The distinction between the primary and secondary qualities of objects was an important theme within British empiricist philosophy, the three key proponents being John Locke, George Berkeley and David Hume.
Locke sets out the distinction in his 'Essay Concerning Human Understanding'. The distinction applies to the "simple" ideas we receive from sensation.
Primary qualities are properties objects have that are independent of any observer and include such properties as solidity, extension, motion, number and figure. They exist in the thing itself, can be determined with certainty, and do not rely on subjectivity. Secondary qualities are properties that produce sensations in the observer, such as colour, taste, smell, and sound. They are effects things have on people. Knowledge that comes from secondary qualities does not provide objective facts about things.
Locke argues that secondary qualities are somehow caused by the arrangements of matter, matter has the power to cause the ideas of secondary qualities. He believes that there is scientific support for his theory based on Boyle's new 'corpuscular hypothesis'.
Locke supports his theory by the use of examples. I will quote directly from Chapter VIII of Book II:
"Take a grain of wheat, divide it into two parts; each part has still solidity, extension, figure, and mobility: divide it again, and it retains still the same qualities; and so divide it on, till the parts become insensible; they must retain still each of them all those qualities. For division (which is all that a mill, or pestle, or any other body, does upon another, in reducing it to insensible parts) can never take away either solidity, extension, figure, or mobility from any body, but only makes two or more distinct separate masses of matter, of that which was but one before; all which distinct masses, reckoned as so many distinct bodies, after division, make a certain number. These I call original or primary qualities of body, which I think we may observe to produce simple ideas in us, viz. solidity, extension, figure, motion or rest, and number.
...Secondary qualities of bodies. Secondly, such qualities which in truth are nothing in the objects themselves but power to produce various sensations in us by their primary qualities, i.e. by the bulk, figure, texture, and motion of their insensible parts, as colours, sounds, tastes, &c. These I call secondary qualities. To these might be added a third sort, which are allowed to be barely powers; though they are as much real qualities in the subject as those which I, to comply with the common way of speaking, call qualities, but for distinction, secondary qualities. For the power in fire to produce a new colour, or consistency, in wax or clay,- by its primary qualities, is as much a quality in fire, as the power it has to produce in me a new idea or sensation of warmth or burning, which I felt not before,- by the same primary qualities, viz. the bulk, texture, and motion of its insensible parts."
Locke's theory of perception is a 'mediated theory of perception'. Accordingly, we do not have direct access to the world around us, but rather this access is mediated through our ideas.
Showing posts with label empiricism. Show all posts
Showing posts with label empiricism. Show all posts
Saturday, October 27, 2012
Sunday, June 17, 2012
Locke and Berkeley
Does Locke or Berkeley give a better account of the primary/secondary property distinction?
I think neither Locke nor Berkeley give a wholly satisfactory explanation of primary and secondary qualities but tend towards Locke having a slightly more coherent view.
In favour of Locke, I can understand the distinction he draws between those qualities which are less prone to subjective "distortion". Physical extension, number, motion and even place in time seem to be "qualities" which are of a somewhat different nature from taste, smell, colour etc. Secondary qualities tend to be highly subjective and depend very much on the "point of view" of the subject.
I reject however, Locke's belief that secondary qualities are "nothing in the objects themselves". There is something (a physical quality) in objects over and above a "power" to produce certain sensations in sentient beings. I believe that our sensations are in fact caused by physical properties of objects and we directly perceive that quality, but the precise nature of our perception depends on the circumstances under which we perceive it.
Locke thinks that a sharp pin having the power to cause the idea of pain is analogous to a tomato having the power to cause the idea of red. I don't think these two example are really comparable in the way Locke does. Pain is not a quality of a pin - sharpness is the quality of the pin which compares to the redness of a tomato.
Berkeley does not make a convincing case for either his epistemological or metaphysical claims. I flatly reject his claim that we cannot abstract qualities. I also reject his proposition that all ideas are entirely dependent on minds. He thinks that ideas are caused by God whereas are more coherent view is that ideas are caused by the external world. Berkeley has no clear conception of what God is, and whether there is only one God or many. Since we cannot have an idea of what God is other than the cause of all ideas I think it makes more sense to replace God with an external world. I accept that in a very strict sense this is an assumption, but feel that the burden of proof lies with those that claim the external world does not exist.
I think neither Locke nor Berkeley give a wholly satisfactory explanation of primary and secondary qualities but tend towards Locke having a slightly more coherent view.
