in this case we construct a simple integrator op-amp and differentiator op-amp circuit and make comparison between memristor implemented circuit and normal circuit. The research verifies the proposed memristor model, the possibilities of implementing memristor model and the advantage implementing the memristor in analog circuit. Keywords memristor, SPICE model, non linear, window functions, analog circuit. Introduction Memristor is the contraction of memory resistor which is a passive device that provides a functional relation between charge and flux. It is a two-terminal circuit element in which the flux between the two terminals is a function of the amount of electric charge that has passed through the device [1]. A memristor is said to be charge-controlled if the relation between flux and charge is expressed as a function of electric charge and it is said to be flux-controlled if the relation between flux and charge is expressed as a function of the flux linkage [2]. In 1971, Leon Chua proposed that there should be a fourth fundamental passive circuit element to create a mathematical relationship between electric charge and magnetic flux which he called the memristor which is short for memory resistor [2]. The current is defined as the time derivative of the charge. The voltage is defined as the time derivative of the flux according the faraday law. A resistor is defined by the relationship between voltage and current dv=Rdi, the capacitor is defined by the relationship between charge and voltage dq=Cdv, the inductor is defined by the relationship between flux and current dà Ã¢â‚¬  =Ldi. The fourth fundamental circuit element completes the symmetry of the relation between charge and magnetic flux dà Ã¢â‚¬  =Mdq. Table 1 show the relationship between the fundamental circuit element. Basic two terminal devices Equation Relationship between fundamental circuit element Resistor,R dv=Rdi v and i Capacitor,C dq=Cdv v and q Inductor,L dà Ã¢â‚¬  =Ldi i and à Ã¢â‚¬   Memristor,M dà Ã¢â‚¬  =Mdq q and à Ã¢â‚¬   Table 1: The four fundamental element (resistor, capacitor, inductor and memristor). In 2008, Stanley Williams and his team at Hewlett Packard had succesfully fabricated the first memristor in physical device form which is a long wait from Leon Chua discovery in 1971 [3]. Memristance is a property of memristor. When the charge flows in one direction through a circuit, the resistances of the memristor increase. The resistance decreases when the charge flows in the opposite direction in the circuit. If the applied voltage is turned off, thus stopping the flow of charge and the memristor remembers the last resistance that it had [1]. In HP memristor model, to create a memristor, they used a very thin film of titanium dioxide (TiO2). The thin film is then sandwiched between the two platinum (Pt) contacts. One side of TiO2 is doped with oxygen vacancies denoted as TiO2-x which x is usually 0.05. The oxygen vacancies are positively charged ion and make it conductive, thus it behaves as a semiconductor. Another side of the TiO2 junction is undoped. The undoped region has insulating properties. The device established by HP is shown in Figure 1 [3]. Figure 1: Memristor model adapt from [3]. When a positive voltage is applied, the positively charged oxygen vacancies in the doped TiO2-x layer are repelled and moving them towards to the undoped TiO2 layer. When the boundary between the two materials moves, the percentage of the conducting TiO2-x layer is increase. Thus, the conductivity of the whole device increases. When a negative voltage is applied, the positively charged oxygen vacancies are attracted and pulling them out of TiO2 layer. This increases the amount of insulating TiO2, thus increasing the resistivity of the whole device. When the voltage is turned off, the oxygen vacancies do not move. The boundary between the two titanium dioxide layers is frozen. This is how the memristor remembers the voltage last applied [1]. Methodology Our aim in this research is to provide a simulation program adequately simulates and can be used as a circuit element in design work. To model the electrical characteristics of the memristor, SPICE would be appropriate way to describe real device operation [4]. Moreover, using the model as a sub-circuit can highly guarantee a reasonable high flexibility and scalability features [5]. We use LTSPICE to create a memristor model and design new symbol of the memristor circuit for the simulation because LTSPICE is much easier to handle compared to others. On the other hand, LTSPICE is a freeware and it will give a great advantage to the students in doing research for this newly devices. We use SPICE model that been adapt from [6] and we made some adjustment so we can use it for several window functions that has been proposed for non linear ion drift model. The SPICE model is created based on the mathematical model of the HP Labs memristor. After the memristor has been modeled, we