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We introduce a low-cost robotic system designed to enable the safe, objective and efficient visual inspection of tunnels. The system captures high resolution images and processes them to produce maps of tunnel linings that are suitable for detailed inspection.It is unique in that the total cost of hardware is an order of magnitude less than most existing systems while producing an equivalent or higher quality of output. The device makes use of consumer-grade digital cameras and high-power LEDs in a rotating rig, carried by a lightweight aluminium frame which is designed to reduce vibrations during data capture. It is portable and installable by hand and has a modular design, making it possible to adapt to different types of carriage units, tunnels and sensors.Within the paper, we share insight into features of the device's design, including lessons learned from trials of earlier prototypes and comparisons with alternative systems. Using field data gathered from a 2km utility tunnel, we demonstrate the use of our system as a means of visualising tunnel conditions through image mosaicing, cataloguing tunnel segments using barcode detection and improving the objectivity of visual condition surveys over time by the detection of sub-mm crack growth.We believe that our device is the first to provide comprehensive survey-quality data at such a low cost, making it very attractive as a tool for the improved visual monitoring of tunnels.

We speak not only of the relation of a city to a country of which it is the capital or of a man to a child of whom he is the father, but of the relation of an object to a function of which it is the argument. But whereas the first relation finds expression in sentences that have in common the expression 'capital of and the second in sentences that have in common the expression 'father of, the function-argument relation finds expression in complex designations such as 'the capital of Holland' and 'Rembrandt's father', which have no expression in common. For this relation is not one that can be put into words at all. We might say, echoing Tractatus 4.121, that it is not something we can express by means of language, but something which expresses itself in language.Because there is no expression for the function-argument relation, such a relation is quite unlike a relation proper. By a relation proper I mean a relation as it is understood in predicate logic. Not that a relation proper is something for which there always exists an actual sign in the language, as there does for the relation capital of or father of. For the purpose of the logician a (first-level) relation is expressed in any sentence (of ordinary discourse) that contains two or more singular terms functioning as logical subjects. Still, it is something we express by means of language, as is shown by the fact that if the language contains no sign for it one can always be introduced. Thus we could introduce by definition a sign for the relation between Leeds and London that is expressed in 'Leeds is farther from Paris than it is from London'.Frege's thesis that a concept is a particular case of a function embodies the fundamental insight that the sense in which we speak of the relation of an object to a concept it falls under is the same as that in which we speak of the relation of an object to a function of which it is the argument. As there is no expression for the latter, so there is none for the former. If therefore we use the locution 'a falls under the concept F' and write 'Gold falls under the concept malleable' in place of 'Gold is malleable', we do not express in words a relation that is expressed in the shorter sentence without words. Frege thus betrays his own insight when he allows himself to be persuaded that because 'falls under' is a transitive verb, it stands for a relation. 1 In place of 'the capital of Holland' we could likewise write 'the value of the function capital of for the argument Holland'. Suppose someone now thought

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