In favour of Locke, I can understand the distinction he draws between those qualities which are less prone to subjective "distortion". Physical extension, number, motion and even place in time seem to be "qualities" which are of a somewhat different nature from taste, smell, colour etc. Secondary qualities tend to be highly subjective and depend very much on the "point of view" of the subject.
I reject however, Locke's belief that secondary qualities are "nothing in the objects themselves". There is something (a physical quality) in objects over and above a "power" to produce certain sensations in sentient beings. I believe that our sensations are in fact caused by physical properties of objects and we directly perceive that quality, but the precise nature of our perception depends on the circumstances under which we perceive it.
Locke thinks that a sharp pin having the power to cause the idea of pain is analogous to a tomato having the power to cause the idea of red. I don't think these two example are really comparable in the way Locke does. Pain is not a quality of a pin - sharpness is the quality of the pin which compares to the redness of a tomato.
Berkeley does not make a convincing case for either his epistemological or metaphysical claims. I flatly reject his claim that we cannot abstract qualities. I also reject his proposition that all ideas are entirely dependent on minds. He thinks that ideas are caused by God whereas are more coherent view is that ideas are caused by the external world. Berkeley has no clear conception of what God is, and whether there is only one God or many. Since we cannot have an idea of what God is other than the cause of all ideas I think it makes more sense to replace God with an external world. I accept that in a very strict sense this is an assumption, but feel that the burden of proof lies with those that claim the external world does not exist.
Monday, January 23, 2012
Hume and the missing shade of blue
I made reference earlier to 'Hume’s Missing Shade of Blue Re-viewed' by John O. Nelson in
Hume Studies Volume XV Number 2 (November 1989).
I think I agree with the following paragraph, which it seems to me is a fair basis on which to consider the case of the missing shade of blue as being not fatal to Hume's philosophy as set out in the Treatise. Indeed, when seen in the context described below, the missing shade of blue is not perhaps the 'exception that proves the rule' but rather 'the exception that proves the nature of the rule.
"One might profitably compare Hume's views in the present regard with Descartes' on essence and existence. According to Descartes, essence and existence are always, at least insofar as God is not concerned,“separable.” Thus, in imagining a triangle (says Descartes) he conceives its essence; nonetheless, ”there may nowhere in the world be such a figure outside my thought." In spite of some appearance to the contrary, Hume, I want to say, similarly maintains that ideas and their relations are separable from existence. Thus, what we discover in a thought experiment, like the color concession under discussion, really says nothing about what exists or does not exist in reality; it at most proves that a certain proposition, namely that stating that all simple ideas have correspondent, precedent impressions, is not an apriori, necessary proposition but a synthetic, aposteriori proposition. On the other hand, the proposition stating that all simple ideas have correspondent, precedent impressions, or the first principle of the science of man, does refer to what exists or does not exist in actual reality. Hence, being only in idea or in one’s thought experiment a phenomenon, the phenomenon of the missing shade of blue projects merely the idea of a contradiction to the first principle of the science of man, not an instance of an actual exception to the first principle and, hence, not something actually falsifying that principle. Thus, without real inconsistency but only an apparent one, Hume is able both to maintain that all simple ideas have correspondent, precedent impressions and that a contradictory phenomenon can be conceived."
I think I agree with the following paragraph, which it seems to me is a fair basis on which to consider the case of the missing shade of blue as being not fatal to Hume's philosophy as set out in the Treatise. Indeed, when seen in the context described below, the missing shade of blue is not perhaps the 'exception that proves the rule' but rather 'the exception that proves the nature of the rule.
"One might profitably compare Hume's views in the present regard with Descartes' on essence and existence. According to Descartes, essence and existence are always, at least insofar as God is not concerned,“separable.” Thus, in imagining a triangle (says Descartes) he conceives its essence; nonetheless, ”there may nowhere in the world be such a figure outside my thought." In spite of some appearance to the contrary, Hume, I want to say, similarly maintains that ideas and their relations are separable from existence. Thus, what we discover in a thought experiment, like the color concession under discussion, really says nothing about what exists or does not exist in reality; it at most proves that a certain proposition, namely that stating that all simple ideas have correspondent, precedent impressions, is not an apriori, necessary proposition but a synthetic, aposteriori proposition. On the other hand, the proposition stating that all simple ideas have correspondent, precedent impressions, or the first principle of the science of man, does refer to what exists or does not exist in actual reality. Hence, being only in idea or in one’s thought experiment a phenomenon, the phenomenon of the missing shade of blue projects merely the idea of a contradiction to the first principle of the science of man, not an instance of an actual exception to the first principle and, hence, not something actually falsifying that principle. Thus, without real inconsistency but only an apparent one, Hume is able both to maintain that all simple ideas have correspondent, precedent impressions and that a contradictory phenomenon can be conceived."