first studied the difference between proposed memristor and then we will start design and implement the memristor with an analog circuit. We also investigate and made a comparison between the memristor circuit with analog circuit to see the difference and study the behavior of the circuits. Model Of The Memristor from HP Labs In the model of a memristor presented here, there is a thin semiconductor film that has two regions, one with a high concentration of dopant that behaves like a low resistance called RON and the other with a low dopant concentration with higher resistance called ROFF [3]. The film is sandwiched between two metal contacts as in figure 1. The total resistance of the memristor, RMEM, is a sum of the resistances of the doped and undoped regions, w is the width of the doped region and D is the total length of the TiO2 layer. ROFF and RON will be the limit values of the memristor resistance for w=0 and w=D. The ratio of the two resistances is usually given as 102 103. (1) (2) From the ohms law relation between the memristor voltages and current, we get (3) Then, we insert (1) into (3). The voltage v(t) across the device will move the boundary between the two regions causing the charged dopants to drift. So, there is a drift ion mobility  µv in the device. The change of the boundary is denoted as in (5). (4) (5) To get x(t), we then integrates the right side of equation (5) which then yields the following formula (6) By inserting equation (6) into equation (4) and since usually RON (7) Where  µv is the average drift velocity and has the units cm2/sV, D is the thickness of titanium-dioxide film ROFF and RON are on-state and off-state resistances and q(t) is the total charge passing through the memristor device. Non Linear Ion Drift Model Even a small voltage across the nanodevices will produce a large electric field [7]. This causing the ion boundary position will move in a decidedly non-linear. Nonlinear dopant drift adds nonlinear window function f(x) to the state equation. The window function decreases as the state variables drift speed approaches the boundaries until it reaches zero when reaching either boundaries [8]. The speeds of the movement of the boundary between the doped and undoped regions are depending on several factors. (8) Where  µv is the dopant mobility. The speed of the boundary between the doped and undoped regions decreases gradually to zero at the film edges [1]. We simulate the nonlinear ion drift memristor model with these window function to see the difference and the issue that been faced by them. Window Function Window function is a function of the state variable. Window function forces the bounds of the device and to add nonlinear behavior close to these bounds. In other words, it creates the boundary for the memristor. Any effective window function should therefore fulfill the following conditions [8]: Take into account the boundary conditions at the top and bottom electrodes of the device; Be capable of imposing nonlinear drift over the entire active core of the device; Provide linkage between the linear and nonlinear dopant drift models; Be scalable, meaning a range of fmax(x) can be obtained such that 0 à ¢Ã¢â‚¬ °Ã‚ ¤ fmax(x) à ¢Ã¢â‚¬ °Ã‚ ¤ 1; Utilize a built-in control parameter for adjusting the model. There are several window functions that have been proposed for non-linear model till date which are by Strukov, Joglekar and, Biolek, and Prodromakis. Strukov proposed the following window function [3]. (9) However, as we can see in the figure 2, this window function lacks of flexibility. Figure 2: Plot of Strukov window function. Another window function was proposed by Joglekar [4], which has a control parameter p which is a positive integer. The purpose of having a control parameter as an exponent is to incorporate scalability and flexibility in window function f(x) that describes the dopant kinetics. (10) Figure 3 displays a graphical representation of the window function described by Joglekar for various p parameter (p=1, 5 and 10). This control parameter controls the linearity of the model, where it becomes more linear as p increases. This window function ensures zero drift at the boundaries. From the plotted graph, we noticed that the maximum f(x) value is occurs at the center of the device and zero is obtained at two boundaries. However, a significant liability of this model lies in the fact that if w hits any of the boundaries (w = 0 or w = D) the state of the device cannot be further adjusted. This will be from now on termed as the terminal state problem. Figure 3: Plot of Joglekar window function for p=1, 5 and 10. Then, Biolek proposed another window function that allows the memristor to come back from the terminal state problem. (11) The reversed bias is now should move back the state variable after it reaches either boundary. This feature is described by a current dependent step function, stp(i), which is a part of a new window function f(x) that behaves differently in each voltage bias direction. (12) Figure 4: Plot of Biolek window function for p=1, 5 and 10. Figure 4 displays a graphical representation of the window function described by Biolek for various p parameter (p=1, 5 and 10). When x starts at 0, we noticed that the function equal to 1. As x increase approaching D, the function approaches 0. Once the current reverse the direction, the function immediately switch to 1. As x decrease back to 0, the function also decreases to 0. Biolek window function eliminates convergence issues at the devices boundaries. The last window function for non-linear model is proposed by Prodromakis [8]. (13) Figure 5 displays a graphical representation of the window function described by Prodromakis for various p parameter (p=1, 5 and 10). As we can see, it allows the window function to scale upwards which implies that fmax(x) can take any value within 0 Figure 5: Plot of Prodromakis window function for p=1, 5 and 10. SPICE Model of Memristor Figure 6: Stucture of the SPICE model from [6]. In the above circuit in figure 6, VMEM is the input voltage and Imem is modeled to be the current through the memristor. The flux is calculated by integrating the voltage VMEM and the charge is calculated by integrating the current IMEM. Figure 7: Resistive port of the memristor model. As we can see in figure 7, the circuit is actually referred to total resistor RMEM. RMEM (x) = ROFF -xà ¢Ã‹â€ Ã¢â‚¬  R where à ¢Ã‹â€ Ã¢â‚¬  R= ROFF-RON. ROFF is the resistor in series voltage source whose terminal voltage is controlled by the formula -xà ¢Ã‹â€ Ã¢â‚¬  R. Figure 8: Differential equation modeling of the memristor. Figure 8 shows the differential equation modeling of the memrsitor. It consist a part of the voltage controlled source xà ¢Ã‹â€ Ã¢â‚¬  R and the differential equation from equation (6) which serves as an integrator of the quantities on the right side of the state equation (6) which is to get the value of normalize x. EMEM is the voltage source whose terminal voltage is controlled according to the formula -xà ¢Ã‹â€ Ã¢â‚¬  R. GX is a current source whose current is controlled according to the equation IMEMf(V(x)) where V(x) is the voltage across the capacitor Cx and it models the normalized width x of the doped layer. F(V(x)) is the window function, k is  µvRON/D2 and x0 is the initial voltage of the capacitor.[6]. The relation between memristor current and voltage is modeled as on the basis of RMEM (x) = ROFF -xà ¢Ã‹â€ Ã¢â‚¬  R where à ¢Ã‹â€ Ã¢â‚¬  R= ROFF-RON. The voltage V(x) across the capacitor CX models the normalized width x of the doped layer. The initial state of x is modeled by the initial voltage of the capacitor. The flux is calculated by the time-integral of voltage, and the charge is calculated by the time-integral of current. Result and Discussion All models were simulated in LTSpice using SPICE model that was given in [6], we add new nonlinear window functions that was proposed by prodromakis and strukov to the model and compare all suggested window functions. memristor Figure 9: Memristor circuit. Figure 9 shows configuration of single memristor for measuring the behavior of memristor model in LTSPICE with a sine wave input voltage of 1.2V with 1Hz frequency. The values for the memristor parameters  µv, D, RON, ROFF and RINITIAL are 10-10cm2s-1V-1, 10 nm, 100ohm, 16kohm and 11Kohm. All model are using same window function parameter p=10. C:UsersFadzDesktopresultstrukovstrukov1.png Figure 10: Strukov memristor model voltage, IMEM, RMEM and normalized x. Figure 10 shows the simulation result of memristor SPICE model for Strukov window function of voltage, IMEM, RMEM and normalized x. As we can see, the current of the memristor, IMEM is varying up to approximately 100 µA for maximum of 1.2V voltage applied. The RMEM for this model show that the values are in range of 11kOhm till 12kohm which means the effect of the voltage applied to the memristor only give slightly changes on the value of the memristor. Noticed that when positive voltage is applied, the conductivity of the device increases thus the memristance is decrease. When negative voltage is applied, the resistivity of the device increase thus the memristance is also increase. This verifies the memristive system on the device. In normalize x graph, we also noticed that the normalized x is at higher state in the beginning. Figure 11 shows the I-V characteristic of the devices and the relationship between charge and flux. The charge and flux curve curves confirms the well known fact that there is a one-to-one correspondence between them in spite of the 1-4 hysteresis effect. Strukov memristor shows lack of flexibility of controlling the device. C:UsersFadzDesktopresultstrukovstrukov4.png Figure 11: Strukov memristor model I-V loop hysteresis and relationship of charge and flux. C:UsersFadzDesktopresultjoglekarjoglekar1.png Figure 12: Joglekar memristor model voltage, IMEM, RMEM and