Hume's Treatise contd.
So far, we have discovered that Hume is intending to employ an empirically based and reasoned approach to his investigation of human nature, or "the ultimate principles of the soul". Hume recognises at the outset that this is not going to be easy. Many others have set out on the same road, only to realise the impossibility the task. Indeed, it may be more prudent not to attempt such an enquiry, and thereby "avoid falling into error"; but we clearly get the impression by this point that Hume is quite willing to give it a try, or even perhaps believes that he has solved the problem.
It seems evident to Hume that we cannot "go beyond experience, or establish any principles that are not founded on that authority" (i.e. experience). Here we have a clear statement of empiricism. It will be interesting to see why Hume thinks this is self evident, and what conclusions he draws even allowing for such limitations.
Book 1 - Of the Understanding
In Section 1 - Of the Origin of our Ideas, Hume begins to lay the groundwork and first draws a key distinction between two different types of perception: impressions and ideas. The difference between these two types of perception is "the degree of force or liveliness with which they strike upon the mind, and make their way into our thought or consciousness."
It is interesting to me that, by starting at this point in his first book on philosophy, Hume has already taken quite a lot for granted. Unlike Descartes in Discourse on the Method, Hume hasn't questioned the concept of self or indeed of perception. It seems to be taken for granted that there is someone who perceives and something being perceived.
Further, we may need to go on to investigate if this distinction between impressions and ideas is the same, or similar, to philosophical dualism; for example, the Cartesian dualism between essence and existence which can be seen in Descartes' writings.
For Hume, impressions are the more vigorous type of perception, and include sensations, passions and emotions. Ideas are described as "fainter images" of these and include thinking and reasoning.
Hume says "I believe it will not be very necessary to employ many words in explaining this distinction." I'm not sure I entirely agree that we can just accept this - a number of objections immediately spring to mind. For example, it is not always the case that emotions strike us more forcefully than reflective thoughts. Also, we have the case of dreams, where the distinction between Hume's impressions and ideas is much less clear-cut. For the time being however, I shall give Hume the benefit of the doubt and move on.
Hume then immediately recognises that the two counter-arguments above may be raised in objection, but concludes that it is nevertheless true that ideas and impressions are "in general so very different, that no-one can make a scruple to rank them under distinct heads".
Next, Hume draws a distinction between simple and complex perceptions (both ideas and impressions). "Simple perceptions ...are such as admit of no distinction or separation. The complex are the contrary to these." For example, the idea of an apple is complex as it comprises a number of components. The components of the idea of an apple such as smell, taste and colour are simple perceptions.
Again, I think we can see what Hume is getting at, but I'm not convinced that our perceptions can be so clearly categorised. Indeed, objections to this theory can be quite extreme, such as the "compositionally nihilist" view, which renounces the literal existence of complex perceptions*.
Hume does not recognise any other possible distinction between impressions and ideas other than the degree of force and vivacity by which they are perceived. He says the two are remarkably similar in all other respects, indeed many (simple) impressions are subsequently perceived as ideas when we reflect upon or recall them. This lack of flexibility is a little alarming, but just because it doesn't at first pass the "smell test" doesn't necessarily make it unhelpful, we shall see.
In Hume's defence, I think we can all recognise the difference between a 'sense perception' and a 'thought'. If this distinction proves to be useful in formulating a theory of human nature, we should probably give Hume some leeway before rejecting his conclusions as being based on dodgy foundations.
Hume claims next that every simple idea has a simple impression that resembles it and vice versa, but this is not necessarily true for complex ideas and complex impressions.
Hume's "general proposition" which will be more fully examined in the Treatise is stated as follows: "That all our simple ideas in their first appearance are deriv'd from simple impressions, which are correspondent to them, and which they exactly represent."
From this we take it that all simple ideas are preceded by (and later we find also caused by) a corresponding simple impression.