normalized x. Joglekar window function seems to be promising as the existence of controlling parameter. Figure 12 shows the simulation result of memristor SPICE model for Joglekar window function of voltage, IMEM, RMEM and normalized x. Same as strukov memristor, when positive voltage is applied, the conductivity of the device increases thus the memristance is decrease. When negative voltage is applied, the resistivity of the device increase thus the memristance is also increase. The current of the memristor, IMEM is varying up to approximately 300 µA for maximum of 1.2V voltage applied. Joglekar window function give higher current compared to others. It shows that the current in the memristor are much easier to move. The RMEM are within range of nearly 0ohm to 11kohm which give full range of value for the memristor. Figure 13 show the I-V hysteresis loop of the devices and the relationship between charge and flux. The switching behavior is much more sensitive on the voltage level than Strukov w indow function. But, in term of stability, Joglekar window function cannot perform for an arbitrary length of time. This failure is caused by the convergence issue where when the memristor reach w=0 or w=D, the state of the device cannot be further adjusted. C:UsersFadzDesktopresultjoglekarjoglekar4.png Figure 13: Joglekar memristor model I-V loop hysteresis and relationship of charge and flux. Biolek window functions are supposed to solve terminal state problem as in literature [4]. It should solve the boundry problem of the terminal state. Figure 14 and 15 shows the simulation result of memristor SPICE model for Biolek window function. The current of the memristor, IMEM is varying up to approximately 220 µA for maximum of 1.2V voltage applied. The RMEM are within range of nearly 1kohm to 11kohm. Figure 15 show the I-V hysteresis loop of the devices and the relationship between charge and flux. From the figures, we observe that the biolek memristor preserve the highly non-linear device characteristic behavior. In addition, Bioleks model allows for general asymmetric I-V device behavior modeling. C:UsersFadzDesktopresultbiolekbiolek1.png Figure 14: Biolek memristor model voltage, IMEM, RMEM and normalized x. C:UsersFadzDesktopresultbiolekbiolek4.png Figure 15: Biolek memristor model I-V loop hysteresis and relationship of charge and flux. Prodromakis window functions are also said to solve the boundry issue. Figure 16 shows the simulation result of memristor SPICE model for Joglekar window function of voltage, IMEM, RMEM and normalized x. The current of the memristor, IMEM is varying up to approximately nearly 180 µA for maximum of 1.2V voltage applied. The RMEM are within range of nearly 3kohm to 11kohm. C:UsersFadzDesktopresultprodromakisprodromakis1.png Figure 16: Prodromakis memristor model voltage, IMEM, RMEM and normalized x. Figure 17 show the I-V hysteresis loop of the devices and the relationship between charge and flux. The hysteresis loop is shown to be asymmetrical while the OFF state of the device is highly non-linear compared with other. C:UsersFadzDesktopresultprodromakisprodromakis4.png Figure 17: Prodromakis memristor model I-V loop hysteresis and relationship of charge and flux. In comparing of I-V characteristic hysteresis loop, as we can see in figure 18, it shows all hysteresis loops for all proposed window functions. By using same parameter we can see the difference in each model. Joglekar window function seems to have a strong memristance compared to others.All models seem to be a good approximation of the measurement of the real memristor produces by HP Labs. But, Prodromakis memristor model satisfies all the prerequisites and improves on the shortcomings of existing models. C:UsersFadzDesktopresultall iv loop hysteresisiv hysteresis loop all.png Figure 18: I-V Hysteresis Loop for all models. C:UsersFadzDesktopresultdiff parameterprodromakis p=1, p=5, p=10.png Figure 19: Prodromakis I-V Hysteresis Loop when p=1, p=5 and p=10. Then, we try change the parameter of p of the model. In this case, we use prodromakis memristor model and change the value of integer p=1, p=5 and p=10 to see the difference. As we can see in figure 19, as the value of p is increase, the hysteresis is shrinking. Similar with changing the parameter p, figure 20 also confirm that the hysteresis shrinks at higher frequencies. C:UsersFadzDesktopresultdiff frequency1hz-5hz.png Figure 20: Prodromakis I-V Hysteresis Loop when frequency f=1Hz, f=2Hz and f=5Hz. In term of power dissipation, as we simulates our results. We can get the value of maximum IMEM for each model. We can calculate the power by using P=IV equation. Table 2 show the maximum power dissipation for each memristor. Memristor model Max IMEM,  µA Power, W Strukov 100 µA 120 µW Joglekar 300  µA 360 µW Biolek 220 µA 264 µW Prodromakis 180  µA 216 µW Table 2: IMEM and Power dissipation for all at the memristor. As in table 2, we can see that the Strukov model give lowest power which is 120 µW while Joglekar model give much higher power dissipation which is about 360 µW compared to the others. We also noticed that as the memristor model is improves, the power become lesser. Prodromakis give quite good power dissipation which is 216 µW as the best windows function and model as till now. In implementing memristor with analog circtuit, we pick a two simple analog circuit to be tested. Figure 21 shows the SPICE topology of the memristor based integrator op amplifier with the input voltage Vp-p=2.4V from -1.2V to 1.2V and C1=25 µF. Using the memristor model that we create earlier with various types of window functions, we see the difference on the simulated result on each model. The values for the memristor parameters are same for all model with uv, D, RON, ROFF and RINITIAL are 10-10cm2s-1V-1, 10nm, 100ohm, 16kohm and 11Kohm. memristor integrator op amp Figure 21: Memristor Implemented Integrator Circuit C:UsersFadzDesktopresultintegrator+ve integrator .png Figure 22: Positive Integrator simulation C:UsersFadzDesktopresultintegrator-ve integrator .png Figure 23: Negative Integrator simulation Figure 22 and 23 shows the simulation result for the implemented memristor integrator op amplifier for positive input and negative input respectively. In this case, we implement prodromakis memristor to the integrator circuit. As we know, the integrator acts like a storage element that produces a  voltage  output which is proportional to the integral of its input voltage with respect to time. The magnitude of the output signal is determined by the length of time a voltage is present at its input as the  current  through the  feedback loop  charges or discharges the  capacitor  as the required  negative feedback  occurs through the capacitor. For positive starting input, we vary the voltage from 1.2V down to -1.2V and going back to 1.2V over time. When positive voltage are applied in the beginning, the output voltage tend to discharge and drop from 0V to negative voltage and charging back to 0V when the input voltage are drop to negative voltage. The output for neg ative voltage applied from starting point give a vice versa result. The charging and discharge are depends the voltage applied over time and the value of the capacitor. We can say the memristor models give quite good result for an integrator. Figure 24: Memristor Implemented Differentiator Circuit. C:UsersFadzDesktopresultdifferentiatordifferentiator.png Figure 25: Saw tooth input of Memristor implemented differentiator op-amp simulation. Figure 25 shows the simulation result for the implemented memristor differentiator op amplifier. We are using prodromakis memristor model for the memristor implementation. As we know, for differentiator op-amp, the magnitude of its output is determined by the rate at which the voltage is applied to its input changes. The faster the input voltage changes, the greater the output voltage becomes. If a saw tooth input signal is applied to the input of the differentiator op-amp a square wave signal will be produced. As we can see in figure 25, the simulation shows a quite good result for differentiator. We also noticed some spikes at the output voltage. Each spikes occurs only occurs the brief moment the saw tooth is changing from one level to the next. The voltage spikes represent a temporary output voltage. Conclusion As a conclusion to this research is that it could bring a new light of familiarization in the integration of memristive components in any kinds of electronic devices that are at nanoscale. It is useful to have a computer model of the memristor as a tool for the analysis of the behavior of the circuits in developing application of this memristor as passive circuit element via simulation. SPICE model will definitely help us to conduct interesting simulation experiments and can be of great importance for such a research in future while the memristor are still hard to fabricate to study the behavior of the circuit. Different models with strong behavior and reason give a lot of benefits in development purpose to create the possibilities of the implementation in an integrated circuit. The possibilities for implementation of the memristor with analog circuit are wide open. Appendix .SUBCKT memristor plus minus PARAMS: + Ron=100 Roff=16K Rinit=11K D=10N uv=10F p=10 *********************************************** * DIFFERENTIAL EQUATION MODELING * *********************************************** Gx 0 x value={ I(Emem)*uv*Ron/D**2*f(V(x),p)} Cx x 0 1 IC={(Roff-Rinit)/(Roff-Ron)} Raux x 0 1T * RESISTIVE PORT OF THE MEMRISTOR * *********************************************** Emem plus aux value={-I(Emem)*V(x)*(Roff-Ron)} Roff aux minus {Roff} *********************************************** *Flux computation* *********************************************** Eflux flux 0 value={SDT(V(plus,minus))} *********************************************** *Charge