With regards to this proposition, Hume challenges us to come up with an exception to prove him wrong. I am slightly cheating here because I remember from my student days one exception which Hume examines next, namely the case of the missing shade of blue. If someone has seen lots of different shades of blue, but not one particular shade, it is argued that they could form an idea of this missing shade of blue, even if that they have not previously perceived that shade via a corresponding impression.**
Hume does not find this exception to be fatal, indeed he manages to convince himself that in a way it is the 'exception that proves the rule'. Ideas "produce the images of themselves" in new ideas, but "as the first ideas are supposed to be derived from impressions, it still remains true that all our simple ideas proceed either mediately or immediately, from their correspondent impressions". Hume believes therefore that his proposition still stands, because in the very rare case where a simple idea is not caused by a corresponding simple impression, that simple idea is in fact caused by copying another simple idea, which in turn was caused by a simple impression.
In the conclusion of section 1, Hume is confident that he has dispensed with any notion of innate ideas***.
I will continue with Section 2 tomorrow.
* See 'Hume on the Individuality of Complex Perceptions' by Jani Hakkarainen (2011) for an analysis of this issue.
** See 'Hume’s Missing Shade of Blue Re-viewed' by John O. Nelson in Hume Studies Volume XV Number 2 (November 1989)
*** Innatism is a philosophical doctrine that holds that the mind is born with ideas/knowledge, and that therefore the mind is not a 'blank slate' at birth, as early empiricists such as John Locke claimed. It asserts therefore that not all knowledge is obtained from experience and the senses. (from Wikipedia)
It seems evident to Hume that we cannot "go beyond experience, or establish any principles that are not founded on that authority" (i.e. experience). Here we have a clear statement of empiricism. It will be interesting to see why Hume thinks this is self evident, and what conclusions he draws even allowing for such limitations.
Book 1 - Of the Understanding
In Section 1 - Of the Origin of our Ideas, Hume begins to lay the groundwork and first draws a key distinction between two different types of perception: impressions and ideas. The difference between these two types of perception is "the degree of force or liveliness with which they strike upon the mind, and make their way into our thought or consciousness."
It is interesting to me that, by starting at this point in his first book on philosophy, Hume has already taken quite a lot for granted. Unlike Descartes in Discourse on the Method, Hume hasn't questioned the concept of self or indeed of perception. It seems to be taken for granted that there is someone who perceives and something being perceived.
Further, we may need to go on to investigate if this distinction between impressions and ideas is the same, or similar, to philosophical dualism; for example, the Cartesian dualism between essence and existence which can be seen in Descartes' writings.
For Hume, impressions are the more vigorous type of perception, and include sensations, passions and emotions. Ideas are described as "fainter images" of these and include thinking and reasoning.
Hume says "I believe it will not be very necessary to employ many words in explaining this distinction." I'm not sure I entirely agree that we can just accept this - a number of objections immediately spring to mind. For example, it is not always the case that emotions strike us more forcefully than reflective thoughts. Also, we have the case of dreams, where the distinction between Hume's impressions and ideas is much less clear-cut. For the time being however, I shall give Hume the benefit of the doubt and move on.
Hume then immediately recognises that the two counter-arguments above may be raised in objection, but concludes that it is nevertheless true that ideas and impressions are "in general so very different, that no-one can make a scruple to rank them under distinct heads".
Next, Hume draws a distinction between simple and complex perceptions (both ideas and impressions). "Simple perceptions ...are such as admit of no distinction or separation. The complex are the contrary to these." For example, the idea of an apple is complex as it comprises a number of components. The components of the idea of an apple such as smell, taste and colour are simple perceptions.
Again, I think we can see what Hume is getting at, but I'm not convinced that our perceptions can be so clearly categorised. Indeed, objections to this theory can be quite extreme, such as the "compositionally nihilist" view, which renounces the literal existence of complex perceptions*.
Hume does not recognise any other possible distinction between impressions and ideas other than the degree of force and vivacity by which they are perceived. He says the two are remarkably similar in all other respects, indeed many (simple) impressions are subsequently perceived as ideas when we reflect upon or recall them. This lack of flexibility is a little alarming, but just because it doesn't at first pass the "smell test" doesn't necessarily make it unhelpful, we shall see.
In Hume's defence, I think we can all recognise the difference between a 'sense perception' and a 'thought'. If this distinction proves to be useful in formulating a theory of human nature, we should probably give Hume some leeway before rejecting his conclusions as being based on dodgy foundations.
Hume claims next that every simple idea has a simple impression that resembles it and vice versa, but this is not necessarily true for complex ideas and complex impressions.