computation* *********************************************** Echarge charge 0 value={SDT(I(Emem))} *********************************************** * WINDOW FUNCTIONS * FOR NONLINEAR DRIFT MODELING * *********************************************** *proposed by joglekar ;.func f(x,p)={1-(2*x-1)**(2*p)} *proposed by biolek ;.func f(x,i)={1-(x-stp(-i))**(2*p)} *proposed by prodromakis ;.func f(x,p)={1-(((x-0.5)**2)+0.75)**p} *proposed by strukov .func f(x,p)={x-x*2} .ENDS memristor Acknowledgment This paper participates in the IEEE Student Conference Research Development SCORED 2012. The author would like to thank Dr. Wan Fazlida Hanim bte Abdullah for being supervisor in this final year project. The author also would like to thank Universiti Teknologi MARA for funding the research work through the Excellence Fund Grant 600-RMI/ST/DANA 5/3/RIF(360/2012).

Strength and Weaknesses of Ontological Argument

The Ontological Argument was, and still is, a hot-topic for debate among philosophers; many famous philosophers have published criticisms of the theory including Immanuel Kant and St. Thomas Aquinas. This obviously raises questions regarding whether or not this argument works.While there is no clear-cut answer to these questions, I personally believe that the negatives of this argument outweigh the positives, thereby making it a weak argument. The first published criticism of Anselm’s Ontological Argument was from Gaunilo in his book In Behalf of the Fool (making reference to the fool in the book of psalms who didn’t believe in God).While Gaunilo was a firm believer in God (and was in fact a monk), he disagreed strongly with Anselm’s method for proving his existence. His problem is with the strand of Anselm’s argument which is put forward in Chapter Two of Proslogion.While Anselm claimed that the God, who is defined as perfect, must exist because an existe nt God is better than a non-existent God meaning that if he didn’t exist, he wouldn’t be perfect and therefore, wouldn’t be God, Gaunilo applied this logic to the example of a Perfect Island.If the perfect Island didn’t exist in the real world, it would be a contradiction to call it the perfect Island. By this logic, the perfect Island must exist seeing as if it didn’t exist, it wouldn’t be perfect1. We obviously know that the Perfect Island does not in fact exist and, by Gaunilo’s reasoning, Anselm’s argument doesn’t work; if it doesn’t work with parallel arguments, it doesn’t work in the example of God. This criticism is very astute and, therefore, severely weakens the argument and its effectiveness.However, Anselm directly responded to his contemporary Gaunilo’s criticism in an attempt to defend his argument and its ideals. Firstly, Anselm pointed out the fact the example of the Island (or any oth er examples for that matter) do not work because it, unlike God, is contingent and not at all necessary; its existence relies on the Earth and the Sea and it would have been entirely possible for it never to have existed. God, however, must exist and depends on the existence of nothing else.Moreover, Anselm goes on to say that the perfect Island is impossible to define; will it become more perfect as it gets bigger? God, however, is specifically defined by Anselm allowing the Ontological Argument to be applicable to him.This response deals with the criticism well and manages to re-strengthen the Ontological Argument to some degree. Another philosopher who disagreed with Anselm’s Ontological Argument was St. Thomas Aquinas. Again, he believed in God but disagreed with Anselm’s argument proving his existence.Aquinas raises questions about God’s self-evident existence. He claims that things can be self-evident in two ways: in itself and both in itself and to us; ev en though something may exist self-evidently in itself, this self-evidence may not be known to us as humans and therefore, its existence would not be self-evident to us.This is exactly what Aquinas proposes God to be. God is self-evident in himself because he is his own essence. However, seeing as this essence is unknown to us (as we do not know enough about him), the statement ‘God exists’ is not self-evident to us.This, again, is another criticism which holds weight against the Ontological Argument, highlighting a glaring weakness in its logic. A third philosopher who published a criticism on the Ontological Argument (though in this case it was directed towards Descartes’ version of the argument which was published several centuries after Anselm’s in 1641) was Pierre Gassendi. In Descartes’ version of the Ontological Argument published in his Meditations, he claimed that God was entirely perfect and, as a result, must possess every possible perfec tion – including the perfection of existence.Gassendi believed that this logic didn’t work because if a thing doesn’t exist, it is neither perfect nor imperfect; it merely doesn’t exist. Therefore, if God doesn’t exist, this logic could not possibly be applied to him in an attempt to prove his existence.Descartes published a response to this criticism. In this response, he claimed that God could not be compared to anything else, proposing that ‘the relationship and essence is manifestly quite different in the case of God from what it is in the case of a triangle’; it is a part of God’s essence to exist.While this does respond directly to Gassendi’s criticism, it does not particularly strengthen the argument seeing as Descartes gives no reason as to why God’s existence is a part of his essence; he merely states that it is true. Yet another philosopher who published a criticism of the Ontological Argument was Immanue l Kant.Kant (who was an atheist) published a book called A Critique of Pure Reason in which he attempted to contradict both Descartes’ and Anselm’s versions of the Ontological Argument in two different ways.In his first argument, Kant begins by hypothetically accepting that existing is indeed a defining predicate of God (which both Descartes and Anselm claim it is). He then goes on to argue that, even if this were true, there would be no contradiction in altogether rejecting the concept of God.For example, you may understand that having a single horn on its head is a defining predicate of a unicorn. However, this does not mean that it would be contradictory to not believe in unicorns or magical horses with horns.By this logic, you could also claim that you agree that if God did indeed exist, he would necessarily exist but that you do not believe in God or his necessity without contradicting yourself. In Kant’s second argument, he attacks the Ontological Argument at its base by claiming that ‘existing’ could not possibly be considered as a defining predicate as it does nothing to change the definition of the being in question; two people – one of whom believes in unicorns and one who doesn’t – would most likely share the same idea of what a unicorn is.While these two people would disagree on whether or not unicorns were real, they would not disagree on what a unicorn was. Therefore, it is impossible to say that existing is a defining predicate of God because it adds nothing to the definition of God.Overall, therefore, while the Ontological Argument is by all means a sound theory to some degree, the criticisms which highlight so many of the argument’s weaknesses show how the theory is weaker than in it is strong.

Uncommon Article Gives You the Facts on Literary Essay with Secondary Sources Samples That Only a Few People Know Exist

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Essay on Euthanasia a Topic Surrounded by Controversies

Euthanasia is a very controversial subject, due to the fact it’s a way of painless killing of a patient suffering from a debilitating disease that cannot be cured, or the patient is in a coma and has no way of coming out of it. In this case some societies consider it’s a good way of dying, as it is done to relieve pain and suffering. Some, especially most of religious individuals, consider this a form of a murder, which raises a question of morality. In this article, the author is discussing the questions of morality and views on this topic in different societies. Keywords: Euthanasia, painless killing, societies, religions, morality INTRODUCTION Euthanasia also known as mercy killing, is a way of painlessly terminating one’s life†¦show more content†¦Justice Devlin once ruled a decision in the case of Bodkin Adams of a doctor being entitled to relieve pain and suffering of a person even if it would terminate their life (ReligionFacts, n.d.). It has always been a discussion among different societies whether maintaining the body’s functions in a persistent vegetative state by life support machines and drugs is considered moral or immoral. People seem to have different opinions on whether such body state with no potential of becoming conscious should be kept on life support systems or disconnected raising a question who should be responsible for such decisions (Pillay, 2010). However, another cases applicable for Euthanasia are patients with severe suffering and almost non-existent chance of cure, who know that they are going to die. It has been made legally possible in countries such as Neth erlands, Belgium, and Luxembourg for any terminally ill patient to be applicable for Euthanasia after an approval. In countries such as Switzerland, Germany, Albania, Colombia, Japan and in the US states of Washington, Oregon, Vermont, New Mexico and Montana it is legally possible for the family of a terminally unconscious patient to be disconnected from the medical life support (Pillay, 2010). Although philosophers like Aristotle, Plato and Pythagoras favored euthanasia, most religions; mainly the Roman Catholic Church, Buddhism, Hinduism; disapprove of it or even forbid it. Religions over all favor theShow MoreRelatedShould Euthanasia Be Allowed?1675 Words   |  7 PagesWhen euthanasia comes to mind, what do you think of? Do you