Hume's "general proposition" which will be more fully examined in the Treatise is stated as follows: "That all our simple ideas in their first appearance are deriv'd from simple impressions, which are correspondent to them, and which they exactly represent."
From this we take it that all simple ideas are preceded by (and later we find also caused by) a corresponding simple impression.
With regards to this proposition, Hume challenges us to come up with an exception to prove him wrong. I am slightly cheating here because I remember from my student days one exception which Hume examines next, namely the case of the missing shade of blue. If someone has seen lots of different shades of blue, but not one particular shade, it is argued that they could form an idea of this missing shade of blue, even if that they have not previously perceived that shade via a corresponding impression.**
Hume does not find this exception to be fatal, indeed he manages to convince himself that in a way it is the 'exception that proves the rule'. Ideas "produce the images of themselves" in new ideas, but "as the first ideas are supposed to be derived from impressions, it still remains true that all our simple ideas proceed either mediately or immediately, from their correspondent impressions". Hume believes therefore that his proposition still stands, because in the very rare case where a simple idea is not caused by a corresponding simple impression, that simple idea is in fact caused by copying another simple idea, which in turn was caused by a simple impression.
In the conclusion of section 1, Hume is confident that he has dispensed with any notion of innate ideas***.
I will continue with Section 2 tomorrow.
* See 'Hume on the Individuality of Complex Perceptions' by Jani Hakkarainen (2011) for an analysis of this issue.
** See 'Hume’s Missing Shade of Blue Re-viewed' by John O. Nelson in Hume Studies Volume XV Number 2 (November 1989)
*** Innatism is a philosophical doctrine that holds that the mind is born with ideas/knowledge, and that therefore the mind is not a 'blank slate' at birth, as early empiricists such as John Locke claimed. It asserts therefore that not all knowledge is obtained from experience and the senses. (from Wikipedia)
Saturday, January 21, 2012
David Hume (1711-1776)
If I had to select one, and only one, philosopher to study (which fortunately I don't!) then that philosopher would be David Hume.
Hume was born in Edinburgh, Scotland and is now recognised as one of the most important figures in Western philosophy, being a key figure in the Scottish Enlightenment. He is often grouped with John Locke (1632-1704) and George Berkeley (1685-1753), all of whom promoted an empiricist approach to philosophy which is based on evidence and observation (i.e. scientific method) as opposed to a priori ('arm-chair') reasoning.
Hume wrote extensively on philosophy, history and economics. To my mind his essays are surprisingly readable considering they are 270 years old. The National Library of Scotland holds several of his manuscripts, all of which are free to request by library members.
Two of Hume's most famous philosophical works are A Treatise of Human Nature (1739-40) and Enquiries Concerning Human Understanding and Concerning the Principles of Morals (1777). It is mainly these two works that I will refer to for subsequent posts on Hume.
His talents were perhaps not fully appreciated by his mother, who is reported to have said of her youngest son "Our Davie 's a fine good natured crater, but uncommon wake-minded". He studied at Edinburgh University, "passing the ordinary course of education with success", leaving with at least a fair knowledge of Latin and at least an acquaintance with Greek.
Literary influences at the start of his career include Cicero and Seneca as well as works by Locke, Berkeley and Joseph Butler (1692-1752). From a relatively early age, Hume displayed a passion for literature and investigations into human nature.
The first choice of a profession, that of law, made for him by his relatives who thought it suited his "studious habits, sobriety, and industry", proved unsuccessful. In 1734 he travelled to Bristol with the intention of entering into a "more active" mercantile life. Fortunately for us, he quickly "found the scene wholly unsuitable" and in the same year left for France. He visited Paris, Rheims and settled in La Flèche, famous in the history of philosophy as the school of René Descartes (1596,1650). It was while resident in France that he wrote Treatise.
Treastise comprises three books (i) Of the Understanding, (ii) Of the Passions, and (iii) Of Morals. The first two volumes were published in 1739 with the third following the next year. Their reception was somewhat underwhelming, as Hume vividly describes "Never literary attempt was more unfortunate; it fell dead-born from the press, without reaching such distinction as even to excite a mumur among the zealots". "But, being naturally of a cheerful and sanguine temper, I very soon recovered the blow, and prosecuted with great ardour my studies in the country".
The disclaimer of the Treatise in the preface to the Inquiry is famous, but has more to do with his disappointment at the reception of the Treatise than its shortcomings as a work of philosophy. The Advertisement, which is printed at the beginning of the 1777 posthumous reprint of Hume's Collected Essays in 1777 (i.e. the Enquiry), declares the author's desire that "the following pieces may alone be regarded as containing his philosophical sentiments and principles"
I will return to Hume's Treatise in my next post.