think of people hurting, do you think of it as suicide, do you think of sick people? The big question is†¦ do you think it’s wrong? Many questions, concerns, and issues have come up with this topic in the past, because there are so many facto rs that go into deciding when euthanasia should be allowed, if at all. Should just anyone be allowed to decide they want to die, and have a physician assist him or her with suicide, or do they have toRead MoreIs Euthanasia Morally Justified? Essay1237 Words   |  5 PagesPhilosophy Paper: Is Euthanasia Morally Justified? Euthanasia is defined in the dictionary as the painless killing of a patient suffering from an incurable and painful disease or in an irreversible coma. It s a practice that is illegal in many countries and only legal in a handful of states here in America. As a future physician, I do believe that assisted suicide is moral if that is what the patient wishes. In this paper I aim to prove that denying someone their right to take back control ofRead MoreThe Controversy Surrounding Selective Infanticide Essay1368 Words   |  6 PagesOver the course of time, selective infanticide has been heavily debated and surrounded by much controversy. Harriet Johnson’s piece â€Å"Unspeakable Conversations† navigates through the discourse between Johnson and selective infanticide advocate Peter Singer. Real world applications of the social and medical model of disability are embedded all throughout Johnson’s personal account of her encounters with Singer, causing audiences to think of these models in ways other than textbook applications. TheRead MoreEuthanasi Right Or Wrong3136 Words   |  13 PagesRachel Blackman 1/5/14 Civics Period 1 Garry Euthanasia: Right or Wrong A topic that has been controversial for a long time in our country s history is euthanasia, or mercy killing. As more cases come along, new ideas come up that challenge its morality. Janet Adkins was a 54 years old woman, who had Alzheimer s disease. At the time, she was still capable of doing things like talking and walking, but she knew things could go downhill fast. She didn t want to live if she wasn t able to communicateRead MoreThe Bill Of Rights : The Amendment Rights2558 Words   |  11 Pagesprovocativeness may be prosecuted and punished as if they were a principal offender.† This is a great example, of controversy some say it shouldn t matter it s their own choice while others for religious reasons see this dishonorable. The 9th amendment creates a lot of mixed feelings in the world because it s not really specified what it protects and what it does not. The controversy continues based on, whether it s right or wrong to request the assistance of a physician to end the patient sRead MoreThe Bill Of Rights : The Amendment Rights2558 Words   |  11 Pagesprovocativeness may be prosecuted and punished as if they were a principal offender.† This is a great example, of controversy some say it shouldn t matter it s their own choice while others for religious reasons see this dishonorable. The 9th amendment creates a lot of mixed feelings in the world because it s not really specified what it protects and what it does not. The controversy continues based on, whether it s right or wrong to request assistance of a physician to end the patient s lifeRead MoreThe Bill Of Rights : The Amendment Rights2572 Words   |  11 Pagesprovocativeness may be prosecuted and punished as if they were a principal offender.† This is a great example, of controversy some say it shouldn t matter it s their own choice while others for religious reasons see this dishonorable. The 9th amendment creates a lot of mixed feelings in the world because it s not really specified what it protects and what it does not. The controversy continues based on, whether it s right or wrong to request the assistance of a physician to end the patient sRead MoreThe Fight For Physician Aid2710 Words   |  11 PagesThe fight for Physician aid in Dying’s nation wide legalization. Ever since Dr. Kevorkian or â€Å"Doctor Death† drove his car around the united states assisting over 40 patients to take the own lives physician aid in dying has been a topic which has sparked controversy (DiManno). Although his actions did receive large amounts of negative feed back it did lead much of the population to the question of whether or not it should be legal for an individual to have medical assistance to take their life inRead MoreHsm 542 Week 12 Discussion Essay45410 Words   |  182 Pages------------------------------------------------- Top of Form Week 1: Introductions/Overview: An Ethical and Legal Framework - Discussion This weeks graded topics relate to the following Terminal Course Objectives (TCOs): A | Given a situation related to reproductive genetics, genetic research, or the human genome project, develop a set of legal and ethical guidelines, which can be applied to genetic issues for the conduct of medical practice and/or research. | B | Given the contentious