To finish, I will just underline the philosophical influence Hume has had by referring to some quotes from other philosophers (from Wikipedia):
Hume was born in Edinburgh, Scotland and is now recognised as one of the most important figures in Western philosophy, being a key figure in the Scottish Enlightenment. He is often grouped with John Locke (1632-1704) and George Berkeley (1685-1753), all of whom promoted an empiricist approach to philosophy which is based on evidence and observation (i.e. scientific method) as opposed to a priori ('arm-chair') reasoning.
Hume wrote extensively on philosophy, history and economics. To my mind his essays are surprisingly readable considering they are 270 years old. The National Library of Scotland holds several of his manuscripts, all of which are free to request by library members.
Two of Hume's most famous philosophical works are A Treatise of Human Nature (1739-40) and Enquiries Concerning Human Understanding and Concerning the Principles of Morals (1777). It is mainly these two works that I will refer to for subsequent posts on Hume.
His talents were perhaps not fully appreciated by his mother, who is reported to have said of her youngest son "Our Davie 's a fine good natured crater, but uncommon wake-minded". He studied at Edinburgh University, "passing the ordinary course of education with success", leaving with at least a fair knowledge of Latin and at least an acquaintance with Greek.
Literary influences at the start of his career include Cicero and Seneca as well as works by Locke, Berkeley and Joseph Butler (1692-1752). From a relatively early age, Hume displayed a passion for literature and investigations into human nature.
The first choice of a profession, that of law, made for him by his relatives who thought it suited his "studious habits, sobriety, and industry", proved unsuccessful. In 1734 he travelled to Bristol with the intention of entering into a "more active" mercantile life. Fortunately for us, he quickly "found the scene wholly unsuitable" and in the same year left for France. He visited Paris, Rheims and settled in La Flèche, famous in the history of philosophy as the school of René Descartes (1596,1650). It was while resident in France that he wrote Treatise.
Treastise comprises three books (i) Of the Understanding, (ii) Of the Passions, and (iii) Of Morals. The first two volumes were published in 1739 with the third following the next year. Their reception was somewhat underwhelming, as Hume vividly describes "Never literary attempt was more unfortunate; it fell dead-born from the press, without reaching such distinction as even to excite a mumur among the zealots". "But, being naturally of a cheerful and sanguine temper, I very soon recovered the blow, and prosecuted with great ardour my studies in the country".
The disclaimer of the Treatise in the preface to the Inquiry is famous, but has more to do with his disappointment at the reception of the Treatise than its shortcomings as a work of philosophy. The Advertisement, which is printed at the beginning of the 1777 posthumous reprint of Hume's Collected Essays in 1777 (i.e. the Enquiry), declares the author's desire that "the following pieces may alone be regarded as containing his philosophical sentiments and principles"
I will return to Hume's Treatise in my next post.
To finish, I will just underline the philosophical influence Hume has had by referring to some quotes from other philosophers (from Wikipedia):
- Kant credited Hume with awakening him from "dogmatic slumbers".
- According to Schopenhauer, "there is more to be learned from each page of David Hume than from the collected philosophical works of Hegel, Herbart and Schleiermacher taken together".
- A. J. Ayer, introducing his classic exposition of logical positivism (Language, Truth and Logic), claimed: "The views which are put forward in this treatise derive from the logical outcome of the empiricism of Berkeley and Hume."
- Albert Einstein wrote that he was inspired by Hume's positivism when formulating his Special Theory of Relativity.
- Hume was called "the prophet of the Wittgensteinian revolution" by N. Phillipson, referring to his view that mathematics and logic are closed systems, disguised tautologies, and have no relation to the world of experience.
- David Fate Norton asserted that Hume was "the first post-sceptical philosopher of the early modern period".
- Hume's Problem of Induction was also of fundamental importance to the philosophy of Karl Popper. In his autobiography, Unended Quest, he wrote: "'Knowledge' ... is objective; and it is hypothetical or conjectural. This way of looking at the problem made it possible for me to reformulate Hume's problem of induction". This insight resulted in Popper's major work The Logic of Scientific Discovery. In his Conjectures and Refutations, he writes: "I approached the problem of induction through Hume. Hume, I felt, was perfectly right in pointing out that induction cannot be logically justified".
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